Handbook on Solar Wind - Effects, Dynamics, Interactions - H. Johannson (Nova, 2009)BBS

HANDBOOK ON SOLAR WIND: EFFECTS, DYNAMICS AND INTERACTIONS

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HANDBOOK ON SOLAR WIND: EFFECTS, DYNAMICS AND INTERACTIONS

HANS E. JOHANNSON EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2009 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com

NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Library of Congress Cataloging-in-Publication Data Handbook on solar wind : effects, dynamics, and interactions / editors, Hans E. Johannson. p. cm. Includes bibliographical references and index. ISBN 978-1-61324-976-5 (eBook) 1. Solar activity--Environmental aspects. 2. Solar wind. 3. Climatic changes. I. Johannson, Hans E. QB524.H36 2009 523.5'8--dc22 2009009167

Published by Nova Science Publishers, Inc. New York

CONTENTS

Preface vii Chapter 1 On The Relationship between Solar Activity and Forest Fires 1

Milan Rodovanovic and João Fernando Pereira Gomes Chapter 2 Statistical Characteristics of the Heliospheric Plasma

and Magnetic Field at the Earth's Orbit during Four Solar Cycles 20-23 81 A.V. Dmitriev, A.V. Suvorova and I.S. Veselovsky

Chapter 3 Solar Energy Research, Sustainable Development and Applications 145 Abdeen Mustafa Omer

Chapter 4 Experimental and Modeling Evidence of the Solar Wind Energy Influence on the Earth Atmosphere 177 L.N. Makarova, and A.V. Shirochkov

Chapter 5 Electrostatic Wind Propulsion 197 Alexander Bolonkin

Chapter 6 Solar Wind and Motion of Interplanetary Dust Grains 227 J. Klačka, L. Kómar, P. Pástor and J. Petržala

Chapter 7 A Role of the Solar Wind in Dynamics of Interstellar Dust in the Solar System 275 M. Kocifaj and J. Klačka

Chapter 8 Solar Wind, Large Diamagnetic Cavities, and Energetic Particles 291 Jiasheng Chen

Chapter 9 Solar Wind Interaction with Artificial Atmospheres 319 L. Gargaté, R. A. Fonseca, R. Bamford, R. Bingham and L. O. Silva

Short Communications 339

Short Communication A Solar Radiation over Dongola, Northern Sudan 341

Abdeen Mustafa Omer

Contents vi

Short Communication B Electrostatic Solar Light-Wind Sail 353

Alexander Bolonkin Short Communication C Solar and Solar Wind AB-Sail 367

Alexander Bolonkin Short Communication D Electrostatic MagSail 379

Alexander Bolonkin Short Communication E The 27-Day Periodicity in Geomagnetic Activity and Solar Wind

Parameters over Solar Cycle 23 391 Ana G. Elias, Virginia M. Silbergleit, Ana Curcio and Patricia A. Larocca

Short Communication F Weibull Parameters for Wind Speed Distribution at Fifteen

Locations in Algeria 403 Y. Himri,, S. Himri, and A. Boudghene Stambouli

Short Communication G On the Limits of Applicability of the Ray Interference Integral

Method for Calculations of the Temporal Structure of Solar Radio Bursts 413 A.N. Afanasiev and N.T. Afanasiev

Index 419

PREFACE The solar wind is a stream of charged particles —a plasma—ejected from the upper

atmosphere of the sun. It consists mostly of electrons and protons with energies of about 1 keV. These particles are able to escape the sun's gravity, in part because of the high temperature of the corona, but also because of high kinetic energy that particles gain through a process that is not well-understood at this time. The solar wind creates the Heliosphere, a vast bubble in the interstellar medium surrounding the solar system. Other phenomena include geomagnetic storms that can knock out power grids on Earth, the aurorae such as the Northern Lights, and the plasma tails of comets that always point away from the sun. This new book presents the latest research in the world on this topic.

Chapter 1 - Fires of large dimension destroy forests, harvests and housing objects. Apart from that, combustion products and burned surfaces become large ecological problems. Very often fires emerge simultaneously on different locations of a region so a question could be asked if they always have been a consequence of negligence, pyromania, high temperatures or maybe there has been some other cause. This study is an attempt of establishing the possible connection between forest fires that numerous satellites registered and activities happening on the Sun immediately before fires ignite. Fires emerged on relatively large areas from Portugal and Spain on August 2005, as well as on other regions of Europe. The cases that have been analyzed show that, in every concrete situation, an emission of strong electromagnetic and thermal corpuscular energy from highly energetic regions that were in geo effective position had preceded the fires. Such emissions have, usually, very high energy and high speeds of particles and come from coronary holes that also have been either in the very structure or in the immediate closeness of the geo effective position. It should also be noted that the solar wind directed towards the Earth becomes weaker with deeper penetration towards the topographic surface. However, the obtained results suggest that, there is a strong causality relationship between solar activity and the ignition of these forest fires taking place in South-western Europe.

Chapter 2 - The review presents analysis and physical interpretation of available statistical data about solar wind plasma and interplanetary magnetic field (IMF) properties as measured in-situ at 1 A.U. by numerous space experiments during time period from 1964 to 2007. The experimental information have been collected in the OMNI Web/NSSDC data set of hourly averaged heliospheric parameters for last four solar cycles from 20th to 23rd. We studied statistical characteristics of such key heliospheric parameters as solar wind proton number density, temperature, bulk velocity, and IMF vector as well as dimensionless

Hans E. Johannson viii

parameters. From harmonic analysis of the variations of key parameters the authors found basic periods of 13.5 days, 27 days, 1 year, and ~11 years, which correspond to rotation of the Sun, Earth and to the solar cycle. The authors also revealed other periodicities such as specific five-year plasma density and temperature variations, which origin is a subject of discussion. They have found that the distribution of solar wind proton density, temperature and IMF is very close to a log-normal function, while the solar wind velocity is characterized by a very broad statistical distribution. Detailed study of the variability of statistical distributions with solar activity was performed using a method of running histograms. In general, the distributions of heliospheric parameters are wider during maximum and declining phase of the solar cycle. More complicated behavior was revealed for the solar wind velocity and temperature, which distribution is characterized by two- or even tree-peak structure in dependence on the phase of solar cycle. Our findings support the concepts of solar wind sources in the open, closed and intermittent magnetic regions on the Sun.

Chapter 3 - People relay upon oil for primary energy and this for a few more decades. Other orthodox sources may be more enduring, but are not without serious disadvantages. Power from natural resources has always had great appeal. Coal is plentiful, though there is concern about despoliation in winning it and pollution in burning it. Nuclear power has been developed with remarkable timeliness, but is not universally welcomed, construction of the plant is energy-intensive and there is concern about the disposal of its long-lived active wastes. Barrels of oil, lumps of coal, even uranium come from nature but the possibilities of almost limitless power from the atmosphere and the oceans seem to have special attraction. The wind machine provided an early way of developing motive power. The massive increases in fuel prices over the last years have however, made any scheme not requiring fuel appear to be more attractive and to be worth reinvestigation. In considering the atmosphere and the oceans as energy sources the four main contenders are wind power, wave power, tidal and power from ocean thermal gradients. The renewable energy resources are particularly suited for the provision of rural power supplies and a major advantage is that equipment such as flat plate solar driers, wind machines, etc., can be constructed using local resources and without the advantage results from the feasibility of local maintenance and the general encouragement such local manufacture gives to the build up of small-scale rural based industry. This chapter gives some examples of small-scale energy converters, nevertheless it should be noted that small conventional i.e., engines are currently the major source of power in rural areas and will continue to be so for a long time to come. There is a need for some further development to suit local conditions, to minimise spares holdings, to maximise interchangeability both of engine parts and of the engine application. Emphasis should be placed on full local manufacture.

Chapter 4 - So far the solar wind energy contribution to energetic balance of the Earth atmosphere was ignored in any atmospheric and climatic research. However the solar wind is a permanent source of a significant amount of the electromagnetic energy emitted by the Sun which is constantly supplied to the near-Earth space. Traditionally this energy was attributed entirely to sustain a definite level of geomagnetic activity expressed as intensity of the geomagnetic substorms and storms. The authors of this paper found in 1997 after analysis of the data of the Russian rocket sounding in the Arctic that enhancement of the solar wind dynamic pressure do influence thermal regime of the polar middle atmosphere. Similar analysis of the atmospheric balloon sounding data obtained at different stations in both the Arctic and the Antarctica shows that the stratospheric temperature closely correlated with the

Preface ix

solar wind electromagnetic energy. After establishing these statistically confident relations it was necessary to find a plausibly reasonable physical mechanism which could explain reality of the found coupling. A concept of the global electric circuit as a physical mechanism for explanation of a direct coupling between the solar wind and the middle atmosphere was suggested. The authors proposed a new, modified version of the global electric circuit with two Electro-Motive Force (EMF) generators: internal EMF generator driven by the thunderstorm activity of the Earth (a common feature of previous circuit configurations) and an external EMF generator driven by the solar wind energy. The passive elements of this circuit are the ionospheric E-layer (external element of previous version of the circuit), stratospheric conducting layer of heavy ions (h=20-25 km) and conducting layer of the Earth surface. In this configuration a previous scheme of the global electric circuit is a part of the proposed version of it. Numerical evaluation of the electromagnetic energy of the solar wind is a very difficult task. It can be done only approximately. Structure of the Earth magnetosphere is changing constantly upon influence of the solar wind as well as a position of a boundary of the magnetosphere (magnetopause). The problem could be solved if the authors present boundary of the Earth magnetosphere and the ground surface as a giant capacitor with external and internal plates correspondingly. The external plate of this capacitor (magnetopause) could be moved toward the Earth under the solar wind pressure. The energy of the solar wind roughly can be calculated by estimation of energy which is required to move the magnetopause for a definite distance. The magnetopause is located at ~ 12 Re (were Re is the Earth radius) under a quite condition of the solar wind. During strong disturbances of the solar wind the magnetopause could approach the Earth at distance of approximately ~ 6 Re. Such estimation shows that energy required for movement of magnetopause at a distance of 6 Re is equal to ~ 5 10 15J. Preliminary numerical estimations showed that under typical conditions such amount of the Joule heating dissipated in stratosphere is comparable with a rate of heating of ozone layer by the solar UV radiation. Furthermore, such amount of energy is sufficient for enhancement of cyclonic activity in the Earth atmosphere. As the next step of exploration a numerical calculation scheme was elaborated, which took into account the abovementioned processes. This numerical scheme was successfully used in one of the global dynamical photo-chemical models of the atmospheric circulations. The results of these model simulations confirmed all previously made preliminary estimations concerning influence of the solar wind energy on the atmospheric processes. There are the definite plans to improve the effectiveness of the proposed physical mechanism describing interaction of the solar wind with the Earth atmosphere. Evaluation of the effects of different degree of the Earth electric conductivity must be taken into account in the next explorations on the subject.

Chapter 5 - A method for space flights in outer space is suggested by the author. Research is present to shows that an open high charged (100 MV/m) ball of small diameter (4–10 m) made from thin film collects solar wind (protons) from a large area (hundreds of square kilometers). The proposed propulsion system creates many Newtons of thrust, and accelerates a 100 kg space probe up to 60–100 km/s for 100–800 days. The 100 kg space apparatus offers flights into Mars orbit of about 70 days, to Jupiter about 150 days, to Saturn about 250 days, to Uranus about 450 days, to Neptune about 650 days, and to Pluto about 850 days.

The author developed a theory of electrostatic wind propulsion. He has computed the amount of thrust (drag), to mass of the charged ball, and the energy needed for initial

Hans E. Johannson x

charging of the ball and discusses the ball discharging in the space environment. He also reviews apparent errors found in other articles on these topics. Computations are made for space probes with a useful mass of 100 kg.

Chapter 6 – Effect of solar wind particulates on motion of dust grain moving in Solar System is derived in space-time. Acceleration of the grain under the effect of solar wind (including the non-radial component of its velocity vector) and grain's mass change are obtained. The results for the effect of solar wind are used in space-time derivation of the effect of electromagnetic radiation.

The contribution considers simultaneous action of the solar electromagnetic radiation and solar wind, together with gravity of the Sun and planets, on motion of interplanetary dust grains with radii of several microns and tens of micrometres. Applications for the standardly used radial solar wind and real solar wind velocity vector are compared. The important results can be summarized as follows: 1. Spherical dust grain can be captured in mean-motion orbital resonances with planet Neptune when the secular evolution of the grain's semimajor axis is an increasing function of time. Nothing like this exists for the Poynting-Robertson effect and radial solar wind. The effect of the real solar wind velocity vector mimics the behavior of the complicated case of the behavior of nonspherical dust grain under the action of solar electromagnetic radiation. 2. Simultaneous action of the Poynting-Robertson and real solar wind effects causes spiralling of the dust grain outward from the Sun, in the zone of outer planets. The flux of interstellar gas is also important in this zone. This additional nongravitational effect stabilizes dust grain's orbit in the zone of the Edgeworth-Kuiper belt.

Chapter 7 – Interstellar dust grains have been detected by the dust detectors onboard the Ulysses and Galileo spacecrafts. Motion of the interstellar dust particles in the Solar System is driven by gravitational and nongravitational forces. As for gravity, theaction of the Sun is the dominant gravitational effect. Nongravitational forces are represented by solar electromagnetic radiation force, similar effect of the solar wind, and, Lorentz force for submicrometer-sized dust grains. Lorentz force originates from the action of interplanetary magnetic field on electrically charged grains and solar wind velocity plays a crucial role in this nongravitational force.

Chapter 8 – The Earth's magnetospheric cusp is a key region for transferring the solar wind energy, mass, and momentum into the Earth's magnetosphere. The solar wind particles can directly access the dayside high-altitude cusp, creating large diamagnetic cavities with strong electromagnetic fluctuations. Different from magnetic reconnection, the cusp diamagnetic cavities are created by the interactions of the solar wind with the local magnetic field, which could depress the field from more than 200 nT into near zero nT, tearing wide and deep magnetic holes in the Earth's magnetosphere. The power spectral density of the electromagnetic fluctuations inside the cavities shows increases by up to four orders of magnitude in comparison to adjacent regions. The strong electric field fluctuations can efficiently energize the cusp charged particles by cyclotron resonant acceleration. The discovery of cusp energetic particle (CEP) events is a major breakthrough in space science. It is changing the traditional view about the structure and dynamics of the magnetosphere and has opened a great avenue for the Sun-Earth connection investigations. The CEPs are detected in the high-altitude cusp region and are always there day after day. They have energies from 20 keV up to 15 MeV, which is also the typical energies of the ring current and outer radiation belt populations. The CEP intensities are observed to increase by as much as four orders of magnitude during cusp diamagnetic cavity crossings. These recent in situ

Preface xi

observations reveal a new, broad and dynamic region of acceleration and trapped radiation in geospace, which centers at the Earth's magnetospheric cusp and has a size of up to 10.5 Earth radii. The new region of radiation can extend to low-latitude region, and can reach 6.6 Earth radii from the Earth's center, providing a direct particle source for the outer Van Allen radiation belt.

Chapter 9 – Active experiments in space involving artificial atmospheres began with the AMPTE releases. In these seminal experiments, a cloud of Barium or Lithium was released and photoionized by the UV radiation from the sun. The cloud expanded and interacted with flowing solar wind, thus providing important data about pick-up ion behaviour, diamagnetic cavity formation, and shock formation. More recently, systems consisting of a dipole magnetic field and a plasma source are being considered and studied in spacecraft propulsion, and as a spacecraft shield from Solar Energetic Particles (SEP) from the sun.

The authors use a 3D massively parallel hybrid code to analyze the behaviour of such systems in the presence of a plasma flow. The model is ideal to study artificial atmospheres interacting with the solar wind, covering the relevant physical scales, and allowing a kinetic treatment of the ions. Arbitrary density distributions, and arbitrary initial velocity distributions can be set, while dynamic load balancing algorithms are used to guarantee parallel efficiency.

The authors focus our analysis in the differences between two distinct scenarios: the unmagnetized scenario of a plasma cloud expanding in the solar wind in the presence of the Interplanetary Magnetic Field (IMF), and the magnetized scenario of a laboratory plasma flow shock against a dipole magnetic field structure. Our results show that both configurations effectively deflect the incoming plasma. The nature of the shocks formed in both situations is different, with a bow shock being formed in the first case, while in the second case there is a compression of the magnetic field, but no bow shock is observed. In the unmagnetized case, the diamagnetic cavity formation is the most significant aspect, with the cloud particles producing the diamagnetic currents as they expand outwards due to their temperature. The dependency of the plasma standoff distance with the plasma density, velocity, and with the dipole field intensity in the magnetized case is highlighted, and the relevance of these scenarios for the shielding of spacecrafts is also addressed.

Short Communication A - A number of years worth of data concerning the solar radiation on a horizontal surface and sunshine duration at Dongola, Northern Sudan have been compiled, evaluated and presented in this short communication. Measurements of global solar radiation on a horizontal surface at Dongola for a whole year are compared with predictions made by several independent methods. In the first method, Angstrom formula was used to correlate relative global solar irradiance to the corresponding relative duration of bright sunshine. Regression coefficient are obtained and used for prediction of global solar irradiance. The predicted values were consistent with measured value (±6% variation). In the second method, by Barbaro et al. (1978) sunshine duration and minimum air mass were used to derive an empirical correlation for the global radiation. The predicted values compared well with measured values (±6% variation). The diffuse solar irradiance is estimated using Page’s, Lui and Jordan’s correlations. The results of the two formulas have a close agreement. The annual daily mean global radiation ranges from 5.27 to 7.65 kW h m-2 per day. It is concluded that Northern Sudan is enjoyed with abundant solar energy.

Short Communication B - The solar sail has become well-known after much discussion in the scientific literature as a thin continuous plastic film, covered by sunlight-reflecting

Hans E. Johannson xii

appliquéd aluminum. The Solar wind propulsion also has many researches. Any solar sail simultaneously is the solar wind sail because the light and solar wind have a same direction and adsorb by a sail material. Earlier, there were attempts to launch and operate solar light and solar wind sails in near-Earth space and there are experimental projects planned for long powered space voyages. However, as currently envisioned, the solar light-wind sail has essential disadvantages. Solar light-wind pressure in space is very low and consequently the solar light-wind sail has to be very large in area. Also it is difficult to unfold and unfurl the solar sail in space. In addition it is necessary to have a rigid framework to support the thin material. Such frameworks usually have great mass and, therefore, the spacecraft’s acceleration is small.

Here, the author proposes to discard standard solar light-wind sail technology (continuous plastic aluminum-coated film) with the intention instead of using millions of small, very thin aluminum charged plates and to release these plates from a spacecraft, instigated by an electrostatic field. Using this new technology, the solar sail composed of millions of plates can be made gigantic area but have very low mass. The acceleration of this new kind of solar sail may be as much as 300 times that achieves by an ordinary solar sail. The electrostatic solar sail can even reach a speed of about 300 km/s (in a special maneuver up to 600–800 km/sec). The electrostatic solar sail may be used to move a large spaceship or to act as an artificial Moon illuminating a huge region of the Earth’s surface.

Short Communication C - The Solar and Solar Wind sail is a large thin film used to collect solar light and solar wind pressure for the moving of space apparatus. Any solar sail simultaneously is the solar wind sail because the light and solar wind have a same direction. The light (photons) and solar wind (protons and electrons) are adsorbed by a sail material. Unfortunately, the solar radiation pressure is very small, about 9 μN/m2 at Earth's orbit. The solar wind pressure is much less. However, the light and wind forces significantly increases up to 0.2 - 0.35 N/m2 near the Sun. The author offers his research on a new revolutionary highly reflective solar sail which performs a flyby (after a special maneuver) near Sun and attains a velocity up to 400 km/sec enabling reaching far planets of the Solar system in short time, and enabling escape flights out of the solar system. New, highly reflective sail-mirror allows avoiding overheating of the solar sail. It may be useful for probes close to the Sun as well as probes to Mercury and Venus

Short Communication D - The first reports on the “Space Magnetic Sail” concept appeared more 30 years ago. During the period since some hundreds of research and scientific works have been published, including hundreds of research report by professors at major research universities. The author herein shows that all these works related to Space Magnetic Sail concept are technically incorrect because their authors did not take into consideration that solar wind impinging a MagSail magnetic field creates a particle magnetic field opposed to the MagSail field. In the incorrect works, the particle magnetic field is hundreds times stronger than a MagSail magnetic field. That means all the laborious and costly computations revealed in such technology discussions are useless: the impractical findings on sail thrust (drag), time of flight within the Solar System and speed of interstellar trips are essentially worthless working data! The author reveals the correct equations for any estimated performance of a Magnetic Sail as well as a new type of Magnetic Sail (without a matter ring).

Short Communication E - Geomagnetic activity and solar wind parameters are analyzed in terms of the periodicity linked to solar rotation that is the 27-day cycle. Its fluctuation in

Preface xiii

frequency and time is studied using the wavelet power spectrum. For this purpose the authors used the geomagnetic activity aa index and three solar wind parameters: magnetic field magnitude (B), density (d) and velocity (v). The sunspot number, Rz, is also analyzed to have a solar activity reference. The study was carried out for the period July 1996 – December 2005, which corresponds to solar cycle 23, except for the last years corresponding to its final minimum level. For the time period and parameters here analyzed, the 27-day periodicity is observed to have enhanced power during maximum and falling phase of the solar activity cycle, with no significant power during the ascending phase, not even in solar activity. Besides the time evolution, a periodicity variation is also noticed along the solar cycle. In some cases the period decreases as the solar cycle approaches minimum levels, as expected from the meridional movement of active regions towards lower solar latitudes during this time. However, periodicites lower than 27.27 days (synodic period at the solar equator ) are also observed, pointing out inner regions of the sun as possible sources of the active regions, or a surface phenomenon arising because of solar activity shifts during solar rotation.

Short Communication F - In the present study the Weibull parameters distribution function were computed for 15 locations in Algeria. The wind data which covers a period of almost 10 years between 1977 and 1988 was adopted. The average wind speed at a height of 10 m above ground level was found to range from 2.3 to 5.9 m/s. The Weibull distributions parameters (c & k) were found to vary between 3.1 and 7.2 m/s and 1.19 to 2.15 respectively. Higher wind speeds were observed in the day time between 09:00 and 18:00 h and relatively smaller during rest of the period. Generally the long-term seasonal wind speeds were found to be relatively higher during spring to the autumn month of September compared to other months. The two parameters of a Weibull density distribution function for the three areas namely (Littoral, Highlands and Sahara) were compared and wider distributions were observed in the Sahara. It is also noticed from this work that the Weibull distribution give a good fit to experimental data. The aim of this work is to provide information about the distribution of wind in different regions of Algeria (Littoral, Highlands and Sahara) and give useful insights to engineers and experts dealing with wind energy.

Short Communication G - The authors discuss the possibility of using the ray interference integral method to carry out calculations of scattering of radio emission from sources embedded in the corona and solar wind. The authors point out that preliminary analysis of the topology of caustics produced by geometrical optics rays and by partial waves forming the interference integral enables correct calculations of the solar radio burst structure.

In: Handbook on Solar Wind: Effects, Dynamics … ISBN: 978-1-60692-572-0 Editor: Hans E. Johannson © 2009 Nova Science Publishers, Inc.

Chapter 1

ON THE RELATIONSHIP BETWEEN SOLAR ACTIVITY AND FOREST FIRES

Milan Rodovanovic1 and João Fernando Pereira Gomes2 1Geographical Institute “Jovan Cvijic”, Serbian Academy

of Sciences and Arts – SANU, Belgrade, Serbia 2Chemical Engineering Department/IBB - IST - Instituto Superior Técnico,

Torre Sul, Lisboa, Portugal and Chemical Engineering Department, ISEL - Instituto Superior de Engenharia de Lisboa, Lisboa, Portugal,

Abstract

Fires of large dimension destroy forests, harvests and housing objects. Apart from that, combustion products and burned surfaces become large ecological problems. Very often fires emerge simultaneously on different locations of a region so a question could be asked if they always have been a consequence of negligence, pyromania, high temperatures or maybe there has been some other cause. This study is an attempt of establishing the possible connection between forest fires that numerous satellites registered and activities happening on the Sun immediately before fires ignite. Fires emerged on relatively large areas from Portugal and Spain on August 2005, as well as on other regions of Europe. The cases that have been analyzed show that, in every concrete situation, an emission of strong electromagnetic and thermal corpuscular energy from highly energetic regions that were in geo effective position had preceded the fires. Such emissions have, usually, very high energy and high speeds of particles and come from coronary holes that also have been either in the very structure or in the immediate closeness of the geo effective position. It should also be noted that the solar wind directed towards the Earth becomes weaker with deeper penetration towards the topographic surface. However, the obtained results suggest that, there is a strong causality relationship between solar activity and the ignition of these forest fires taking place in South-western Europe.

Milan Rodovanovic and João Fernando Pereira Gomes 2

1. Global Climate Changes and Forest Fires

On the basis of contemporary data realization, it has become obvious that relatively frequent forest fires, seizing areas in several states almost simultaneously, cannot be simply explained by intentional or unintentional anthropogenic cause. It has been logical the causes should look for in climate changes. “The frequency, size, intensity, seasonality, and type of fires depend on weather and climate in addition to forest structure and composition. Fire initiation and spread depend on the amount and frequency of precipitation, the presence of ignition agents, and conditions (e.g. lightning, fuel availability and distribution, topography, temperature, relative humidity, and wind velocity)” (Dale et al., 2001). However, problem of fires emerged in the area of (not only) Europe out of time, e.g. at the beginning of March or at the end of November. Cases occurring during winter months (as shown in figure 1) and at the beginning of spring are especially interesting for the scientific researches. “Since the winter season add very a few amount of rain, there where 6 841 fires between January and March. These fires where responsible for 10 777 ha of burned area. On the 10th of January there was a fire in the Guarda district that burned 348 ha of shrub land. In the month of March, there were 7 fires larger than 100 ha mostly of those, concentrated in littoral district of Viana do Castelo and Aveiro” (http://www.fire.uni-freiburg.de/programmes/eu-comission/EU-Forest-Fires-in-Europe-2005.pdf)1

On the other side, it seems there are severely opposing opinions even in the field of climatology itself. “The biggest problem we have with the climate debate is that the big mathematical models can't predict what'll really happen since the models contain simplifications that are probably wrong in important ways. We end up having to guess what will happen. Nature continually makes the climate change even without humans getting involved. So, even once, a change has happened and it is yet impossible to figure out how much of this change was caused by humans” (http://www.futurepundit.com/). Many pages could be written on this theme, but for this occasion a concise survey of the results in the last ten years will be presented.

Taking over the role of the institution for arousing human conscience the Intergovernmental Panel on Climate Change (IPCC) according the estimation from 1995 claimed the Earth’s temperature increased between 0.3 and 0.6 °C during the 20th century. According the estimation from 2001, the increase is from 0.6 to 0.2C. According the World Meteorological Organization Report (WMO, 1999) that increase in the previous century is 0.7 °C. By the year 2100. models of the IPCC (the making of which 2 500 scientists took participation) predict the increase of global temperature of 1.4-5.8 °C. The last estimations date from 2007. and according them the air temperature could increase between 2 and 4.5 °C till the end of this century, providing the anthropogenic CO2 emission continues.

1 The data relate on 2005 for Portugal

On The Relationship between Solar Activity and Forest Fires 3

Figure 1. Numerous fires were scattered across Southeast Asia on January 21, 2007, when the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Aqua satellite passed overhead and captured this image http://earthobservatory.nasa.gov/NaturalHazards/ natural_hazards_v2.php3?img_id=14085)

The paper by Mann et al., (1998) gave was significant stimulus to global warming

advocates because of excessive atmosphere pollution with greenhouse effect gases. The results they came to have pointed that the 20th century, which is the period from 1990 was the warmest in the previous 600 years (it looks like hockey stick in the figure, by which this term was included into scientific literature). Citing Mann and Jones (2003), McGuire (2004) concluded the period after 1980 was the warmest in the last 2 000 years. He also writes that “another nail in the coffin of the global warming skeptics was provided by a research team led by Qiang Fu”. Schär et al., (2004), similarly to Beniston (2004) and Beniston and Diaz (2004) conclude that the only explanation for the heat wave in Europe i.e. in Switzerland in 2003 is that increasing concentration of greenhouse gases in the atmosphere increases climate variability as it simply raises global temperatures. Regarding eventual solar influence on weather and climate, very often the views similar to what Barron (1995) stated could be met: “Solar variability over the next 50 years will not induce a prolonged forcing significant in comparison with the effects of the increasing concentrations of CO2 and other greenhouse gases”. In common representation of papers from this field, we get an impression that thousands and thousands of pages were written, which convincingly present evidences, on the basis of which the base for Kyoto protocol was founded, above others. “The biggest catalyst for climate change today are greenhouse gases". (http://www.giss.nasa.gov/research/news/20011206/)2.

2 Shindell D. T.


Above many others, the paper of Girardin et al., (2006) has also appeared where it is written: “Human-induced climate change could lead to an increase in forest fire activity in Ontario, owing to the increased frequency and severity of drought years, increased climatic variability and incidence of extreme climatic events, and increased spring and fall temperatures. Climate change therefore could cause longer fire seasons, with greater fire activity and greater incidence of extreme fire activity years… Fire has also been recognized as a significant source of greenhouse gas emissions into the atmosphere. Most of this is in the form of carbon dioxide (CO2), but quantities of carbon monoxide, methane, long-chain hydrocarbons, and carbon particulate matter are also emitted”. One of the arguments showed in this paper are also described in figure 2.

Figure 2. (a) Reconstruction of area burned in the province of Ontario for 1782–1981 (thick line). Thin line represents instrumental data (1917-2003). (b) 10-year window polynomial curve (Girardin et al., 2006).

However, very soon serious criticisms have appeared on the account of the presented results. “This recent article is a perfect example of confusion the public must feel regarding important elements of the greenhouse debate. One camp could take the article and claim that numerical models are forecasting an increase in forest fires (actually, no global climate model makes such a direct prediction) and that the evidence from Ontario indeed shows an increase in burned area in recent decades. You decide, but as this essay shows, the deeper you dig into this article, the less evidence there is for any claim that the buildup of greenhouse gases has resulted in an increase in wildfires in Ontario”.

(http://www.worldclimatereport.com/index.php/2007/04/25/torching-the-forest-fire-myth/#more-232).

Advocates of the dominant influence of the anthropogenic greenhouse effect on climate changes, i.e. global warming published a large number of scientific papers. Nevertheless, it seems those conditionally claiming opposite, more and more persistently try to leave the category of sporadic and isolated achievements. It was necessary to point out the opinions of


the scientists who are less present both in science and public due to the criticism of possible suggesting the views by selective approach. “Just when you were starting to believe that variations in the amount of energy coming from the sun weren’t responsible for much of the observed surface warming during the past 20 years, comes along a Scafetta and West (2006), that concludes otherwise: “We estimate that the sun contributed as much as 45–50% of the 1900–2000 global warming, and 25–35% of the 1980–2000 global warming. These results, while confirming that anthropogenic-added climate forcing might have progressively played a dominant role in climate change during the last century, also suggest that the solar impact on climate change during the same period is significantly stronger than what some theoretical models have predicted”.

(http://www.worldclimatereport.com/index.php/category/climate-forcings/). Regarding concretely established links between Sun and climate in the past, Hallett et al.,

(2003) point out: “Highinferred water levels during solar (sunspot) minima and lower water levels during solar maxima suggest a response to climate and solar variability. …A broad distribution of sites would increase our understanding of the potential impacts of global warming on fire regimes and water balance in British Columbia. …High fire frequencies also occur in the giant sequoia forests of the Sierra Nevada between AD 1000 and 1300 …and tree-ring data from subalpine conifers in the Sierra Nevada indicate that summer temperatures exceeded late twentieth-century values between ad 1100 and 1375”. It follows the claims of Mc Guire (2004) and Mann and Jones (2003) do not refer to British Columbia.

Komitov (2005) described the existing relations very picturesquely “Unfortunately during the 70s years the WMO demonstrate a very negative position to the results of these studies. As a result after 1975 all solar-climatic studies results are ignored and this is labeled as a ‘forbidden’ area for all scientific conferences and symposiums under the aegis of WMO. This is the cause why on the field of solar-climatic relations during the last around 30 years mainly space physics specialists, but not meteorologists are working”.

Agerup’s (2004) “brave” results have also appeared: “For all climate scientists know, climate might have cooled by the year 2 100!” Considering that CO2 concentration reached the level of 0.037% at the end of the last century, terms “global warming” and “greenhouse effect” became the part of the standard scientific vocabulary (Ducic, Radovanovic, 2005). The attempt to study as much material on global climate changes as possible has influenced to meet many scientific papers classified in so-called opposition science. In other words, contrary to the prevailing opinion, there are more and more papers treating the question of global warming as over dimensioned. Dmitriev (1997), Michaels (1998), Arking et al., (2001), Agerup (2004), Agerup et al., (2004), Radovanovic, Ducic (2004), as well as many others have stated very severe criticisms on the account of applied methodology and results in the scenarios of IPCC.

Mentioned authors point out the phenomenon of global (that is regional) climate changes does certainly exist, but they are in the first place the consequence of the natural processes, while man’s influence on them is far less. “Having examined all 40 scenarios, we have noticed the projected anthropogenic CO2 emission in all models is 6900 GT for 2000. However, on the basis of the recent data, it may be seen the emission was 6315 GT. It is 10.7% lower than the one IPCC predicted. This could be the significant failure in the projections of the future CO2 emission, especially because the period from the prognosis to the prognosticated year was relatively short. That points out the fact one should be careful in


accepting these prognosis, especially those of the long-term character”. (Ducic, Radovanovic, 2005).

Contrary to catastrophic predictions of IPCC for the 21st century, Landschieidt (2000a) expects mild temperature decrease in period to 2010. Similar conclusions Komitov (2005) also came to: “As a result near to 2050 AD the mean Earth nearsurface air temperature will be at about 1°C lower than present. The warming will start again at the beginning of 22nd century when for a very short time the level from the end of 20th century will be reached”. Some reports from this (2007) year point to the occurrences that will come after but also contrary to those predictions the scientists of IPCC have given. (Abdusamatov3) emphasized that NASA’s data on warming on Mars and researches of ice from deep holes on Antarctica and in Greenland have confirmed the conclusion of the study from the Pulkov laboratory that the natural causes, not man’s industrial activity dictated global warming on Earth. Nevertheless, as he said, the Chinese scientists’ researches, whose results were published in January 2007 and have also predicted the natural reduction of Earth’s global temperature during next 20 years and confirmed the results of the Russian research”.

(http://www.mycity.co.yu/Geografija/Precizna-prognoza-klimatskih-promena.html). Even on the short temporal series (for period 1979-1998) level, Santer et al., (2000) have

got negative trends. “All model surface – 2LT trend differences are negative, unlike the observations”, shown in figure 3..

Figure 3. Least-squares linear trends and associated 95% confidence intervals in modeled and observed surface (A), 2LT (B), and surface − 2LT (C) temperature time series.

3 Habibulo Abdusamatov, laboratory manager for cosmic researches of the Main Pulkov Observatory of the Russian Academy of Sciences.


Areas where man’s influence is much expressed locally and regionally (urban areas, industrial areas) are not controversial. Those areas where such influence is reduced, while the warming trend is also proved are not controversial either. However, changes on the regional level are the focus of the research, i.e. there are also areas on Earth showing the trend of, conditionally saying, stagnation, as well as those areas where decreasing air temperature trend was noticed also including some urban areas. Przybylak (2002) calculated for period 1951-2000 that the linear trend of air temperature (C/10 years) in the area of Arctic has the following values: the Atlantic region 0.00, Siberian region 0.04, the Pacific region 0.33, the Canadian region 0.17, the region of Baffin Sea -0.19, the Arctic 1 (the data from 37 Arctic stations) 0.08, the Arctic 2 (for 60-90 N geographic latitude) 0.16 and NH (land and ocean- average temperature for the Northern hemisphere) 0.09.

Figure 4. Changes on glaciers since 1970 (http://en.wikipedia.org/wiki/Effects_of_global_warming)

We may see from the previous figure the changes on glaciers are really impressive. In some cases it is the reduction of 1.4 meters/year. However, it is not clear why is the phrase “thinning” used in the lower part of the figure when numerous locations may be noticed whereto it comes to their increase, i.e. growth, disregarding significantly smaller amount.

Climate changes which also included the area of Antarctica have reflected on the changes within vegetation. “In particular, there are reports from Antarctica that show a dramatic reaction by vegetation to the recent changes in climate; there were 700 species found growing in 1964 and 17,500 in 1990”.4 If we only relied on this index, it was obvious it would lead us to conclusion Antarctica generally lies on dramatic turning point meaning melting the large quantities of ice. Nevertheless, it might be supposed the climate conditions are so much improved that the number of plant species increased 25 times in 27 years. However, figure 5

4 Science News. Vol. 146. N 334, 1994


shows very illustratively the influence of climate changes on the condition of the ice on Antarctica.

Figure 5. In some parts of Antarctica, such as East Antarctica, the ice sheet is thickening (+ symbols), whereas in others, primarily in West Antarctica it is thinning (- symbols). (Vaughn, 2005)

Looking at figure 5 it may be noticed the surfaces registering the ice growth are much

larger. Contrary to them, the surfaces where ice melts are far smaller but the melting amount is considerably larger.

The following quotations show it is not about the results of rare fanatics: - “Measurements taken by weather stations in the McMurdo Dry Valleys - the largest

ice-free area in Antarctica - show that on average this region cooled by 0.125 Fahrenheit a year between 1986 and 2000.

- Scientists found the cooling was especially strong during the autumn and summer seasons, and they theorize it is due to a complex interplay between ocean currents.

- The distorted view that the continent is warming might be traced to the fact that most weather monitoring stations are based in the Antarctic Peninsula - the tongue of land projecting northward from the continent toward South America - an area which is, indeed, warming dramatically”.


(http://www.ncpa.org/iss/env/2002/pd011402d.html)”5. Egorova et al., (2000) point out the analysis of temperature, pressure and wind

observation in the Arctic station of Vostok shows the variations of the cosmic radiation make the crucial influence on the condition of the troposphere in the vicinity of the polar region in winter conditions. Perhaps this may be a subjective impression, but it seems that around 15 references used by the authors in the first part of the paper, do not belong the group of those that could be relatively frequently met in high-cited scientific papers. It is about the studies which prove the cosmic and solar radiation influence on the circulation regime of the troposphere, cyclone activity, cloudiness, air pressure, air temperature and ozone shell. According van Geel et al., (1999) “We therefore postulate, that - periodically - sudden and strong increases of cloudiness, precipitation (snow) and declining temperatures as a consequence of solar/cosmic ray forcing have played a crucial role in the regularly occurring iceberg discharges as recorded in North Atlantic deep sea cores and the synchronous events in the Southern Hemisphere”.

On the results of the researches of mentioned Mann et al., (1998) serious criticisms have appeared. McIntyre and McKitrick (2003, 2005) have used a part of the program Mann et al., (1998) used, and they have found serious problems. Not only the program does not perform the conventional PCA6 but the data normalization was performed in a way that can be described only as the wrong one.

The results Soon et al., (2001) came to may be summarized through the following conclusions:

1. “The increased surface temperature of about 0.5 °C to 0.6 °C over the last one

hundred years is a natural phenomenon - because 80% of the rise in levels of atmospheric CO2 during the twentieth century occurred after the initial major rise in temperature.

2. Surface temperatures (based on land and sea measurements) peaked by around 1940, then cooled until the 1970s; since then, there has been a surface warming.

3. The primary impact of the greenhouse effect of added CO2 is in the lower atmosphere (rather than at the surface), but accurate measurements of that layer of air by U.S. National Oceanic and Atmospheric Administration (NOAA) satellites over the last 22 years have not shown any hint of global warming”.

The beginning and the end of the text of Monibot et al., (2005) perhaps best illustrate

tense confrontation of opinions: “The science of climate change is under attack …Isn’t it time you started fighting for your science?” In some cases the reactions to the researches classified as the opposition science, can hardly be called the academic ones. “Some prominent scientists are becoming increasingly restive about the shrill portrayal of global warming science in popular media. The latest round concerned a paper by A. L. Westerling (where it is written)7 …relating an dramatic increase in western forest fires to regional warming and changes in the onset of snowmelt”.

5 Peter Doran 6 Principal Component Analysis 7 Translator’s note


(http://www.worldclimatereport.com/index.php/2006/07/). It follows stating scientifically argumentative view, which does not fit into the prevailing

opinion, is almost treated as heresy. The complete problem has deeply infiltrated even the level of the political conflicts. “Famously, Inhofe declared on the Senate floor: "With all of the hysteria, all of the fear, all of the phony science, could it be that man-made global warming is THE greatest hoax ever perpetuated on the American people? It sure sounds like it".

(http://www.newwest.net/index.php/city/comment/9136/C396/L396). Citing Prim (1997), Landscheidt (1998) wrote: “Recent studies show that solar variability

rather than changing CO pressure is an important, probably the dominant climate forcing factor ...The current and anticipated fleet of spacecraft devoted to the study of solar and solar-terrestrial physics will therefore probably prove to have more bearing on the understanding and forecasting of climate change than the orchestrated assessments by politically motivated international panels biased towards global warming exclusively by the enhanced greenhouse effect.” Gray (2000) presented the concise perception of this problem: “Three of the four methods of measuring global temperature show no signs of global warming:

- proxy measurements (tree rings, sediments etc) for the past 1000 years, - weather balloons (radiosondes) for the past 44 years, - satellites (MSU8) for the past 21 years. The fourth method, surface measurement at weather stations, gives an averaged mean

global rise of more than 0.6 °C over 140 years, but is intermittent and irregular. Individual records are highly variable, regional, and sometimes, particularly in remote areas, show no change, or even a fall in temperature”.

In his references Gray does not make a citation that follows, simply because he could not have known for it, since it appeared six years later. However, it seems this report represents the direct confirmation to his observations. “For over a century, a national network of “weather nerds” (for lack of a better term) have monitored backyard weather stations where they kept track of daily maximum and minimum temperature and precipitation using standardized instruments and measurement techniques. Called the U.S. Cooperative Observer Network (co-op for short), these data, which were submitted monthly for many decades on paper logs, were often used to fill in gaps from the more comprehensive observations taken by trained weather service employees at far fewer locations. But the utility of the co-op records to climate analysis was limited by their cumbersome, paper format. However, recently the interest in climate change spurred the government to digitize these paper records, thus adding many new stations to the existing network. With the addition of the co-op data, the number of stations from roughly 1890 to 1947 doubled or tripled relative to the previous baseline. …Not only did the frequency of extremes vary markedly in the early 20th century days of very low greenhouse gas levels, but the frequency of extreme events in the late 1890s was at least comparable to that in our current climate. Kunkel did some statistical tests demonstrating that the most recent period (1983-2004) was not statistically different from the earliest period (1895-1916) for many combinations of event severity and return period,

8 Microwave Sounder Units


although a few were significantly different. At the end of the text it was written: “If we are faced with such uncertainty with the world’s best data set, how much confidence can we really place in our interpretations of the very sparse records from Africa, Asia, and South America, not to mention the paucity of records from the world’s oceans?”

(http://www.worldclimatereport.com/index.php/2006/03/15/an-extreme-view-of-global-warming/)9.

The readers to whom the geographic problem is not close, it is necessary to emphasize that about 71% of our planet is under water; for such a vast part of Earth there are not long-range series of the meteorological i.e. climate element observations.

Nevertheless, Wiin-Neilsen (1997) also gave similar observations: “The comparison between the MSU data and the ECMWF10 data indicate that middle tropospheric temperature deviations show a satisfactory agreement between the two data sources. …For the two data sets we may say that none of them indicate any systematic change of the middle and lower tropospheric temperatures”. Keeping in mind the importance of these results especially comes in effect if they are observed through paleo climate prism (climate changes throughout millions of years back, without any man’s influence), the statement is especially interesting: “The present man caused increase of the greenhouse effect is causing climate changes which are much faster than Milankovic’s changes of the temporal scales that lead to an unknown future.” (Krstic et al., 2004). McGuffie, Henderson-Sellers (1997) are more cautious with their statements: “While the Milankovitch forcing offers an interesting ‘explanation’ for long-term, cycle climatic changes, the energy distributions within spectral analyses of climate and of orbital variations are interestingly different, and only recently have models begun to produce observed temperature changes from observed forcing. Almost certainly, these external changes trigger large feedback effects in the climate system which are yet to be fully understood”.

Solanki (2002) concludes on the basis of the presented results in his paper (figure 6) that there is agreeable causative link between open magnetic flux from the surface of the Sun and 10Be concentrations in ice which supports, but does not prove the Sun had important, perhaps dominant influence on our climate in the past. However, in spite of that his results relate up to 2000, he also writes: “After 1980, however, the Earth’s temperature exhibits a remarkably steep rise, while the Sun’s irradiance displays at the most a weak secular trend. Hence the Sun cannot be the dominant source of this latest temperature increase, with manmade greenhouse gases being the likely dominant alternative”.

It seems the author did not accept the results of already mentioned Gray (2000) who, talking on the data for the air temperature based on relatively recent observations emphasizes: “The subsequent measurements indicate the complete absence of any positive trend”. In any case, the significance of the figure 20 is that on the basis of it long-periodic links may be clearly noticed between open solar flux on one side and Be concentration in the ice crust on Earth on the other side.

Transport of material from the Sun and Space towards the Earth represents an extremely significant sign of the sensitivity of our planet to the influences from the outside. “Every year the Earth accumulates about 40,000 tons of cosmic detritus, mostly as billions of tiny flecks

9 World Climate Report, March 15, 2006 10 European Centre for Medium-Range Weather Forecasts


ranging in size from sand grains to peas.” (http://www.meteorobs.org/ maillist/msg21568.html)11.

Figure 6. Evolution of the open magnetic flux at the solar surface since the end of the Maunder minimum in 1700. Model predictions by Solanki et al. (2000) are represented by the red curve, reconstructions by Lockwood et al. (1999) based on geomagnetic indices by the green curve and the 10Be concentrations in ice cores (corresponding to the inverted scale on the left y-axis, Beer et al. 1990) by the dotted curve (Solanki, 2002)

Do energetic waves penetrate together with physical depositing of the material from the Space into the Earth’s magnetosphere and atmosphere? This question is extremely significant for understanding not just atmosphere disturbances. Is the total energy coming to the Earth changeable category, if we exclude already determined variability of the solar constant?

The statements that “shyly” move around low value trends bring additional confusion. “Surface thermometer measurements indicate that the temperature of the Earth is warming at an average rate close to +0.20 deg. C/decade since 1979, while the satellite data shows a warming trend of about half of this. These differences are the basis for discussions over whether our knowledge of how the atmosphere works might be in error, since the warming aloft in the troposphere should be at least as strong as that observed at the surface” 12 (http://www.ghcc.msfc.nasa.gov/MSU/msusci.html).

The results Fris-Crisstensen and Lassen came to, in essence prove the connection of the air temperature in the northern hemisphere on one and solar activity (i.e. the length of the solar cycles) on the other side. It is interesting that the comparison with air temperature above

11 Duncan Steel 12 Roy Spencer, 2006


land has shown extremely good connections with straightened curves of different length cycles (Ducic, Radovanovic, 2005). Developing such approach, other authors have also shown it could be of a great importance for understanding the causative-effective Sun-Earth connection (figure 7).

Figure 7. Length of solar Cycle LSC (filled circles), maximum ionospheric electron density in respective 11-year sunspot cycle (plus signs), Northern Hemisphere temperature anomalies (empty triangles), and local temperature anomalies in San Miguel de Tucuman, Argentina (empty circles) show a significant covariation (Adler, Elías, 2000)

Commenting this figure Landscheidt, (2003b) states: “The last value in the LSC time series seems to indicate a downward movement, a switch from short cycles to longer ones, whereas the three other curves follow their upward trend. From this divergence, Thejll and Lassen …draw the conclusion that the impact of solar activity on climate, prevailing for centuries, suddenly is no longer valid. Jumping to such a conclusion is not justified. Thejll and Lassen do not take into consideration that temperature lags solar activity by several years”.

With proper respect on the manner of behaving of scientific institutions toward newspaper articles, we do not know that anyone reacted to the following quotation: “Scientists have not established a direct link between global warming and the fires that became particularly devastating in Portugal, France and Spain this summer. Nor could such a link be expected. But most people see the two phenomena as related” (August 15th 2003, Inter Press Service).Therefore, what is necessary to keep in mind and clearly say is that clearly formulated conclusion may rarely be seen in the scientific papers that THERE IS NOT SCIENTIFICALLY CONFIRMED DIRECT LINK BETWEEN GLOBAL WARMING AND METEOROLOGICAL CONDITIONS WITH FIRES. Thus, we should not disregard, as it has already been emphasized, there are opposite and severely opposing opinions regarding global warming or perhaps to say more precisely regional climate changes. In other words, the presented mutually opposing results convincingly speak of how much our notions are limited viewing climate changes, but also of the insufficiently clear interaction of meteorological i.e. climate elements and forest fires the causes of which are not determined.


Long droughts, high temperatures, vegetation, terrain configuration, lightning and similarly may most probably in certain conditions cause and dictate the conditions of the forest fires development. “At especially dry locations, summertime blocking events can lead to increases in area burned even in the absence of antecedent drought. At particularly xeric location summertime cyclones can also lead to increased area burned, probably due to dry lightning storms that bring ignition and strong winds but little precipitation” (Gedalof et al., 2005).

McKenzie, Gedalof et al., (2004) for example, with high responsibility state that above all: “Although associations between fire and quasi-periodic patterns (PDO13 and ENSO) have been identified, we have little understanding of how these indices will respond to climate warming. Thus, our ability to extrapolate these latter associations into the future is poor. ...The 10-yr running means of PDSI14 and percentage scarred are correlated (r = -0.375, p < 0.001) during the period of record (1684-1978). Prior to 1901, the 10-yr running means of PDSI and percentage scarred are more strongly correlated (r = -0.577, p < 0.001), indicating that the relationship between fire and climate in the 20th century is weaker than in the previous two centuries”. Shubert et al., (2004) point that there is correlative link of low-frequent precipitation variation in Great Valley (USA) with the variation in Pan-Pacific part of SST15. The link is not always direct one, but noticed regularities point to the directions that should be further advanced. The mentioned authors used simulation grid point NSIPP-1 AGCM model. Every paragraph of the paper bears seriousness and professionalism. Acknowledgement the authors deserve is greater since they were also able to treat their results critically. “While SST force a global-scale response in the height field that is generally consistent with the precipitation changes over the Great Plains (including heights during pluvial conditions and enhanced heights during drought conditions), the exact mechanism by which the precipitation is impacted (in terms of changes in the storm tracks, suppressed rising motion, and changes in moisture transport) has not been established”. It is also said in the next paragraph that: “It is not clear, for example, why the model generates consistently dry conditions during the 1930s, but not during the 1950s when the pan-Pacific SST pattern has a sign and amplitude that is similar to that of the 1930s”. McKenzie, Hessl et al., (2004) showed that certain quantitative connection between fires and drought periods do exist in eastern Washington, as well as quasi-periodical connection with ENSO (3-7 years periodically) and PDO (20-30 years periodically).

Let us mention one more interesting example about the results of the link between drought and fire. “An important article appeared in the literature recently with some surprising results given the predictions of the climate models. Andreadis and Lettenmaier have published a paper in Geophysical Research Letters entitled “Trends in 20th century drought over the continental United States,” and the results are peculiar — in light of climate model projections — to say the least. In the abstract, they write “Droughts have, for the most part, become shorter, less frequent, and cover a small portion of the country over the last century”. ...So, what is the relationship between drought in the western U.S. and global warming? There isn’t any. Statistically speaking, the correlation zero, which means, as

13 Pacific Decadal Oscillation 14 Palmer Drought Severity Index 15 Sea Surface Temperature


humans have warmed the planet, they haven’t influenced western drought. This lack of a relationship holds whether one starts at the beginning of the Palmer record, which is 1895, or the starting year for Westerling’s study, which is 1970. ...Seen as we have had about a hundred years of global warming, about half of which is “natural” and the other half caused by people. The fact that there is no relationship between global temperature and western drought should be reassuring, especially because the relationship between drought and fire is quite real.”. (http://www.worldclimatereport.com/index.php/2006/07/).

The essence of this concise survey of different opinions in the field of climate variability refers to the fact that we cannot claim with certainty what weather circumstances we are expecting even after a week, not to mention longer temporal intervals. “It is hard to predict accurately where and how much rain will fall next week. It is harder still to forecast next year's rainfall patterns” (http://earthobservatory.nasa.gov/Study/NAmerDrought/NAmer_drought.html). There are more and more texts showing helplessness of the contemporary science to predict climate changes that follow. “Land-use and water-use by humans; large-scale atmospheric circulation changes caused by ocean temperatures; feedbacks between the land and atmosphere: they all play a role. Climatologists can't yet put these factors together to predict what will happen many years in advance. Next winter is mystery enough. Will it bring much snow and relief? No one knows”. (http://science.nasa.gov/headlines/y2004/21may_drought.htm?friend%20).

We get an impression that just because of that on September 14th 2006. ESA put the following as the strategic goal, i.e. task:

- “Quantify, as completely as possible, the Sun-induced climate oscillations on Earth,

affecting its atmospheric circulations, air and sea temperature, global water and energy circulation, radiation balance including effects of clouds, global vegetation patterns, etc.;

- Resolve, as far as possible, the causes and effects of the observed variability in the physics of the Earth system, attempting to identify key primary parameters governing the Sun-induced oscillations;

- Elaborate hypotheses on the mechanisms of Sun-Earth connection, gathering as much evidence as possible;

- Attempt to discuss quantitatively through extrapolation of the result obtained in this study, how much of the recently observed global warming can be attributed to the Sun’s increasing activity in contrast to the part possibly caused by anthropogenic activities” (http://esamultimedia.esa.int/docs/gsp/EO_2005-2006.ppt).

We may ask ourselves whether there is any sense to plan any activities, according to the

projections of climate changes in the following 50 or 100 years. Document signing referring to reduced emission of the atmosphere polluters should certainly be supported. Anti cyclonic weather conditions, especially over industrial areas and urban areas in valleys, in combination with toxic polluters of the atmosphere, certainly influence man’s health as well as climate changes of the area. However, we have seen many results on the previous pages suggesting us that the change of the connection between the Sun and Earth has stronger influence on climate changes than the contemporary anthropogenic activity is. In order not to come to


wrong interpretation, it is necessary to emphasize once again that one of the main messages of this book is the necessity of reducing the emission of harmful material in the atmosphere, disregarding our views on global or regional climate changes and whether we agree or not on the influence of the processes on the Sun, meteorological and climate conditions, anthropogenic activity or any other factors on the forest fire phenomenon.

2. What Is Missing in the Explanation of the Sun-Atmosphere Connection?

During the last few years several papers have appeared working on the influence of the cosmic radiation and Sun to certain meteorological, i.e. climate elements from different aspects. Schuurmans (1991) reported that after solar proton events a decrease of the atmospheric temperature (about 1.4°C) was observed at altitudes between 5.5 and 11.7 km during 10 days. This effect is apparently followed by the development of clouds and aerosols. “There has been more controversy about other parameters such as the open solar flux from the Sun, the geomagnetic aa index and the galactic cosmic ray (GCR) flux, which varies inversely with solar activity” (Kristjansson et al., 2004). The results Shnidell et al., (1999) have come to are also interesting: “Solar cycle variability may therefore play a significant role in regional surface temperatures, even though its influence on the global mean surface temperature is small (0.07 K for December-February). The radiative forcing of the solar cycle, resulting from both irradiance changes and the impact of greenhouse trapping by the additional ozone, is also small (0.2 W m-2 for December-February)”.

Contrary to ‘conservative’ ideas we get an impression the scientists are more and more turning toward the Sun. Landscheidt (2003 a) gives detailed list of papers where the link Sun-atmospheric processes is being proved: “The empirical relationship, presented here, would have a practical value even if there were no theoretical background. Many practices in meteorology are on this heuristic level. Yet there are hundreds of observations which show that within a few days after energetic solar eruptions (flares, coronal mass ejections, and eruptive prominences)16 there are diverse meteorological responses of considerable strength (Balachandran et al., 1999; Bossolasco et al., 1973; Bucha, 1983; Cliver et al., 1998; Egorova et al., 2000; Haigh, 1996; Herman and Goldberg, 1978; Landscheidt, 1983-2003; Lockwood et al., 1999; Neubauer, 1983; Markson and Muir, 1980; Palle, Bago and Butler, 2000; Prohaska and Willett, 1983; Reiter, 1983; Scherhag, 1952; Schuurmans, 1979; Shindell et al., 1999; Sykora et al., 2000; Yu, 2002).” Having in mind the weather circumstances reflect the other physical-geographic processes, the results of Mauas, Flamenco (2005) do not surprise: “...that there is a very strong direct correlation between solar activity, as expressed by the yearly Sunspot Number, and the stream flow of Parana river, in intermediate, interdecadal, scales. This correlation implies that wetter conditions in this region coincide with periods of

16 Prominences are magnetic fields of very hot gas having a shape of an arch (noose, knot), captured inside.

Sometimes, when fields become unstable, they are erupting and arise from the Sun in just a few minutes or hours. If the eruptions are directed toward Earth they may cause significant auroras and other geomagnetic activities, translator’s note.


higher solar activity, in agreement with the paleoclimatic studies of the Asian monsoon mentioned above.”

Supposition that the significant increase of the Solar flux came during the 20th century Lockwood et al., (1999) have researched, concluding that between 1964-1996 the increase of the total magnetic flux ejected from the Sun was 41% (± 13%).

Figure 8. The total solar magnetic flux emanating through the coronal source sphere Fs. Shown are the values derived from the geomagnetic aa data for 1868–1996 (black line bounding grey shading) and the values from the interplanetary observations for 1964–1996 (thick blue line). The variation of the annual means of the sunspot number ‹R› is shown by the area shaded purple and varies between 0 and a peak of 190 for solar cycle 19 (Lockwood et al., 1999)

Previously mentioned author emphasizes in the same paper not only that there is a strong link between the solar magnetic field and spots (figure 8) but that: “The variation found here stresses the importance of understanding the connections between the Sun’s output and its magnetic field and between terrestrial global cloud cover, cosmic ray fluxes and the heliospheric field”. The estimate for making conclusion was obtained on the basis of the equation:

Fs = (1/2)4πR0

2B0 = 2πr2Br = 2πr2sBBsw17

Shaviv (2005) has concluded that “…increased solar luminosity and reduced CRF over

the previous century should have contributed a warming of 0.47 ± 0.19°K, while the rest should be mainly attributed to anthropogenic causes. Without any effect of cosmic rays, the increase in solar luminosity would correspond to an increased temperature of 0.16 ± 0.04°K”. The rest, attributed the anthropogenic causes is 0.13 ± 0.33K. Thus, according this author the

17 B0 is the coronal source field at Ro from the centre of the Sun, Bsw is the IMF magnitude, where r = 1 AU for

observations near Earth. The factor of one-half arises because half the field threading the source surface is inward, the other half outward, Br observed annual means of the IMF radial component for 1964–96, Br = sBBsw


cosmic radiation influence in relation to solar one is at least twice as larger as regarding air temperature increase on Earth. Even in the extreme variant, according this author, the temperature increase attributed to anthropogenic activities is a little lower than cosmic and solar influence.

Kristjansson et al. (2004), Svensmark, Friis-Christensen (1997), Marsh, Svensmark (2000), Udelhofen, Cess (2001), Kristjansson et al. (2002), Usoskin et al.(2004), Palle (2005), Zherebtsov et al. (2005) and many others wrote on the link of the cosmic radiation (also including the solar one) and global i.e. regional cloudiness. According Tinsley, Yu (2004) “there is no decisive result at present to determine how much of the observed decadal variations are due to particle flux inputs as compared to total or spectral irradiance changes. However, there is no such ambiguity concerning the correlations of atmospheric dynamics with particle fluxes on the day-to-day timescale.” Perhaps these words illustrate best the notions they have come to: “Although a detailed physical model quantifying this connection is still missing, correlation studies support its validity” (Usoskin et al., 2004). McGuffie, Henderson-Sellers (1997) had similar confusions: “The situation is still further complicated by the lack of understanding of how the radiative properties of clouds may change. The size of the droplets in a cloud has an important influence on how the clouds interact with the radiation, and the amount of water in the clouds also changes the way the clouds interact with radiation. Clouds with larger drops have a lower albedo than clouds composed of smaller drops but with the same amount of liquid water must account for the competing effects of changing drop size and liquid water path which will ultimately affect the nature of the interaction with the solar and terrestrial radiation streams.” However, Sun, Bradly (2004) thought differently: “This reply thus further confirms our earlier conclusion that there is a lack of evidence to support the GCR-cloud hypothesis.”

Above all mentioned, Litensten, Bornarel (2006) still have suggested that: “It seems that cosmic radiation favors the formation of nucleation cores in the lower atmosphere, on which droplets of water can condense, giving rise to clouds. The physico-chemical process is still not well understood, but measurements taken during the last solar cycle showed that on a planetary scale nebulosity is higher during a period of low solar activity than during a period of high activity, probably owing to this process. …A whole field of geophysics remains to be pioneered.”

If there are already strong indications (in most of presented papers) referring to the connection of the solar and/or cosmic radiation with cloudiness phenomenon, we may ask whether it means the precipitation is also predisposed by influences from outside? The justification of such ‘heretic’ question is based on the fact that high precipitations (rain, snow, hail) may only occur from cloud. In that sense, the paper Bhattacharyya, Narasimha (2005) wrote seemed shockingly: “Using wavelet techniques it is also found that the power in the 8-16 years band during the period of higher solar activity is higher in 6 of the 7 rainfall time series, at confidence levels exceeding 99.99 %. These results support existence of connections between Indian rainfall and solar activity.”

That certain predispositions do exist between the processes on the Sun and not only those climate elements which were mentioned, Mukherjee (2006) has also shown: “It may be noted that the sudden snowfall on the northern hemisphere continents on the 25th of December, 2004 has sufficient bearing on Star-Sun-Earth’s atmosphere interaction.”

Habbal, Woo (2004) consider that: “The combination of solar wind dynamic pressure and magnetic reconnection leads to the formation of the tear-drop shaped magnetosphere, and the


entry of solar energetic particles into the Earth’s ionosphere”. According Stevancevic’s (2004, 2006), heliocentric hypothesis, electromagnetic waves coming us from the Sun, seize air masses by hydrodynamic pressure (after penetration through magnetosphere) directly causing moving and weather circumstance changes of certain region. If moisture saturation exists in the touching zone of different air masses, and depending also on the solar wind (SW) characteristics, then both clouds and precipitation may appear. The mechanism of the precipitation formation was explained by the principle of electron valence. Thus not only the cloudiness and precipitation phenomena but the phenomenon of hot waves and dry periods are first of all caused by electromagnetic characteristics of SW, location wherefrom it is ejected from the Sun and its chemical structure. Depending on the mentioned parameters, i.e. their combinations, the atmospheric processes of certain regions will also be dependant on.

Landschieidt (2000 a) thought similarly: “The strongest contributors to the solar wind intensity are energetic solar eruptions (coronal mass ejections, flares, and eruptive prominences) which create the highest velocities in the solar wind and shock waves that compress and intensify magnetic fields in the solar wind plasma. Coronal holes have a similar effect. So it suggests itself to investigate whether periods of strong plasma ejections on the Sun are connected with temperature on Earth. Not all strong eruptions have an impact on the near - Earth environment. The effect at Earth depends on the heliographic position of the eruptions and conditions in interplanetary space. Indices of geomagnetic disturbances measure the response to those eruptions that actually affect the Earth.” Whether the interactive link exists or not, this is no more the question for Palamara, Bryant (2004): “The crucial question now relates to how solar/geomagnetic activity is coupled to the lower atmosphere.”

The findings of Baliunas, Soon (2000) have also confirmed the hypothesis that besides active regions, coronary holes play an extremely important role on the processes in the lower parts of troposphere: “The temperature of the lower troposphere measured by Microwave Sounder Units (MSUs) aboard NOAA-NASA satellites has been recorded since 1979. Along with the MSU temperature curve is plotted the changing area of the Sun covered by the coronal holes the open magnetic field regions, from which high-speed particles flow. The changing flow of high-speed particles from the Sun, represented by the increase and decrease of the Sun's surface area covered by coronal holes, corresponds well with the warming and cooling of the lower troposphere.”

On the basis of the recent exchange of opinions with colleagues who treat this problem similarly, the idea on the particle penetration from the Sun (and Cosmos) to the Earth’s surface turned out to be hardly accepted. However, there are sources clearly pointing out this still occurs “When cosmic rays hit Earth's upper atmosphere, they produce a shower of secondary particles that can reach the ground”. (http://science.nasa.gov/headlines/y2005/07oct_afraid.htm).

According Hebera: “In other words, the particles were capable of tunneling all the way through Earth’s atmosphere to reach the ground”. (http://science.nasa.gov/headlines/y2007/22feb_nosafeplace.htm).

Let us mention one more example: “The most intense burst of solar radiation in five decades accompanied a large solar flare on January 20, 2005 shaking space weather theory and highlighting the need for new forecasting techniques. The solar flare occurred at 2 a.m. ET, tripping radiation monitors all over the planet and scrambling detectors on spacecraft within minutes. It was an extreme example of a flare with radiation storms that arrive too


quickly to warn future interplanetary astronauts. …Normally it takes two or more hours for a dangerous proton shower to reach maximum intensity at Earth after a solar flare, but the particles from the January 20 flare peaked about 15 minutes after the first sign. …The event also shakes current theory about the origin of proton storms at Earth. Since about 1990, we've believed that proton storms at Earth are caused by shock waves in the inner solar system as coronal mass ejections plow through interplanetary space. But the protons from this event may have come from the Sun itself, which is very confusing" (http://www.nasa.gov/centers/goddard/earthandsun/solar_fireworks.html#bctop).

SW represents in fact the output flux of the solar particles and magnetic fields that are spreading as interplanetary front. “Тhe sun's magnetic field is generated by dynamo action, though the details are still not entirely understood. …The Sun's energy output varies on time scales ...and takes two principal forms: electromagnetic radiation and the emission of charged particles” (http://umbra.nascom.nasa.gov/spd/secr/). Analyzing the case from November 2000 Lockwood et al. (2003) have concluded, on the basis of data from two satellites (ACE and WIND), the similar but not identical variations of interplanetary magnetic field may be observed. At strong eruptions SW also brings highly energetic particles- nucleons, the energy of which is measured in millions of electron volt.

The quotation that follows may seem very long, but due to significance of the contents, it has been decided to present it on the whole. “Solar/cosmic ray forcing of global climatic change, as may be inferred from the above records, is controversial among physicists and climatologists. Attempting to explain a physical link on the basis of the relationship ‘solar wind-magnetosphere-ionosphere-atmosphere’ is difficult because of a very large difference of the solar wind energy and the energy of the atmospheric processes (4 orders of magnitude). Thus, it is necessary to develop another approach in the problem solution: the solar irradiance remains the main source of the energy affecting the atmosphere, but some agents controlled by solar activity must act directly on the atmosphere and change the amount of the solar energy reaching the Earth surface. Clearly a positive feedback mechanism is needed, explaining how relatively small variations in solar activity can cause significant climate changes” (van Geel et al., 1999). Landschieidt (2000 a) states: “Willis (1976) has calculated that the solar wind energy flux is less than one millionth of the Sun's electromagnetic power deposited near Earth. However, this estimation is based on the total cross-sectional area of the globe. It does not take into account that the solar wind energy may preferentially penetrate into areas smaller than the total disk where it can dominate other energy sources. Herman and Goldberg (1978) have shown that the solar wind energy concentrates on a narrow circumpolar latitude belt near the auroral zone. Taking additionally into account the slant incidence of the Sun's radiant flux, they calculated that the available power of the solar wind would reach 20% of the Sun's electromagnetic energy flux. If Svensmark could show in detail in his laboratory experiments, planned in cooperation with CERN, how galactic cosmic rays, regulated by the solar wind, affect cloud development, we would even have to concede that the energy of starlight is sufficient to affect climate. Cosmic rays and starlight inject nearly the same amount of energy into the atmosphere.”

Disregarding lack of detailed knowledge of the mechanism of interactive connection Ponyavin et al., (2005) emphasize that with usage of certain techniques, connections may be confirmed. “Historical sunspot and climate records were analyzed by means of nonlinear tools to study long-term trends and relationships with the solar activity variations. Cross Wavelet technique and Recurrence Plot analysis were applied to the data (for annual averages


of air-surface temperature in Central England, Stockholm and St.Petersburg) to find their similarities and phase coherence at different time and time-scale. ...The second half of 20th century demonstrates unusual response of climatic system to the solar signal.”

Russian scientists also noticed the connection of the regional changes regarding some climate elements and forest fires on one side and processes occurring on the Sun on the other side. “This is similar to behavior of cloudiness in Europe depending on solar activity and it explained by displacement of southern and northern paths of western Atlantic cyclones with increase of solar activity to the middle latitudes” (http://www.ans.kiruna.se/meetings/comaar/pdf/V_Solovyev.pdf).

According Stevancevic (2004, 2006), the key explanation of the mentioned causative-effective link is vector circulation of the interplanetary magnetic fields (IMF). If the Bz component of the IMF has negative sign, in relation to Earth’s magnetosphere field, it comes to their linking up i.e. reconnection (in areas above north and south pole). Otherwise, it may come to the rejection and then principally SW does not reach air masses. It is interesting that even regarding SW ejection from the Sun, the magnetic field vector more and more gains on importance. Wang (2005) says: “Without the detailed knowledge about the vector magnetic fields in the photosphere, the coronal heating and activity can not be properly understood.” Nevertheless, it may be concluded the Earth’s magnetic shield does not present such a powerful defensive mechanism of our planet, as it has been believed recently. “The cracks were detected before but researchers now know they can remain open for long periods, rather than opening and closing for just very brief intervals. This new discovery about how the Earth's magnetic shield is breached is expected to help space physicists give better estimates of the effects of severe space weather”18.

For the first time, as far as we know, Stevancevic indicated that even forest fires (the causes of which are not officially determined) may directly depend on the mentioned predispositions19. “First larger opening of the magnetic field occurred in February 2002, in Siberia when it came to greater forest ignition. Immediately after that, in the period from 2nd-4th of March the Solar Wind reached the borders of our country starting a series of fires in the vicinity of the towns of Bor and Zajecar” (Stevancevic, 2004). In that respect, it seems that a significant step forward was made regarding the notions Auclair (1992) came to, whose results have shown the areas under forest fires are larger (North America) when the Sun is more active.

18 (http://www.nasa.gov/centers/goddard/news/topstory/2003/1203image_cluster.html) 19 PhD M. Flannigan suggested that there are similar researches: “Check for Vines (an Australian - think it was Neil

but may be wrong on the first name)”. However, all the efforts to come to the researching results of this author were unsuccessful.

Table 1. Total number of forest fires (1) and fire seized surfaces (2) in Europe for period 1991-2001 (according to FAO, 2002)20

year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 1 56490 79058 69588 77771 85107 87580 92526 120742 118263 140316 106692

2 (ha) 585774 462100 488236 804814 435517 296510 364824 707920 362704 928416 463186

Table 2. Total number of forest fires for Europe and South European countries for period 1991-201 (according to FAO, 2002)

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Σ Europa 56490 79058 69588 77771 85107 87580 92526 120742 118263 140316 106692 1034133 South Europa 45779 57150 56811 61117 72675 66419 71232 86895 70613 95484 65881 750057

20 Within these data Moldavia, Ukraine, Belarus and Russia are not included while the data for Turkey and Israel are included

On The Relationship between Solar Activity and Forest Fires

23

Table 3. Number of forest fires of known (1-3) and unknown (4-6) causes per European countries for period 1999-2002 (according to FAO, 2002)

1 2 3 4 5 6 Country 1999 2000 2001 1999 2000 2001 Armenia 15 35 ... - - ... Belarus 2876 1705 ... 1083 864 ... Belgium 8 - 3 8 1 1 Bulgaria 93 403 206 227 1307 619 Croatia 94 187 ... 129 519 ... Cyprus 9 205 210 11 80 89 Czech Rep. 921 959 ... 482 540 ... Denmark ... ... 4 ... ... 4 Estonia 116 105 ... 14 53 ... France 1599 1341 1995 3353 4401 2262 Germany 675 681 680 503 529 352 Greece ... ... 660 ... ... 1998 Kazakhstan 96 122 ... 850 815 ... Latvia 1196 915 ... - - ... Lithuania 966 619 278 56 35 9 Norway 32 22 ... 116 75 ... Poland 8994 11187 ... 23655 20445 ... Portugal ... ... 957 ... ... 25943 Romania 81 448 ... 58 240 ... Russian Federation 28300 16200 ... 3400 2600 ... Serbia & Montenegro 190 115 149 74 224 137 Slovakia ... 787 ... ... 37 ... Slovenia 27 53 ... 26 45 ... Spain 14560 20084 12251 3677 4033 6846 Sweden ... ... 2924 ... ... 1850 Switzerland 30 53 ... 11 - ... The f.Y.R. of Macedonia 12 42 ... 48 140 ... Turkey 1633 1926 2068 442 427 563 Ukraine 6055 3683 3187 15 13 18

3. Why Do Forest Fires Appear

According to the data of FAO (2000) we may notice the total number of the forest fires in Europe with certain deviations as well as surfaces which they seize is considerably increasing (table 1). Observed in such a way, certain analogy with the sudden air temperature increase is noticed especially in the last decade of the 20th century. From the presented table we can see the largest number of the fires was noted in 2000 (140316) and we can also notice that then

Milan Rodovanovic and João Fernando Pereira Gomes

24

the largest fire seized surfaces were in Europe (928416). According to incomplete data of the Global Forest Resources Assessment 200521 the average annual surface of the fire seized forests in 1998-2002 was 1597000 ha in Europe. The data (table 2) are especially interesting pointing the greatest number of the fires appears in the Mediterranean zone. No matter how much it has seemed to us we live in the period of the sudden development of science and technologies, the facts are inexorable and they really show how much we are helpless to perceive clearly what such large number of fires is caused by. Thus, overtaking suitable measures of the protection looks more like “wandering through fog”.

Absolute values from the table 3 showed that the greatest number of the forest fires of known cause was noted in Russia in 1999 (28300) and Spain in 2000 (20084), while the fires of unknown cause were the most numerous in Portugal in 2001 (25943) and Poland in 1999 (23655). The data relating to Poland are especially significant. Namely, in 1999 the number of the forest fires of known cause was about 2.5 times less in relation to those of unknown cause. The next year the number of the established causes little increased in relation to unknown ones. It has seemed the situation in forestry drastically improved in Poland the following year so that according to the recent data “unknown causes varied about levels of 7 % to 8 %” for 2005 (http://www.fire.uni-freiburg.de/programmes/eu-comission/EU-Forest-Fires-in-Europe-2005.pdf). Nevertheless, according to the same source almost incredible 70 455 fires were noted in this country in 2003.

It may seem almost impossible to understand any spatial connection, whether it is about occurrences with known or unknown cause; even if we keep in mind all lacks of gathering and data processing.

It is noticeable the data for Russia are also missing in the table 4, so the significance of this table considerably lessens. Still, we may notice that as for the surfaces burnt without established cause, Portugal is in the first place (75727 ha in 2001) while Spain bears the first position as for known causes (168163 ha in 2000).

Regarding the concrete indexes for Europe, it is important to point out there are little different data: “Since 1985, the average size of burnt surface areas has diminished. However the increase in the number of fires still remains a concern, which shows the importance of an improved struggle against the causes of fires, all the more so in Europe because 53% of the fires remain of an unknown origin.”

On one side, we may conclude from the previous source that the fire seized surfaces show decrease during certain temporal period, but on the other one, the domination of the cases of unknown cause is especially fully expressed: 40% in period 1950-1991. (table 5) and 53% from 1985 Let us remember that Nikolov (2006) also stated similar values for the Balkans, i.e. according to this author 37.9% are fires of unknown cause.

In lack of the rational explanation we can often find the comments relating to the unclear influence of the weather circumstances: “During the last few years an increase of fire danger and elevated number of fires and area burned have been observed in Poland as a consequence of more frequent occurrence of extreme fire weather conditions during the fire season. These weather conditions that were uncommon in earlier years are accompanied by rapid changes of atmospheric fronts. Moreover, regional climate warming, associated with increasing

21 Chapter 4, Forest health and vitality


25

Table 4. Forest fire seized surfaces (ha) of known (1-3) and unknown (4-6) causes per European countries for period 1999-2001 (according to FAO, 2002)

1 2 3 4 5 6 Country 1999 2000 2001 1999 2000 2001 Armenia 53 43 ... - - ... Belgium 1 - 1 1 0 0 Bulgaria 6170 15320 ... 2121 42086 ... Croatia 3645 12208 - 2408 55958 ... Cyprus 1 1342 1891 2 6693 2939 Czech Rep. 213 207 ... 123 168 ... Estonia 1056 683 ... 47 1 ... France 7914 17456 10926 7950 3003 9543 Germany 247 296 84 168 285 38 Greece ... ... 4376 ... ... 13966 Kazakhstan 7718 9443 ... 18783 18044 ... Latvia 1544 1341 ... - - ... Lithuania 480 340 110 14 12 2 Portugal ... ... 36108 ... ... 75727 Romania 221 2308 ... 161 1299 ... Serbia & Montenegro 701 2670 1433 1094 5305 2025 Slovenia 192 219 ... 241 46 ... Spain 70682 168163 46055 11537 18863 46331 Sweden ... ... 1071 ... ... 182 Switzerland 18 42 ... 4 24 ... The FYR. of Macedonia 142 1380 ... 1687 12289 ... Turkey 4865 23601 5632 939 2752 1762

Table 5. Fire origin in “Landes Forest” from 1950 to 1991 was as following: (http://www.feudeforet.org/english/forets_europe.htm#haut):

Unknown 40 % Lightning 29.7 % Carelessness 11.5% Accident 9.6 % Starting up again of fires 3 % Others 5.3 %

occurrence of relatively warm and snowless winters have also contributed to prolongation of the fire season. Thus, winter and autumn months are no longer considered free of fire risk. The year 1999 is an example when the maximum of fires (2106) was observed in September. Compared with the period 1990-1998 this number is equivalent to an increase of September fires of more than ten times, contributing to more than a fourth of the total number of yearly fires” (Ubysz, Szczygiel, 2002).

Applying HIGRAD/FIRETEC computer model, the numerical simulation has shown that wind, locally, does not always cause fire spreading in the suitable direction. “In all simulations, the magnitude of the convective heat transfer is greater than that of the radiative heat transfer; however, these processes and their relationships to the three-dimensional


26

structure and evolution of the fire are shown to depend both on the ambient wind speed and on the specific location along the fire front (e.g., at the head of the fire where the fire is spreading in the direction of the ambient wind, or on the flank of the fire where the fire is spreading in the direction almost perpendicular to the ambient wind)” (Linn, 2007). The local wind influence certainly plays an important role in the fire spreading. However, it is necessary to point out the question of side spreading of the fire, which advances almost under the right angle in relation to air circulation.

Having in mind that satisfying explanation on the influence of any climate element (or a combination) to the initial phase of the fire phenomenon has not been given in 40% of the cases then it is the question of appropriateness of the models, which in the first place base the prediction of the variations of these catastrophes according to global warming. That is why the following statement does not surprise: “Thus, research on fire protection and control is challenging, and predictive tools for fire protection and control are often based substantially on expert opinion and anecdotes, rather than on documented research evidence” (Gorte, 2000). Quoting Boychuk and collaborators (1997), Ryu et al. (2004) have pointed that “The primary approach of landscape management is to maintain states of fuel loading similar to those that existed prior to European settlement to achieve sustainable ecosystem management. However, a substantial gap remains between the principles of fire accommodation and emulation and their application. A clear understanding of the relationships among fire, weather, fuel, and disturbance across scales is essential”. That it is about the impossibility of viewing the key aspects of the whole problem best confirms the quotation pointing the recent activities “only confirmed that the strategy followed until then did not solve the problem” (Gomes, 2006).

However, decisive and clear stating of the existing condition is not always present in the scientific papers. Gonzalez et al. (2006) have claimed for example that beyond the fact fires are highly stochastic phenomenon, their model and its parameters are significant and the testing results are consistent, i.e. as such they may be used in practice. In that sense Landscheidt (2003a) is categorical: “Anyway, the correct forecast of the U. S. drought beginning in 1999 and a dozen of further successful climate forecasts, exclusively based on solar activity, show already now that the IPCC’s claim that there has only been a negligible solar effect on climate change in recent decades is not tenable. Ironically, just drought, the greatest threat attributed to alleged man-made global warming, has turned out to be regulated by variations in the sun’s eruptional activity”.

Nevertheless, it is useful to mention that even in such circumstances there are certain attempts of the long-term prognosticating. Brown et al. (2004) have done the projection models of the fires for the western USA for periods 2010-2029, 2030-2049, 2050-2069 and 2070-2089. Special significance was given to the temperature increase, especially to relative air humidity.

Flannigan claims that forest fires during 2003 were “glimpse of what the future will be like” and that “we can expect more severe fire seasons in the future”. …Continued warming will produce greater seasonal contrasts which, combined with an expected 44 % increase in lightning strikes, is expected to increase the area burned by 78 % in the next 50 years. (http://www.davidsuzuki.org/Forests/Forests_101/FIRE/Climate_Change.asp).

Previously mentioned author admits that the connection is not quite clear, but depending on the climate disturbances the fire frequency may also depend: “Although both the number of fires and area burned have increased over the past 40 years, we cannot detect consistent


27

trends in weather indices associated with these large fires. However, we do expect that a changing climate will make fire weather conditions more severe, resulting in an increase in area burned in the future” (Flannigan et al. 2002).

On the basis of available literature it is necessary to point out the following: even above all mentioned here, the prevailing opinion both in public and scientific circles is based on:

a) the supposition the forest fires are mostly the consequence of the intentional or

unintentional man’s activity. Under this it is also meant on direct influence of the greenhouse effect (global warming) to the development of the weather conditions, as well as to accidentally or intentionally caused fires;

b) the supposition that lightning is the most frequent cause of fires in the sub polar areas.

In distant, unsettled areas, if there was not any lightning the cause of fire has

automatically been attributed to irresponsible men’s behavior, because it seemed that simply there has not been other explanation. “The relationship between lightning characteristics and ignition probability is incompletely understood, and not all strikes have characteristics required to initiate a fire …A long continuous current cannot be detected with current technology, and not all lightning strikes are recorded …There was no evidence to suggest the location of lightning detectors …influenced lightning indices …We must consider that initiation patterns (and fire regimes) change over long time scales (e.g. multiple disturbances) and reflect the intrinsic stochasticity of mixedwood boreal stand development …In Alberta, mature pine is considered a “go, no-go” fuel type (assuming ladder fuels such as a spruce understory are not present) where fire behavior is considered low except under strong winds …Initiation was not sensitive to the amount of open (e.g. muskeg) area in a landscape” (Krawchuk et al. 2006). Perhaps it may be useful to mention for the sake of the reading public the typical sub polar climate where Alberta lies, characterizes long cold winters and short cold summers. Besides, Farr et al. (2004) quoting Andison (2003), point out that the forest fires do not have progressive growth in all the regions. Concerning Alberta “Historical records suggest that prior to 1950, fires were more frequent ...burning at least 1 % of the forest per year. It is possible that fire suppression during the past few decades has reduced the incidence of fire in the study area. Alternatively, recent weather and fuel conditions may have been less conducive to fire than several decades ago.”

The attempts of modeling the impacts of the electric discharge in the atmosphere on fires left modest also, simply because there are still many unknowns in that field: “Beyond its powerful beauty, lightning presents science with one of its greatest local mysteries: How does it work? It is common knowledge that lightning is generated in electrically charged storm systems, but the method of cloud charging still remains elusive. (http://science.howstuffworks.com/lightning.htm).

Anyway, when it is about lightning affecting the vegetation, it is necessary to have in mind already mentioned conclusion it is mostly followed by precipitation (Kourtz, Todd, 1991). It is obvious the precipitation quantity, first of all in such situations defines whether fire would spread over or it would be extinguished. It seems the lack of more detailed studies on this theme does not offer the strong enough support to understand the questions to what extent electric discharges participate in the initial phase of the fire phenomenon.


28

It is founded that: “From 1990 to 1998, over 17000 naturally ignited wildfires were observed in Arizona and New Mexico on US federal land during the fire season of April through October. Lightning strikes associated with these fires accounted for less than 0.35 % of all recorded cloud-to-ground lightning strikes that occurred during the fire season during that time. Natural wildfire ignitions in this region are often attributed to what is referred to as ‘dry’ lightning, or lightning with little or no precipitation” (Hall, 2007). Citing the results of the National Interagency Fire Centre, Rowell, Moore (2000) have pointed out that“ for 1997 for North America three quarters of the land burned – 76 % - was due to lightning.” Beside different temporal intervals of data processing, the ranges of impacts of lightening on forest burning are at least contradictory.

An English oak more than hundred years old is one of the tourist attractions of Kuman (northern Banat, Serbia). According to the local residents’ words it is remembered this still alive tree to be struck by lightning for seven times and it has never been burnt. It is clear that such examples cannot be used as proof that lightning is not the frequent cause of the forest fires. However, it is absolutely clear this is not an isolated case and all such examples rather fit into the results Hall (2007) has given.

4. Hypothesis on the Processes on the Sun as the Cause of Large Forest Fires

The visual effect of the figure 9, suggests on the significant link between fires in south Europe (13 states-75% of fires) and total number of fires for the whole continent in period from 1991-2001. The estimate of the correlation coefficient (for table 6) has shown it is high 0.91 with the statistically significant level of confidence of over 99%. Disregarding the cases of known or unknown causes are about, the correlation coefficient points to their spatial and time link. However, the correlation link between series of data for south and the rest part of Europe is much lower: 0.64. In other words, the link which evidently does exist is much weaker than it could be concluded on the basis of integrated data.

EUROPE

0

20

40

60

80

100

120

140

160

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Thousands / Milliers

EUROPE SOUTHERN EUROPE

Number of fires / Nombre d'incendies

SOUTHERN EUROPE / EUROPE MERIDIONALE:Albania, Bulgaria, Croata, Cyprus, France, Greece, Israel, Italy, Portugal,Slovenia, Spain, Serbia & Montenegro and Turkey .

Figure 9. Forest fires registered in Europe (total) and Southern Europe for period 1991-2001. (FAO UN, 2002)

Table 6. Comparative survey of the locations of forest fires in Europe recorded by satellite and the parameters of the highly energetic regions and SW that have immediately preceded them

Proton fluence Protons/cm2-day-sr Date of recorded fires

Location on Europe

Coronary hole

Energetic region(s)

Magnetic structure

Max temperature of particles (°K 000)

Max radial speed of particles (km/s)

Max density of particles (p/cm3) during 3-4 days before the fires >1 MeV >10 MeV >100 MeV

23. 11. 2002 Caspian Lake

CH NN 10091 Beta gamma delta

>1 000 000 800 54 2.0e+06 1.1e+04 2.9e+03 and 24. 11. 3.1e+03

02. 03. 2003 Southwest Russia

CH 23 10296 Gamma delta 600 000 630 20 6.1e+05 1.2e+04 2.9e+03

26. 03. 2003 Balkan, east Europe

CH 26 10314 Beta gamma 960 000 870 23 5.5e+06 1.2e+04 2.8e+03

24. 07. 2003 Italy CH 49 10410 Beta gamma delta

500 000 575 7 1.5e+06 1.2e+04 2.7e+03

28. 07. 2003 France CH 49 10422 Beta gamma delta

>1 000 000 850 60 1.7e+06 1.2e+04 and 29. 07. 1.3e+04

2.7e+03

13. 09. 2003 Portugal CH 55 10456 Beta gamma delta

>1 000 000 770 10 1.7e+06 1.2e+04 2.7e+03

28. 07. 2004 Portugal, Spain

CH 106 10652 Beta gamma delta

>1 000 000 968 54 2.7e+08 9.5e+06 3.1e+03

23. 08. 2004 Volga CH 110 10661 Beta gamma delta

400 000 550 11 5.8e+05 1.6e+04 3.8e+03

28. 07. 2005 Greece CH 177 10792 Beta-gamma-delta

500 000 635 23 1.2e+07 and rising till 01. 08 5.9e+07

2.2e+06, 29. 08 -2.8e+06 and 30. 08. - 2.3e+06

6.7e+03

03. 08. 2005 Portugal CH 198 10792 Beta gamma 500 000 630 56 5.9e+07 1.5e+06 4.9e+03 24. 08. 2005 Portugal CH 183 S583 Beta delta >1 000 000 800 33 2.6e+08 1.7e+07 1.1e+04

The data about the forest fires have been taken from Natural Hazards >> Fires >> NN- marking of the coronary holes starts from 2003: The data for coronary holes have been taken from http://www.dxlc.com/solar/index.html The parameters of the energetic regions have been taken from http://www.sel.noaa.gov/ace/ACErtsw_data.html The data for protons have been taken from http://umtof.umd.edu/pm/crn/ Term energetic region means the location on the Sun, containing certain number of spots, having different magnetic structures.


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Summing up the data, it was calculated that according the official data between 1999 and 2001. 116352 forest fires occurred in Europe for which the cause was not determined. Proceeding from these facts it was thought that the existing situation could not be explained by ‘classic’ methods, i.e. explanations. At one moment the idea has appeared to check the hypothesis Stevancevic (2004) stated. It was decided the establishing of the eventual time connection, i.e. causality between forest fires and eruptions on the Sun to be the test step. Necessary satellite data were united only for 10 cases, for period from November 2002 to August 2005.

Since this as an ‘unusual’ research, it was suggested to check the same way whether similar had been happening with another fire on August 24th 2005 in Portugal. After successful attempt to have the data completed, in this eleventh example the noticed regularity was also confirmed. Further efforts to get to the information whether these 11 fires have any causes found were unsuccessful.

At the very beginning it was clear that it would be impossible to make more detailed data base (certainly not large enough for statistically representative samples), but even on this level especially significant results have not been expected. However, it turned out similar situation on the Sun had preceded all the observed fires. Namely, immediately before the destructive power of fires, energetic regions were in geo effective position emitting strong electromagnetic waves toward the Earth, too. In all the cases, without exception, it was the energetic regions with coronary holes co effect about. Having in mind obvious lacks regarding the available data fund, the application of any statistical apparatus has appeared as significant problem. Because of that it has been tried to point out the justification of the approach based on time sequence of the occurrences.

The particles’ velocities were of 550 km/s, while in some situations even over 1000 km/s. Presented temperatures are for proton, ion and nucleon SW particles. It is measured on 1.5 million km from the Earth while ACE satellites make the observations (http://www.sel.noaa.gov/ace/ACErtsw_data.html). Particle temperatures reached even over a million of °C in some situations. Under the SW velocities of e.g. about 800 km/s, we can estimate that highly energetic particles, having also high thermal temperature, arrived to Earth for about 45 minutes from the moment when the instruments had registered them.

Suspicion the fires in northern piedmont area of Caucasus (figure 10) may be the possible consequence of the eventual terrorist actions, was eliminated by noticing several locations burning also on the southern slopes of the mountain. Let us mention that in the very same region many fires also occurred on March 2nd and March 31st 2003 (http://earthobservatory.nasa.gov/NaturalHazards/archive). This practically means the meteorological conditions in all three cases, in accordance with suitable part of the year, cannot cause the initial phase of fire. Persistent searching for the information whether the local population was preparing the terrain for working in the fields on both sides of the mountain by burning vegetation just at the end of November and at the beginning of February i.e., at the end of March, also left without results.

It has been noticed that wider area around Caspian Lake has been fire seized relatively frequently in the last few years. With this example, as well as with all the rest examples from the previous table, a sudden proton energy rise in all ranges has always been registered immediately (mostly about 2 days) before fire breaking out (Figures 11 and 12). It is not possible to show recordings for all the cases due to limited scope of this monograph, but they certainly may be checked in corresponding sources.


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Figure 10. Satellite recording of the fires at the utmost southeast of Europe on 23.11.2002. (http://earthobservatory.nasa.gov/NaturalHazards/Archive/Nov2002/SERussia.AMOA2002325_lrg.jpg)

Figure 11. Sudden proton energy rise at the beginning of 21. 11. 2002. (http://www.sel.noaa.gov/ace/ace_rtsw_data.html)


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Figure 12. SW parameters were characterized by extremely high particle density, high velocity and temperature in the area of Caspian Lake immediately before fires (http://www.sel.noaa.gov/ace/ace_rtsw_data.html)

Reconsidering our own results, an idea occurred that perhaps certain geographic i.e. geophysical specification exists in Europe, which is not present on other continents or it is less prevailed. However, while surveying superficially, it has turned out that in other parts of our planet similar phenomena also exist as well as on Old Continent (figures 13 and 14).

Figure 13. The strongest flare on the Sun in the history of the satellite observations belonged to X28 class (http://sohowww.nascom.nasa.gov/hotshots/2003_11_04/c2.gif)


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It is interesting that in period from October 18th to November 4th 2003. a series of extremely strong flares occurred on the Sun, unprecedented in the history of satellite measuring. Here is how media described occurrences in the USA those days: “The fires that blackened 775,000 acres and 2,400 homes in Southern California this October. ...The state has never seen a loss of this magnitude” (http://www.hcn.org/servlets/hcn.Article?article_id=14457). Eruption which occurred on November 4th that year belonged to X28 class and as such it was an absolute recorder according its strength (figure 13). It seems that our planet had luck since disregarding that ranges of electromagnetic waves were very high, the main emitting directions were directed out of earth’s orbit.

We ask is the fire in India, in the foothill of the Himalaya (recorded on November 6th 2003, figure 14) in time coincidence with the strongest flare or is it something else about?

Figure 14. Tens of the locations were fire seized in the foothill of Himalaya two days after the strongest X28 flare (http://earthobservatory.nasa.gov/NaturalHazards/Archive/Oct2003/India.AMOA2003296_lrg.jp)

Citing D. Beker, Bond (2004) notices: ”We have never seen such a powerful enhancement and distortion of the radiation belts. From 1 to 10 November the outer belt had its centre only about 9 600 km from Earth’s equatorial surface. ...This is a place where ordinarily there are almost no energetic electrons at all.” Let us remind that on November 3rd 2003 many fires in New Guinea were detected, while on November 10th 2003 fires in Northern Brazil as well as in West Africa were also detected.

Analyzing satellite recordings it follows that at the same time when X28 occurred, several energetic regions were in geo effective position (with 10467, 10495, S299 signs), as well as the coronary hole bearing CH 0065 sign (figure 15). In other words, it is similar as in all 11 cases. And again it comes to a sudden flux of electromagnetic waves (figure 16).


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Figure 15. Recording of the coronary hole and energetic regions on the Sun day after Х28 (http://www.dxlc.com/solar/)

Figure 16. Sudden rise in proton energy at the end of October and the beginning of November 2003 was directed toward Earth in two waves (http://sec.noaa.gov/ace/SWEPAM_7d.html)

Fires in Australia, recorded in January 2005 also characterized similar analogy. “Firefighters tentatively contained a large wildfire in the mountains east of Perth on Jan. 20, 2005. This image shows the burned areas as well as still-burning portions of the fire.” (http://earthobservatory.nasa.gov/NaturalHazards/Archive/Jan2005/Australia4.AMOA2005020_lrg.jpg).

Those days, proton velocities exceeded measuring abilities of the instruments several times (figure 17).


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Figure 17. From 12th-23rd of January values of proton’s velocities were several times above measuring abilities of instruments (http://umtof.umd.edu/pm/crn/)

It is important to emphasize the forest fires are not always preceded by the phenomenon of coronary holes and energetic regions which emit exclusively strong electromagnetic waves. There are some cases when danger from plant mass ignition still exists even under relatively weaker sources. The example could be the series of forest fires in Serbia in the period from March 13th-19th. The public was then informed that 18 fires were burning between Rudnik and Takovo, 10 ha (66 localities) fire seized in the vicinity of the town of Kragujevac (central Serbia), while in the surroundings of Leskovac (southeastern Serbia) fire seized 300 ha of forest. In the nearby of Svrljig (eastern Serbia) 16 fires were registered, while around 50 in the District of Rasina (five municipalities south from Krusevac toward Kosovo and Metohia).

In Podgorina (surroundings of Valjevo), in the village of Vragocanica –small village of Stojkovic, according local residents’ words forest burned being ignited by a shining red ball which landed from the sky! D. Simic, a local resident, described the event: “It was about 18.00 hours when I saw fire burning in the forest, like a road cut through for about 100 meters long. It only burned by one side and the fire did not spread over. Above flame, there was one red firing band in the sky such as the depth of an arm is, resembling the white aerial trail. Nobody was passing by the forest, neither anybody do anything. I do not know what was it, but I am sure that the fire did not occur just like that.” In this case firemen rejected the possibility that eventually a meteor caused the ignition, because there was not crater from the fall of the meteor, although it was not possible to notice it at night. N. Bozic who is an astronomer in Petnica Researching Center near Valjevo said that it was possible the fall of the meteor had caused fire in Vregocanica, but only under certain circumstances. “While burning out in the atmosphere, meteor leaves a track in a shape of a tail. Theoretically, it may burn out


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even one meter above land not making a crater, but causing the ignition. However, since it is a great velocity about, a sound effect must have been heard such as missile flying is and striking wave that would break treetops. If it had not happened, then meteor fall was not the fire cause.” S. Stojkovic, a local resident, does not also believe the clearing of the forest with fire may be the cause of the mentioned disaster. As he says, on Sundays (when mentioned fire occurred near Valjevo) no one worked in the village.

(http://arhiva.glas-javnosti.co.yu/arhiva/2007/03/21/srpski/T07032002.shtml).

Figure 18. A day before the fires in Serbia, 10946 energetic region was recorded in the east of the Sun (in geo effective position), while at the same time electromagnetic waves from CH260 coronary hole were emitted toward Earth (http://www.dxlc.com/solar/)

Figure 19. Sudden flux of the SW highly energetic particles was especially registered in ranges of 1.8-3.3 and 3.3-6.4 MeV/n from 12th-16th of March 2007


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Figure 20. Proton velocities were reaching the values of mostly over 600 km/s from 11th-16th of March 2007

Fires in Tasmania Fires triggered by lightning in February 2007 continued to burn in March. This image shows the fires on March 21. Event Date: 2007-03-21 00:00:00 Number of Images: 1 Topic: Fires

Fires in the Southern United States Numerous fires were burning across the southern United States in early March 2007. This image shows the area on March 20, 2007.

Event Date: 2007-03-07 00:00:00 Number of Images: 2 Topic: Fires

Fires in Myanmar Hundreds of fires were burning in Myanmar and surrounding countries in March and April 2007. Event Date: 2007-03-02 00:00:00 Number of Images: 6 Topic: Fires

Figure 21. Fires in different parts of our planet at the time when relatively small fires occurred in Serbia


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As it has already been mentioned the figures 18 to 20 as well as all cases cited before point to similar situations on the Sun before braking out of the forest fires. In relation to some previously mentioned cases, in this example it is relatively smaller fire about. However, by the inspection into available data, it turned out that during that period fire did not just seize the area of Serbia. The disaster was more expressed in the southern part of the USA and Myanmaris, while in Tasmania fires burned on relatively smaller number of the locations, but they lasted more than 20 days (figure 21).

Notions on possible extreme values of SW parameters were probably insufficient in the time when satellite instruments had been constructed. How else explain the situations when instruments cannot record e.g. proton flux (figure 22) even during several days in a row.

Let us remind that fires appeared in France (coastal area of the Mediterranean Sea) on July 28th 2003. Many cases, especially those after 2000., point to the necessity of expanding the measuring range of the instruments i.e. the possibility of measuring greater values of SW parameters than recently. Satellites detecting particle flux, measure in essence electric convection current which flows from the Sun and towards the Earth. Picturesque description of the cosmic radiation under extremely strong emissions Cowen (2001) presented: “2005 has been a surprisingly active year on the sun... Since January, astronomers have counted 14 powerful X-class solar flares and an even greater number of CMEs". (http://science.nasa.gov/headlines/y2005/07oct_afraid.htm).”

Figure 22. Values of proton velocities were exceeding measuring abilities of instruments at the beginning of 27. 07. 2003 in all days to 03. 08. 2003. An exception is 28. 07. (http://umtof.umd.edu/pm/crn/).


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It is similar with the satellite data of the observation lasting of proton, electron, neutron flow, chemical structure, speed, temperature, intensity of convectional current, their vector direction, but which are being observed out of Earth’s magnetosphere. Many instruments, positioned for those purposes, stopped working just because of damage or complete destruction. The reason: -‘close encounter’ with electromagnetic waves of the cosmic (and/or solar) origin, of so high energies, the instruments of which obviously had not been adequately protected (Iucci et al., 2006).

Strong flares also indicatively suggest the intensified solar activity may be brought into connection with increased number of fires in the last few years, as shown in Table 7. It is necessary to emphasize that according other sources five strongest flares relate the period after 2000 (http://umtof.umd.edu/pm/flare/5flares.gif). On the other side, not all strong flares were directed toward Earth.

Table 7. Five strongest flares since 1976. (According http://www.spaceweather.com/solarflares/topflares.html)

Ranking Day/Month/Year X-Ray Class 1 04/11/03 X28 2 02/04/01 X20.0 2 16/08/89 X20.0 3 28/10/03 X17.2 4 07/09/05 X17

The hypothesis on the certain processes on the Sun, as possible causes of plant mass

ignition, is based on the supposition that highly energetic particles, in certain conditions, penetrate to vegetation combustion material and by burning through, on the molecular level, they cause the initial phase of fire. If there are clouds, the particles of large energetic load have reduced possibilities of penetration to the topographic surface in places of the penetration in the atmosphere of our planet. By itself, in such circumstances, according mentioned hypothesis, danger from the destructive power of fires is reduced. Simply said, vapor contained in developed cloudy systems, as an integral part of the atmosphere, absorbs particles arrived from cosmos.

According Stevancevic’s views, it does not mean the fires may appear by chance, but penetrations above poles and equators cause them. Further particle circulation contained in the SW toward Earth depends on several parameters and their combinations, which greatly makes harder the exact prediction of the potential centers. It is clear the SW suffers considerable losses in temperature and speed on its way to Earth. By recent inspection of the SW penetration through magnetosphere has shown they can be classified into two main groups: penetrations above approximately 65º of the magnetosphere latitude and penetrations in the area of 5º northern and southern from magnetosphere equator near geomagnetic anomalies (Radovanovic et al., 2003 b). Tinsley, Yu (2004) came to similar (indirect) results, what may be seen from figure 23.


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Figure 23. Percentage changes in Jz and near-surface Ez for a Forbush decrease of 35% (polar) to 12% (equatorial) for longitude 72.5° E. The departures from symmetry about the equator are due to the variations in surface altitude, that have greatest effect on the near-surface Ez. Adapted from Sapkota and Varshneya (1990)1 (Tinsley, Yu, 2004)

Values ΔЕz about 65º, as well as ΔJz about 5º of the northern geographic latitude are particularly noticeable. According the author: “The treatment of this effect by Sapkota and Varshneya ...for a relatively large decrease of GCR flux, of 35 % at high latitudes and 12 % at equatorial latitudes. The values of ΔJz and ΔEz, the changes in Jz and Ez from values before the GCR flux change, are plotted against latitude for longitude 72.5° E. The effect of changes in surface altitude (orography) and thus in nearsurface resistivity with latitude and longitude cause the departures from symmetry about the equator. The effects are especially important for Ez that is proportional to the altitude dependent near-surface resistivity. ...The effects of aerosols on chemistry and climate are sensitive to particle size and concentration, which are influenced significantly by nucleation processes that are not well understood” (Tinsley, Yu, 2004).

According Stevancevic (2004), SW penetrations prevail above belt of 65º magnetosphere latitude, characterized by highly energetic protons but also the particles of relatively heavier chemical elements. According this author, the process of reconnection is not any rarity, to what relatively small deviation point of both vertical profile of current density and vertical electric field. “Perhaps most surprising is that 8 May 2004 was just relatively a normal day for the Earth’s magnetic field. There were no large magnetic storms on Earth, or spectacular aurorae to fill the night sky. However, Cluster and Double Star revealed that energetic particles from the Sun were blasting their way through the Earth’s magnetic shield and penetrating the Earth’s environment”.

(http://www.esa.int/esaSC/SEM5ZTKKKSE_index_0.html). Contrary to the pole itself, as it may be seen from the previous figure, deviations to 65º

reduce. In the area around geographic, that is magnetosphere equator, SW penetrations are mainly connected with particles of less weight, but higher velocity, which first of all may be seen through relatively stable values of the vertical current density.

1 Jz = vertical current density, Ez = vertical electric fields


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Time will certainly tell how much the hypothesis of the previously mentioned author is correct. However, it is evident that at certain moments the hypothesis offers possible explanations making a step forward far ahead of the current suppositions in science. “Previous satellite observations have found that, during this late stage, the flows of plasma (a gas of charged particles populating Earth’s magnetosphere) in the magnetotail exhibit a reversal in direction. In recent years it was generally thought that a flow reversal region is where magnetic reconnection takes place, that is where the energy of the magnetic field is converted into particle energy (dissipation effect), resulting in high-speed plasma flows that hurl towards Earth, like space tsunamis”

(http://www.esa.int/esaSC/SEMZMD7DWZE_index_0.html).

5. Case Analysis-Fires in Portugal on 24.08.2005

During July and August of 2005, more than 270, 000 ha of forest burned in Portugal. In these two months fires burned in 81% (273216 ha) of the total burned area from that year (http://www.fire.uni-freiburg.de/programmes/eu-comission/EU-Forest-Fires-in-Europe-2005.pdf). Assuming that in tropical zone, due to geomagnetic anomaly i.e. weak geomagnetic field over the Atlantic (as well as over the Pacific and Indian Ocean), reconnection does not have to exist but under the strong SW it comes to a direct penetration of the SW into lower layers of atmosphere (figure 24).

Figure 24. Map of region where the UOSAT spacecraft showed memory upsets, superimposed on a magnetic field strength map. The projection is not the same, but is comparable in the South Atlantic region, where the intensity of the energetic particles is high and the field strength is low (http://space.rice.edu/IMAGE/livefrom/sunearth.html)

In the context of strengthening the Solar activity Lockwood (1999) talked about, parallel comes the weakening of the Earth’s magnetic field for about 10% in the last 150 years. “Over the southern Atlantic Ocean, a continued weakening of the magnetic field has diminished the shielding effect it has locally in protecting the Earth from the natural radiation that bombards our planet from space”


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(http://www.space.com/scienceastronomy/earth_magnetic_031212.html)2. This problem certainly deserves more space, but for this occasion it will be prepared in

the context of the SW penetration through geomagnetic anomaly (figure 25). Let us assume that penetration of the SW is followed by air mass influence in tropical

zone due to kinetic energy effect. Clearly defined parameterization for proving such assumption was not established, although it seems that vast quantity of energy necessary for breaking through magnetosphere still exists, not only in the extreme conditions, enabling the particles breaking through the surface. “The magnetic field in the solar wind near Earth is about 5 nT, or 5 x 10-5 Gauss. The magnetic field on the surface of the Earth is about 0.5 Gauss”.

(http://helios.gsfc.nasa.gov/physicist.html). If such assumptions do exist during ‘weaker’ interplanetary magnetic fronts, we may ask

why not they also occur during stronger ones. “Solar flares are known to contain as much as 1029 joules of energy and can accelerate electrons and protons to energies of many MeV and even hundreds of MeV at times. …These coronal mass ejection ...events, as they propagate away from the sun, are also capable of accelerating interplanetary particles to higher energies - perhaps many tens of MeV. The relationship of these CME events to solar phenomena such as sunspots and flares is not yet well understood. However, CMEs are now known to be important sources of disturbances of the interplanetary medium and of the space environment of Earth, even during years of low sunspot conditions. …Space weather influence on the Earth's weather and climate is still a developing topic” (Marhavilas et al. 2004).

-Bz - of interplanetary magnetic field

+Bz – of interplanetary magnetic field

Location of the strongest defense

Location of the weakest

magnetic field

Figure 25. The schematic review of the SW particle penetration into the Earth’s magnetosphere (Stevancevic, 2006)

2 Andrew Bridges, 2003


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Therefore, the idea on the magnetic Earth’s shield penetration is not new. Absence of model that could explain this does not mean something similar is really occurring. “However, space storms, which can dump 1,000 billion watts - more than America's total electric generating capacity - into the Earth's magnetic field, indicated that the shield was not impenetrable” (http://www.nasa.gov/centers/goddard/news/topstory/2003/1203image_cluster.html).

Since the beginning of this century the papers written on this theme have at least been considered as insignificant. "Like the first meteorologists with a small number of measuring stations, we had an incomplete and at times misleading view of the magnetosphere before IMAGE, because we couldn't see the big picture.32 The night-side region of the magnetosphere, which is stretched out by the solar wind, sometimes snaps back and shoots plasma violently toward Earth. The plasma becomes heated to several hundred million degrees and whirls around Earth in multi-million-amp currents. IMAGE discovered that such plasma occasionally is most dense on the Earth's day side, which was unexpected. Researchers are currently studying the phenomenon”.

(http://science.nasa.gov/headlines/y2001/ast25jan_1.htm). The initial parameters for determining the quantitative values of electric convectional

current of the SW particles, getting into the upper layers of troposphere (approximately 150mb) relate to the fact that the SW structure consists of particles of different electric load, different density per volume unit and different velocity and temperature. Total density of the convectional current of the SW particles may be defined by relation:

J = N1e1v1 + N2e2v2 + …Nn en vn N is the number of the SW particles which bear free electric loads per volume unit, e-

single electric load of particles, and V- velocity of SW. Kinetic energy of the SW and altitude of the penetration through magnetosphere define to

what magnetosphere i.e. geographic latitude SW particles will get through. By declining of the kinetic energy and due to effect of gravitational force, the SW moves spirally towards the Earth’s surface. In case when the speed of SW v is perpendicular (at the right angle) to the vector of induction B of Earth’s magnetic field, then electromagnetic force acting upon particles of SW is:

F = q v x B q refers to free electric loads. The relation shows the electromagnetic force is trying to bend the trajectory of the

particles. If r is momentary radius of the bend trajectory of the particles, we see that: mv2/r = qvB

32 Thomas Moore


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The circle motion of the SW particles is possible only in tropical region where the magnetic field is weak and when the vector of the speed is perpendicular to the lines of the geomagnetic field. However, on locations of the weakest magnetic field, as the central zone of geomagnetic anomaly is (and its direct closeness) the conditions for the formation of the cyclogenesis should not exist. The reason lies in the opposite directions of the magnetic field’s vector circulation in north and south hemisphere (figure 26).

Geomagnetic equator

5° south magnetospheric

latitude

+ 5° north magnetosperic

latitude В

В

Figure 26. Schematic review of the magnetic field’s vector circulation around geomagnetic equator (Stevancevic, 2006)

Other scientists have also noticed there are unclear details on the mechanism of the SW penetration as well as the parameterization of losses in speed, temperature and chemical structure of the particles. “The associated changes in the Brewer–Dobson circulation have a non-local effect on the thermal structure in the lower tropical stratosphere leading to significant solar signals in e.g. temperature, cloud cover, precipitation in the tropical troposphere. …It must however be noted that many questions concerning the impact of solar variability on the atmosphere are still open. E.g. the observed solar signal in stratospheric ozone can so far not be reproduced by models. The contribution of energetic particles to the solar signal is not yet well understood” (Langematz et al., 2005).

Most frequently occurs that the vector of the speed v of the SW particles makes some angle θ with the vector of induction B. When we separate the speed v of the SW particles into one component which is in the direction of the field, v cos θ and the component perpendicular to the direction of the magnetic field of Earth, v sin θ, the result will be that the trajectory of the SW particles is helix (spiral), where the radius r is:

r = mv sin θ/qB

while the step of the helix (spiral) is: d = 2π r/vsinθ x vcosθ = 2πm vcosθ/qB The speed of the SW particles is: v = rqB/m sin θ


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while the speed of wind in atmosphere, namely, air masses influenced by the SW particles is: v = (rqB/m sin θ)ή

where ή refers to the degree of sliding (Radovanovic, Stevancevic et al., 2003 a, Radovanovic, Stevancevic et al., 2003 b, Stevancevic et al., 2006).

Due to simultaneous effect of the gravitational force and magnetic field, the air mass trajectory, as we already mentioned, should be getting a form of the spiral. With deeper penetration in atmosphere, the speed of the particles v reduces because of friction, and thus the radius of the spiral r also reduces.

When SW enters the atmosphere, ionized atoms which are in the structure of the SW are being carried in. Due to mutual effect between electronic shell and newly formed ions the electrostatic pressure increases, having direction opposite the gravitational force. Electrostatic pressure pulls air masses and reduces the total atmospheric pressure (figure 27).

Then the total pressure in A point is: PА = P + Pe + Msv

where P is the mass of air, Pe is electrostatic pressure in point A, while Msv is the mass of the SW particles. With deeper and deeper penetration into atmosphere the number of ionized atoms increases, electrostatic pressure increases, while atmospheric pressure decreases in point B. Thus, Pa > Pb, while the angle of the SW penetration determines the gradient of pressure i.e. higher angle- larger gradient. Distribution of air mass velocities under the SW jet points that the highest velocities are near jet. It means that in such conditions the speed of wind does not depend from the air pressure, but from friction between air masses and SW. If air pressure in such situation caused the speed of motion, than the speed of wind would be the highest at the surface of Earth, because it was the place of the largest gradient. The mentioned motion is the consequence of hydrodynamic effect of the SW.

According Stevancevic (2006), the SW particles are moving through jet (tube) which is limited by magnetic walls (figure 29).

If we assume the current of the SW particles is homogeneous in the jet of radius a, then the lines of the magnetic field lie at surfaces which are perpendicular to the axis of the jet. Within the jet, the intensity of the magnetic induction B increases linear with the distance from the axis of the jet and it is equal to current J which penetrates through the observed contour when r ‹ a, where

B = µo2rI

µo refers to porosity of the vacuum (1.2566 x 10-6 Hm-1), I - current intensity, a- the

radius of the tube, r- an arbitrary distance from the center of the tube.


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Electronic belt

Point А Earth Point В

Pe (A) Pe (B)

Pa (A)

Pa (B) Earth’s wind

SW jet

Vertical streams

Figure 41. Schematic penetration of the solar wind (SW) jet into the atmosphere, entering in point A and proceeding to Point B. Pe refers to the electrons flow current and Pa to the particles flow current (Stevancevic, 2006)

Figure 29. Schematic review of the SW jet (tube) which penetrates through atmosphere (Stevancevic, 2006)

By the circulation of the vector of magnetic induction the magnetic wall is being formed around the jet not allowing dispersion. Applying the Ampere’s law on the circle contour, the diameter of which is r › a, the result will be:

∫c

d = B 2πr = µoI

Magnetic wall of tube

Direction of the vector circulation of the magnetic field tube

a


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where B = µo rπ2

I

On the basis of the above, the intensity of the magnetic induction B out of jet is inversely proportional to the distance of the radius of the circle contour from the axis of the jet.

We may see from the previous figure that the low wind was carrying smoke towards west, i.e. towards the Atlantic. The linear cluster of fires suggests the connection of air mass motions in the figure 33. Therefore, it is important to emphasize two moments. The first moment relates the fire spreading in the south-north direction, i.e. in the direction of air mass blowing, from above to downward. The second one, which is also important, is that the low winds (according smoky plumes) blew in the east-west direction. According the hypothesis Stevancevic has given, the SW jet which penetrates through atmosphere is always characterized by spiral circulation of the magnetic fields around main axis of the penetration (similar to the motion of a drill).

Figure 30. Satellite recording of fires in Portugal on 24. 08. 2005 (http://earthobservatory.nasa.gov/NaturalHazards/Archive/Aug2005/Portugal_fires.TMOA2005234_lrg.jpg)


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In other words, air masses, attacked by the hydrodynamic pressure of the SW, are moving from above to downward, from the south to north direction. Due to vortex sinking, in lower layers also comes to air motion approximately in the east-west direction. It would have been logical to expect the wind was blowing the flame around from Spain, namely from Portugal if regionally dominant direction of air flow had been from east to west, or vice versa, what did not happen in this case.

As in other cases from the table 11, this time also the energetic region was in the geo effective position on the Sun, as well as coronary hole (figure 31). At that time over the north western bank of Africa, in the upper layers of troposphere, winds were blowing having the speed of over 50 m/s (figure 32). The isolines clearly show the motion of air masses of the highest speeds is directed toward the Pyrenees Peninsula (Gomes, Radovanovic, 2008). Spiral motion proofs the direction of penetration toward lower layers by the principle of the left spiral (figure 33).

Figure 31. Image of the Sun a few days before fires started to ignite in Portugal (http://www.dxlc.com/solar/index.html)


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Figure 32. Wind Shear in the 150-300 mb layer mean minus 700-925 mb layer mean (http://cimss.ssec.wisc.edu/tropic/real-time/europe/winds/wm7shr.html)

Figure 33. Satellite recording of the air masses breakthrough over West Europe on 24. 08. 2005 (http://www.sat.dundee.ac.uk/pdus.html)


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Figure 34. Sudden rises in protons in all energetic ranges at the beginning of 22nd.08.2005 (http://umtof.umd.edu/pm/crn/CRN_1996.GIF)

Table 8. The number of protons of certain energies a few days before and after the fires phenomena in Portugal (http://umtof.umd.edu/pm/crn/)

(protons/cm 2-day-sr)

Date >1 MeV >10 MeV >100 MeV 2005 08 20 1.1e+06 1.6e+04 4.0e+03 2005 08 21 1.1e+06 1.6e+04 4.3e+03 2005 08 22 1.0e+07 7.2e+05 4.8e+03 2005 08 23 1.4e+08 1.7e+07 1.1e+04 2005 08 24 2.6e+08 5.1e+06 4.8e+03 2005 08 25 3.2e+07 2.9e+05 3.2e+03 2005 08 26 2.7e+06 4.6e+04 3.6e+03 2005 08 27 2.3e+06 2.2e+04 3.3e+03

After decrease of the kinetic energy the jet stream of the SW particles descends towards

the Earth’s surface under the effect of the gravitational force and the laws of the magnetic fields. The spiral in a form of funnel is the trajectory of the descending, the wider end of which is turned upward.

Two days before forest fires in Portugal it had come to a sudden influx of the highly energetic particles from the Sun (figure 34).

On the basis of the table 8 we may see the number of the highly energetic particles per volume unit has increased in all energetic ranges to 23rd. i.e. 24th.08. After that, the values were declining, but they still have had higher values than before the fires. Such data are in keeping with the information of Natural Hazards >> Fires >>: “Drought-ravaged forests in Portugal continued to burn in the fourth week of August 2005. Wildfires were burning out of


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control in several locations, and the government had declared a state of emergency in the central part of the country.”

Analysis of synoptic situation and meteorological parameters showed that before 24th. 08 was a relatively longer period of dry, sunny and very warm weather. During the warmest days maximum temperatures were exceeding 40 degrees (www.weatheronline.com). The Iberian Peninsula was influenced by Azorean anticyclone of clear weather (http://wetterzentrale.de/ topkarten). The last breakthrough of fresh and cold air with clouds and precipitation was recorded in the period from 08th to 10th August, while considerably weaker breakthrough without precipitation was around 18th August. From 20th-24th August the relative humidity was very low (about 30%), while satellite recordings (figure 33) have shown there were no clouds, i.e. little humid content was in the troposphere over Portugal. From 23rd-25th August in the area over Iceland, the existing cyclone circulation intensified, what was most probably the indication of the proton particle penetration into lower layers of troposphere. The Iberian Peninsula was on the southern side of the cyclone, in warm sector with dominant western and southwestern flow. The cyclone was intensifying and cold atmospheric front were coming closer the Iberian Peninsula. We get a conviction that under those conditions the SW also penetrated the atmospheric layers deficient in moisture into lower layers of atmosphere from southwest, while a part of highly energetic particles just ‘dispersed’ over Portugal.

Lucio (2005) pointed to the connection between interplanetary magnetic fields and development of weather conditions in Portugal: „Hence, in this work we evaluate the existence of empirical evidence to support the hypothesis that solar variability is linked to the Earth’s climate through regional-scale temperature and precipitation stochastic processes. One possible linkage to climate change is the sun’s influence over the local flux of galactic cosmic rays via the fact that as the solar magnetic field gets stronger; fewer cosmic rays are able to penetrate to the inner solar system and Earth. Because the galactic cosmic rays contribute for ionizer air molecules in the lower atmosphere, they might play a role in processes like cloud formation.”

However, on September 15th the same year the proton’s velocities again exceeded the measuring abilities of instruments (http://umtof.umd.edu/pm/crn/CRN_2034.GIF). Fires were seizing again the northern part of Portugal (figures 35 to 37).

Figure 35. Forest fires in the village of Agua de Alto, near Agueda, northern Portugal, 18.09.2005 (http://www.sltrib.com/utah/ci_4096129#top)


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Researching the links between processes on the Sun and physical-geographic processes on Earth, on the basis of available literature, seems more and more to be directed toward synchronized phenomenon of the SW and geomagnetic disturbances. Palamara and Bryant (2004) have concluded similarly: “Therefore, we conclude that geomagnetic activity plays an important role in recent climate change, but that the mechanism behind this relationship needs further clarification.”

Figure 36. As in other analyzed cases, geomagnetic disturbances had preceded fires (small red columns in the lower part of the figure). Just at the end of 15.09. the values of proton flux has descended on the level of normal state (upper part of the figure) (http://www.sec.noaa.gov/rt_plots/satenv.html)

Figure 37. Sudden rise in proton energy of all ranges was arriving toward Earth at the end of 13.09.2005 (http://umtof.umd.edu/pm/crn/CRN_1996.GIF)


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6. Fires in Central and South Europe from 24th-26th03.2003: Case Analysis

The development of the idea on the SW penetration over geographic poles will be briefly presented. “In 1961, J. Dungey predicted that cracks might form in the magnetic shield when the SW contained a magnetic field that was oriented in the opposite direction to a portion of the Earth's field. In these regions, the two magnetic fields would interconnect through a process known as "magnetic reconnection," forming a crack in the shield through which the electrically charged particles of the SW could flow. In 1979, G. Paschmann detected the cracks using the ISEE spacecraft. However, since this spacecraft only briefly passed through the cracks during its orbit, it was unknown if the cracks were temporary features or if they were stable for long periods. In the new observations, the IMAGE satellite revealed an area almost the size of California in the arctic upper atmosphere (ionosphere) where a 75-megawatt "proton" aurora flared for hours (figure 38). This aurora, energetic enough to power 75000 homes, was different from the visible aurora known as the Northern and Southern lights. It was generated by heavy particles (ions) hitting the upper atmosphere and causing it to emit ultraviolet light, which is invisible to the human eye but detectable by the Far Ultraviolet Imager on IMAGE”

(http://www.nasa.gov/centers/goddard/news/topstory/2003/1203image_cluster.html).

Figure 38. Sudden hit of SW into upper layers of atmosphere may cause the phenomenon of shining ring (http://www.nasa.gov/centers/goddard/news/topstory/2003/1203 image_cluster.html)

The following results confirm Stevancevic’s assumption (2004, 2006) that after the SW penetration through magnetosphere, the particles may seize air masses by their spiral motion: “A dynamical link between the solar irradiance and the stratospheric polar vortex has been attributed to an interaction between ultraviolet radiation and the ozone in the stratosphere” (Balachandran et al., 1999). According Black (2002) the results are in keeping with the view where potential anomalies of vortex in the lower part of the stratosphere, associated with changes in strength of stratospheric polar whirlpool (vortex), are causing zonal symmetric wind disturbances, spreading down toward the surface.


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Figure 39. Continuing reconnection occurred on 17/18.09.2000. Aurora was observed in the period from 01:00-10:00 on 18.09.2000 when instruments registered the disturbance (Frey et al., 2003)

Thoughts on the SW penetration into Earth’s magnetosphere have been considered as unfounded recently. But the views have definitely changed since 2003. “Relying on observations collected by NASA's Polar spacecraft and Japan's Geotail spacecraft, scientists associated with the International Solar-Terrestrial Physics (ISTP) program have gathered the first direct evidence that a process known as magnetic reconnection occurs naturally in the Sun-Earth system. Until now, reconnection had only been observed under contrived conditions in a few physics laboratories. During reconnection, magnetic fields that are heading in opposite directions - having opposite north or south polarities - break and connect to each other. …Reconnection is the fundamental process for transferring and exchanging energy in the Sun-Earth system3” (www.nassa.gov 2003). Therefore, not only the described process is contested, but it gains more on its importance. “Magnetic reconnection – a phenomenon by which magnetic fields lines get interconnected and reconfigure themselves - is a universal process in space that plays a key role in various astrophysical phenomena such as star formation, solar explosions or the entry of solar material within the Earth's environment” (http://www.esa.int/esaCP/SEMDI3T4LZE_index_0.html).

In extreme cases, as showed in the previous two figures, almost the whole ring of about 65° represents input, through which electromagnetic waves penetrate (Radovanovic et al., 2003 a, Radovanovic et al., 2003 b, Stevancevic, 2004). Polar light phenomenon usually follows such manifestations. "We've observed high-altitude auroras during all of the coronal

3 A. Nishida


55

mass ejection events that engulfed Earth since the instrument became operational ...But we still don't understand the process that is causing them" (ucsdnews.ucsd.edu/newsrel/science/mcsun.htm). Lilensten and Bornel (2006) emphasize certain unknowns in a domain of parameterization of the origin of the polar light mechanism: “From space, satellites can see a luminous oval that is brighter on the night side since the particles are accelerated when they pass through the neutral layer (in what way is still not known) and produce more brutal collisions. Mechanism that would explain the penetrations of highly energetic particles through atmosphere in polar areas was also the research subject of Galand (2001). “Using a coupled electron/proton transport code to analyze the data they show that the unusual low-altitude peak of thе red emission observed from ground is produced entirely by proton precipitation, the major particle energy source around the time period and in the region of the strong red aurora. ...In addition, Patterson et al. еxplain how such observations can be used to infer the effective ion-electron recombination coefficients in the ionosphere, coefficients whose values are subject to large uncertainties. ...Our abiltiy to accurately model the proton aurora is now mainly limited by the uncertainties in the input data (Basu et al.): cross sections, phase function, atmospheric neutral model, and characteristics of the incident proton flux. As consequence, proton modeling relies strongly on future laboratory experiment and in situ observations.“ Chisham (2005) states similar views: “The measurement of magnetic reconnection requires: a) detecting regions of different magnetic connectivity and b) measuring the transport of magnetic flux between them. ...However, methods of detection of this spectral width boundary (SWB) and an understanding of how the boundary relates to the open-close boundary have a history of confusion with conflicting conclusions drawn in different studies.”

As from the case of Portugal, the hypothesis bases on the view that by penetration into lower layers the SW moves air masses by hydrodynamic pressure and thus it may cause the disturbances in the lower layers of troposphere. The recent researches show that in case when Bz component of IMF has direction opposite to the geomagnetic field, namely, when it has got a negative sign, the magnetosphere opens (magnetic reconnection). Then the SW particles enter the Earth’s atmosphere (magnetospheric door) in the form of a jet stream and advance along geomagnetic lines to the magnetosphere equator. Therefore, the process is occurring in the area where Earth’s magnetic field is the strongest (figure 40). Otherwise, the SW does not penetrate through Earth’s magnetosphere but passes i.e., it rejects from it. “We found that the events occurring during closed geomagnetic conditions do not show common peaks at all the high latitude stations and tend to be coherent only among Antarctic stations, while there is a lack of coherence between high latitude opposite hemispheres. Conversely, during open geomagnetic conditions the pulsation events are characterized by discrete frequencies, the same at all stations, and are generally highly coherent between high and low latitudes and between opposite hemispheres” (Lepidi et al., 2005).

The strongest and weakest magnetic fields of Earth may be seen in the figure. The areas of the reconnection even under weaker SW penetrations are over Canada and Siberia, while under the influence of the kinetic energy of the SW the penetrations occur over the western Atlantic, central parts of the Pacific and south from Australia.


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Figure 40. Earth’s magnetic field intensity (Mc Lean et al., 2004)

The position of the opening of the magnetospheric door greatly depends on the moving of the geomagnetic poles, for it is clear the magnetosphere coordinates (including also geomagnetic anomalies) link magnetic poles, and not geographic ones (figure 41). This is an essential factor about, the studying of which should represent the integral part of the prognostic models.

Kinetic energy of the SW determines to which geomagnetic latitude the particles will arrive. The input angle also plays an important role under such motions, so that under certain conditions polar light may appear (although much rarely) in lower geographic latitudes (figure 42).

When the strongest flares on the Sun ab. 12) appeared, the polar light also appeared over south part of the USA. “During the past two weeks, number 486 and two other large sunspots set off nine other major flares. It was one of the stormiest periods of activity ever witnessed, all experts agree. The number of intense flares, some shooting out within a day of another, was unprecedented. Auroras were seen as far south as Texas and Florida. The second strongest flare in this historic two-week series was an X17 event on Oct. 28. It was aimed at Earth and generated severe geomagnetic storming when it blew past the planet less than 24 hours later”.

(http://www.space.com/scienceastronomy/xtreme_flare_031105.html). Connection of the SW penetrations in lower layers of troposphere and change in the

development of the synoptic situation was also noticed in the area of Antarctica. “One can see that increase in the ground temperature is determined by power of the negative BZ action: the longer BZS field exposure (and the higher electric field intensity) the more is the temperature


57

deviation and shorter is time delay between the key moment and the temperature change: at stations Vostok and Dome C the 15-hours exposure affects the effective warming (up to DT= +20) after >>12 hours at level of statistical significance 0.99” (Troshichev et al., 2005).

Figure 41. North magnetic pole from 1900-2005 (http://www.mrinbetween.com/thirdparty/pdf/N_magpl.PDF)

Figure 42. Recording of aurora over Athens4 (http://www.the-eggs.org/articles.php?issueSel=18)

4 A. Ayiomamitis


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Van Geel et al. (1999) also pointed to the link of highly energetic particles and ozone: “Shumilov et al. (1992, 1995), Stephenson and Scourfield (1992) and Kodama et al. (1992) showed that solar proton events (known as SPE), which generate the solar cosmic rays, may produce ozone ‘mini-holes’ at the high latitudes (the decrease of the total ozone content is about 10-15%) and these are accompanied by a decrease of the temperature in the stratosphere of 2.4°C.” However, contrary to the previous quotation there is an opinion that under certain conditions, the SW, by entering the upper layers of the atmosphere, extrudes electrons from atoms of air due to high speed and makes large electric charges, which increase ozone concentration. Thus, the highest ozone density determines the place of the SW input into upper layers of the atmosphere (Stevancevic, 2004) (figure 43). One of the basic conclusions from the 20th Quadrennial Ozone Symposium, held from 01st-08th June 2004 in Greece was: “We have still a long way to go to understand the complex system of interactions between ozone and a globally changing environment and the best tools we have at present are the continuation of global quality observations both from ground and from space” (http://www.the-eggs.org/articles.php?id=54#).

In any case, figure 43 also points to time sequence of occurrences. Therefore, similar situation on the Sun had preceded the increased concentration of ozone over North Pole. Before the reconnection occurred, a sudden proton rise had been noticed in all energetic ranges. Three days after that (24.03.2003) many fires occurred in the area of south Baltic and Poland (figure 44). In Southeastern Europe, two days later, forest fires were recorded in about ten states, also including the south of Italy (figure 45). Chronologically viewed, the wildfire was moving from north to south, namely, toward the Balkans and south of Italy.

Figure 43. Opening of magnetospheric door on 21.03.2003 three days before fires in the southern part of the Baltic coast (http://www.cpc.ncep.noaa.gov/products/stratosphere/sbuv2to/gif_files/sbuv16_nh_latest.gif)


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The analysis of the synoptic situation and meteorological parameters from March 2003., has shown that to 15th March cyclone circulation of the frequent cold and wet air breakthrough was prevailing, causing cloudiness and precipitation in the area of the Baltic and Poland. Maximum air temperature was from 0 to 10 degrees (www.weatheronline.com). After that, the cyclone circulation was getting weaker and in lower layers from the Central Europe toward that area the anticyclone was spreading and strengthening (http://wetterzentrale.de/topkarten). Such synoptic situation caused stable and clear weather from 20th March. Then it comes to the influence of strong circulation from the northern Atlantic. From 22 to 24.03 in the area of the Baltic and Poland the breakthrough of warm air is starting and warm sector of cyclones with clear weather is being formed. Relative humidity was the lowest those days (45%), while the sky was without clouds. It is possible the part of the highly energetic particles penetrated to the surface in the area of clearness in warm sector of the cyclone under simultaneous regeneration and development of the cyclone in the north of the Atlantic, what may be explained by the SW penetration to the lower layers of atmosphere. Veretenenko, Thejll (2004) wrote on the similar developments of the weather conditions: “The most pronounced effects of energetic solar proton events were observed near the south-eastern Grenland coast which is the North Atlantic part of the arctic front and a cyclogenetic area. The energetic solar proton events are accompanied by the intensification of re-deepening (regeneration) of well-developed cold cyclones in this region.”

Figure 44. Satellite recording of numerous fires on the south banks of the Baltic Sea on 24.03.2003. http://earthobservatory.nasa.gov/NaturalHazards/Archive/Mar2003/NEEurope.AMOA2003083_lrg.jpg

We call readers’ attention to the previous figure, where it may seem the number of burning localities is relatively small. Those are small red spots (hot spot), which are really far


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more than it may seem at first sight. The visual effect will certainly be much larger if the recording is additionally enlarged.

We get an impression the most sensitive part of the hypothesis is exactly the part on the contact of the highly energetic particles on the molecular level with plant mass. The particle distribution is in the direct dependence from the characteristics of the SW which is moving to the surface. In Stevancevic’s (2006) opinion, in every concrete situation under penetration through atmosphere, the SW jet is dispersing in several smaller sheaves, due to increase of the geomagnetic induction B and the reduction of the radius of circulation of the SW particles in keeping with relation

r = mV/qB The radius of the SW movement is proportional to mass m and velocity V, and inversely

proportional to electric charge of particles q and the value of magnetic induction B. We unavoidably need experimental laboratory researches that would confirm or refute

the assumption that e.g. protons or neutrons, under certain conditions, may burn through plant mass.

Table 9. Number of protons of certain energies a few days before and after fires in Eastern and Southern Europe (http://umtof.umd.edu/pm/crn/)

(protons/cm 2-day-sr)

Date >1 MeV >10 MeV >100 MeV 2003 03 19 2.8e+06 1.5e+04 2.4e+03 2003 03 20 3.4e+06 1.2e+04 2.1e+03 2003 03 21 7.0e+06 1.1e+04 2.4e+03 2003 03 22 8.4e+05 1.2e+04 2.7e+03 2003 03 23 5.5e+06 1.2e+04 2.7e+03 2003 03 24 8.0e+05 1.2e+04 2.8e+03 2003 03 25 1.4e+06 1.2e+04 2.7e+03 2003 03 26 9.7e+05 1.2e+04 2.6e+03 2003 03 27 4.2e+05 1.1e+04 2.6e+03 2003 03 28 4.5e+05 1.1e+04 2.6e+03

According to table 4 the density of the highly energetic particles of the SW had very high

values on days when many fires were noted (namely, one day earlier), after what their number per unit surface gradually decreases.

Contrary to extreme situations, in this case the proton velocity was not exceeding the measuring abilities of instruments (figure 46). However, the limit considered as ‘normal value’ i.e. 500 km/s (a broken line in the upper part of the figure) was surpassed on days when fires burned. In order not to make any confusion, figure 46 was recorded on 26.03, when the proton velocity had been declining. As already mentioned the satellite recordings may be taken only when fire is in its developed phase, and the moment of the ignition, by the rule occurs one day earlier.


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Figure 45. Many fires on 26.03.2003. were spreading from Italy over the Balkans, Hungary, Romania, Ukraine, Slovakia and Poland (http://earthobservatory.nasa.gov/NaturalHazards/natural_hazards_v2.php3?img_id=8620)

Figure 46. Proton velocities were exceeding values of 500 km/s from 20th to 24th03.2003. (http://umtof.umd.edu/pm/crn/)


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7. The Possibility of Prognostic Modeling

Respecting recent results in the research field of the interactive Sun-Earth link, the contemporary science seem to be burdened by many questions. No matter how much the period we live in seem progressive and successful in many areas of the scientific creativity, it is necessary to emphasize that according official data the causes of about 40% of the fires in Europe were not determined. The initial base for considering this question is the possible influence of the processes on the Sun upon Earth’s biosphere. However, renowned scientists such as Lilensten and Bornarel (2006) have emphasized that: “For instance, we are partly capable of describing the solar magnetic field but quite incapable of predicting it, with its various irregularities and, in particular, the triggering of coronal mass ejections. The same can be said of the photon flux and of life on the Earth, in particular in the ultraviolet and X-rays. In the interplanetary medium, we cannot quantify the dynamic pressure of the solar wind or the frozen interplanetary magnetic field found there. Consequently, it is as yet impossible to determine in advance the position of the magnetic shield formed by the magnetopause: is it on this side or the other of the orbit of geostationary satellites? The characteristics of the radiation belts are not yet well known either. Furthermore, they also depend on the cosmic radiation of all the other stars that also have to be kept under surveillance. The phenomena which enable solar particles to enter the magnetosphere are still not understood: the aperture on the day side when the solar magnetic field reverses is only a model, a theory which stands up better then others to the facts. Our knowledge concerning the porosity of the magnetospheric wall of or the collisions in the reconnection zone on the night side is relatively poor, for lack of observations.”

The problem is also the stochastic phenomenon of energetic regions on the Sun, as well as extremely strong flares, what is impossible to predict for now. “It is still unclear which of the various possible nonlinear quenching mechanisms is of primary importance to the solar dynamo” (Bushby, Mason, 2004). Veselovsky (2005) thought similarly: “At present, with no diagnostics of subphotospheric processes and very poor knowledge of the solar interior dynamics, one can say that SEEs5 are practically not predictable.” Let us mention Eredelyi (2004): “What is the source of plasma heating in the solar (and stellar) atmosphere? How do perturbations dissipate efficiently, resulting in hot plasmas? The latest results of theoretical and observational studies provide some answers, but there remains much to be learned.” The confusions from this domain may be seen from many statements. “Even after more than a decade of spacecraft observations of magnetospheric plasma waves, we understand very little about how they are generated”

(http://ssdoo.gsfc.nasa.gov/education/lectures/magnetosphere/index.html). But as in the case of determining the link between solar activity and meteorological

conditions, the cosmic radiation additionally complicates such sort of the research. “Cosmic rays are different—and worse. Cosmic rays are super-charged subatomic particles coming mainly from outside our solar system. Sources include exploding stars, black holes and other characters that dwarf the sun in violence. Unlike solar protons, which are relatively easy to stop with materials such as aluminum or plastic, cosmic rays cannot be completely stopped by any known shielding technology” (http://science.nasa.gov/headlines/y2005/07oct_afraid.htm).


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On the basis of available literature, we get an impression that cosmic radiation has also its pulsations, namely, it is not constant. It is noticed that when the Sun is more active, the electromagnetic waves coming out of the solar system penetrate harder towards Earth and vice versa. However, sometimes in spite of intensified solar activity, at certain moments the striking fronts of the cosmic particles still arrive to us. The penetrations of such radiation may be the significant problem for the operation of the satellite instruments, but also for the estimate of the SW entering into atmosphere. Energies from the Space are traveling in a form of cloud of particles of high electric charges that may reach 450 million electron volts. Electric charge of the SW particles rarely reaches 100 million of electron volts. It seems unnecessary to emphasize that in this segment we are not even closer to the representative enough data base upon which statistics could show any trends on the global level.

Except noticing the signals on the connection of the forest fires and processes on the Sun, the crucial importance of the acquired results relates to the basic directives with an aim to make prognostic models.

Following the rotation speeds of the coronary holes and active regions on the Sun, by the estimate of appearing in geo effective position and on the basis of data on the magnetic field, structure and strength of the ejected energy which is coming toward Earth in the form of IMF (Figure 60), it is possible to prognosticate place and time of the jet stream enter into magnetosphere, its approximate moving toward atmosphere and influence on meteorological phenomena (atmospheric fronts, cyclones, cloudiness etc.) (Radovanovic, Stevancevic et al., 2005). Having in mind that according heliocentric hypothesis, the SW jet when in contact with Earth’s magnetosphere splits into several smaller sheaves, great problem is the positioning of the locations on Earth whereto they are going to influence. “The solar electromagnetic radiation varies the least at visible wavelengths (the regime that most directly affects weather and climate) …The charged particles that carry a portion of the Sun's energy include both the relatively low-energy plasma of the solar wind and high-energy particles, such as solar energetic protons, which have been accelerated to velocities near the speed of light. The solar wind varies both recurrently, as a function of the Sun's 27-day rotational period, and sporadically, in response to violent eruptive events in the corona, which also accelerate energetic particles to near-relativistic velocities”

(http://umbra.nascom.nasa.gov/spd/secr/). From the previous figure we clearly see that electromagnetic waves from the Sun do not

spread linearly, but their path is twisted. Nevertheless, mathematical parameterization of the IMF movements is caused by moss, meaning that any calculation is possible only after observed preliminary elements on the Sun. In that sense Neugebauer et al. (2000) have given some indications: “It might be explained as evidence for some sort of internal structure (such as an irregularity on the core-mantle boundary) or an aspect of the internal dynamo that allows it to "remember" some longitudinal feature in spite of the reversals. Since the interiors of the Sun and stars are so different from the interior of a planet like the Earth, the correspondence is even more puzzling.”

5 Solar extreme events


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Figure 47. Twisted line of the magnetic field in certain situations ‘leads’ the jet of the SW particles to Earth’s magnetosphere (http://www.windows.ucar.edu/tour/link=/sparc/images/imf_big_jpg_image.html)

The recent following of the processes on the Sun has shown there are several sectors of the magnetic fields (Figure 48). Belonging of some energetic regions to a certain sector points to the character of the magnetic fields (alpha, beta, gamma, delta) which, when in geo effective position, direct electromagnetic energy of a ‘certain type’ towards Earth.

Figure 48. Sector distribution of the magnetic fields on the Sun. Black small square at the bottom of the recording represents the Earth, while the circumference in the middle represents the Sun (http://www.lmsal.com/forecast/modelEIT/index.html)


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A scenario that should especially be considered relates to the SW penetrations into areas above geomagnetic equator under the dominant effect of kinetic energy first of all. According Litensten, Bornel (2006) the kinetic pressure of the SW may be:

Pc = ½ n m v 2 = n kB T

n refers to the number of particles per volume unit, m-mass of particles, V-their velocity, Kb Boltzmann’s constant (1.38 x 10-23 JK-1), and T- absolute temperature of the SW. If the estimate includes Archimedes’ spiral, i.e. angle θ between the SW and Earth-Sun axis, then Pe may be:

pSW = 21

cos2 θ nSW v SW2

According previously mentioned authors the magnetic pressure is:

pm = 0

2

2μB

The synoptic situation development depends on the whole series of circumstances.

Following the energetic regions and coronary holes, as the first step it is necessary to define geo effective position which is not static (Melony et al., 2005). According Naitamor (2005): “From all identified events (from January 1997 to September 2004) the geo effective CMEs scattered in latitude (S40, N40) and in longitude (E50, W60). These results also show that 62% events occurred on the west and 38% events in the east. Therefore CMEs which occur in the west part of the sun disk can affect the earth geo magnetosphere.” Width of the ejected jet that is emitted from mentioned sources directly determines whether they are directed towards Earth. The direction of Bz component, velocity, density, temperature, chemical structure, the input angle of the SW into magnetosphere as well as the size of the opening of the magnetospheric door are the initial elements necessary for making the prognostic models. However, it is clear that there is large number of possible combinations, so that at this moment, the defining of the resultant penetration is an extremely complex task.

Baliunas, Soon (2000) emphasized the importance of not only 11 years long but 20 years long magnetic cycle of the closest star to us: “The Sun's changing magnetism has several consequences, some only recently learned. For example, the surprise of the last 20 years is the observed fact that the total light, or brightness, of the Sun also changes in step with the magnetic cycle.” It seems that among others, Stevancevic and collaborators gave in the papers ‘more courageous’ elements to what direction the research methodology should be developed. We assume the new solar cycle is about to start on April 2008 so that soon we should get into a period of calmer activities on the Sun. In other words, we should expect a little lower temperatures and also smaller number of forest fires on Earth. According Cranmer (2002): “At solar minimum, the high-speed wind dominates at high latitudes (greater than ±20–30°) and the low-speed wind coexists at lower latitudes with occasional high-speed streams.” If the link between large forest fires (it is meant on most fires of unknown cause) and strong


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eruptions (also including strong corpuscular radiation from the coronary holes) directed towards Earth proves, the scenarios predicting further increasing of forest fires won’t have basis. Mentioned conclusion relates the period of the first half of the cycle that is in front of us, i.e. approximately to April 2013. Quassim and Attia (2005) have concluded similarly: “According to our prediction, the Gleissberg Cycle have been started its declining phase and it seems to be slower than the increasing phase, i.e. the firing of solar activity is going to its end and it is expected to return to the average level detected through the far cycles 13, 14 and 15. A relative reduction in heating rate is predicted; it will reach its minimum in 2012, next increasing with slow rate, but lesser than the previous rate, is expected. Because of the large contribution of the artificial influence we are still in the critical stage.”

Studying Sun’s spots, Hathaway and Wilson (2006) have come to similar results. According them, entering the second phase of the solar cycle, it is possible to expect an extremely strong solar activity (figure 49). Investigating the link between geomagnetic disturbances and Sun’s spots, it is noticed that: “Cross correlating sunspot number vs. Inter-hour Variability Index (IHV), they found that the IHV predicts the amplitude of the solar cycle 6-plus years in advance with a 94% correlation coefficient. "We don't know why this works"6 …The underlying physics is a mystery. But it does work" (http://science.nasa.gov/headlines/y2006/21dec_cycle24.htm?list53210).

Figure 49. Prediction of the amplitude of the Solar cycle 24 (Hathaway, Wilson, 2006)

However, the importance of the heliocentric hypothesis among others is that, it in the foreground emphasizes only those coronary holes which direct their energy towards us.

6 Hathaway


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Landschiedt (2000 c) has thought similarly: “Moreover, it is quite clear now that all models that back cast the Sun's effect on climate on the basis of sunspot numbers yield misleading results. The number of eruptions does not depend proportionally on the intensity of 11-year sunspot maxima. Cycle 20 with the highest monthly sunspot number R=106 was much weaker than cycle 21 (R=165) and cycle 22 (R=158), but it produced nearly as much flares as cycle 21 and considerably more than cycle 22. You would expect that current cycle 23, which is at the same level as cycle 20 should produce a similar number of flares. Not so. The flare activity is weaker than at any time after the beginning of observations in the thirties. Those who do not take this into account draw conclusions that do not conform to reality.”

Regarding establishing the link with climate interactive connections, the recent researches are in keeping with the results Komitov (2005) has given: “The generalized conclusions about the solar 10-11 and 20-22 year cycles effects over Earth climate are:

1. Quasi 11-year oscillations are observed in many climatic parameters, but mainly in

temperatures. They can to track in climatic data series of separated stations as well as in planetary scale. These cycles are relatively better expressed in winter as in summer and mainly on middle and high geographic latitudes.

2. For the atmospheric circulation the quasy-20-22 year oscillations are typical. As a result from 20-22 year cycle influence over Iceland baric minimum position and activity, the same cyclity in rains and pressure over South –East Europe and particularly –over Bulgaria is observed.”

One of also important segments that should be taken into consideration when making the

prognostic models relates to the weakening of Earth’s magnetic field. “Previous studies have shown that the strength of the Earth's magnetic shield has decreased 10 percent over the past 150 years. During the same period, the north magnetic pole wandered about 685 miles out into the Arctic, according to a new analysis by Stoner. …A major uncertainty, however, has remained regarding how long this process takes” (http://www.space.com/scienceastronomy/earth_poles_040407.html)7.

Studying storms in Britain, Wheeler (2001) relied on general aspects of the procedure Corbyn had used. Those aspects are based on the variations in the Sun’s behavior, its magnetic field, coronary eruptions and fluctuating character of the SW. Therefore, that is the methodology which, as observed on the whole, does not have anything in common with most contemporary prognostic models in use. The result was that in the period from October 1995. to September 1997., four out of five strong storms were correctly prognosticated. The fifth one had the mistake of 48 hours, while such mistake (from the aspect of the methods just about to develop) may be considered as marginal one, simply because the prognosis had been done months earlier. As far as we know, Corbyn did not publish his methods anywhere, because they have been used in commercial purposes.

In that context Landscheidt (2003 a) also made, we may say, significant step forward: “I have shown that ENSO events, the North Atlantic Oscillation (NAO), the Pacific Decadal Oscillation (PDO), extreme in global temperature anomalies, drought in Africa, and European floods are linked to cycles in the sun’s orbital motion around the center of mass of the solar

7 Robert Roy Britt, 2003


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system. So the next extended wet period should begin around 2007 and last about 7 to 8 years …A draught peak, indicated by LPTC …is to be expected from 2025 on and should last about five years.” The same source enclosed the proof the prognosis was done several years in advance: “Dr Theodor Landscheidt claimed several times in the above paper that he had successfully predicted key climatic events (such as the current El Niño) years before the actual events, making reference to papers currently archived on this website and to other papers he has published elsewhere. I can certify that the papers he refers to were indeed published on this site on the dates indicated and that his forward predictions made on this website to events that have now already happened were indeed made well ahead of their time, just as he says they were. In particular, he predicted the current El Niño 3½ years in advance, in a paper published in January 1999. I can therefore fully confirm the authenticity of that prediction, as can the many expert reviewers who participated in the subsequent open review in 19998.”

Radovanovic, Lukic et al. (2005), Stevancevic, Radovanovic et al. (2006) have also pointed that by working out the heliocentric hypothesis the long-term forecasts can be done, with a special review on the possibility of the practical application. On the basis of the experience, Stevancevic, Radovanovic et al. (2004, 2006) have pointed to the positive sides but also the mistakes appearing by using such approach. Todorovic, Stevancevic et al. (2005) have also given some indications the processes on the Sun may cause forest fires.

8. Conclusions

We may conclude that the number of forest fires as well as surfaces they occupy has increased from year to year. Difficult which has existed during the research relates to modest database. Unsuccessful was the attempt to unite necessary satellite data with data on fires for period 1991-2001. That is why it was decided to add FAO UN results to establish whether there is a signal of the eventual causality. Observation Wang (2005) gave seems interesting: “Following E. N. Parker, when the mathematics becomes too much complicated in the study, is seems the time to stop to find new physics, while when the observations get into too many details, it seems the time to stop to think what physics we are working on“.

Proceeding from the official data, the cause for about 43% of the forest fires was not established. The monograph points out the hypothetic possibility that certain processes on the Sun could be the explanation. As mentioned in the Introduction, certain segments of basic idea need detailed research in order to confirm or refute the heliocentric approach. On basis of the recent researches, it is certain that destructive power of fires, not only rages vegetation throughout the world from year to year, but also endangers the environment. With all accomplishments of modern age, as well as with undertaken measures (on general level), we can conclude the society was caught with fire phenomenon. In such circumstances “guilt” imputes to intentional or unintentional burning by man or by electric discharges from the atmosphere. We have seen that in some parts of the USA lightning practically represents minor cause of the initial phase. According to previous estimation, even over 50% of “responsibility” was attributed to lightning. On the other side, we have clearly seen that

8 John L. Daly


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modern science is not able to explain an extremely large quantity of electric power in clouds. Rain that should follow thunder is also in a domain of sporadic interests. Thus, we have come to global warming, that is, climatic disturbances for which man bears most responsibility. On basis of such arguments, some officials claim men guilty for even over 95% of the cases.

This “trend” in science is dominating so much that at the beginning of the research there was a worry into the coherence of developing at any other different approach. However, there are more and more scientists stating their own arguments for opposite view from different aspects. In accordance to estimation that the hypothesis may be contested, especially on delicate places which objectively do exist, the monograph gives a great number of quotations just because of possible reproaching for selective choice and arbitrary interpretation of some scientific papers. In any case, there is a strong belief the successful measures of prevention may only realize on bases of better notion of what is happening on the Sun, of processes happening in the magnetosphere and atmosphere, as well as manifestations that charged particles make in the contact with biomass. Generally, the situation we are in now characterizes the impossibility of making both successful prognostic models and prevention: “purely analytical system“ (Hardy, Hardy, 2007).

According to hypothesis Stevancevic developed, depending on solar wind parameters, the differences concerning the regional development of the weather conditions seem to give a universal approach in the only possible way for now. “One hypothesis for these clustered dates (Agee 1993) is that these were times of sunspot minima associated with periods of lower than normal solar activity (Stuiver and Quay 1980). These global cooling periods may be linked to changes in the factors associated with large fire events in more recent times in the wetter portions of the Pacific Northwest: drought, lightning activity, the occurrence of east winds, or less summer onshore flow of moist air. We do not understand these linkages well, or linkages between fires and other episodic but potentially catastrophic disturbances“ (Agee, Krusemark, 2001). Moore et al. (2002) thought similarly: “Many aspects of fires in the landscape remain obscure and more reliable data on fire causes, impacts and research on fire behavior is required to effectively understand and then address the fire issue“ If we only rely the data from the table 11, we could say the connection is direct and the observed fires are in temporal accordance with mentioned process on the Sun. “Obviously we need to understand first what happens in the Sun's convection zone when perturbations in the torque cycle occur. …I think that these problems can only be solved by a joint interdisciplinary effort of open-minded scientists“ (Landschieidt, 2000 b).

Viewing from presented perspective, Lynch et al. (2004) for example, understood the domain of the key question, but obviously without clear vision how further to develop the measures of prevention: “Our results therefore support other recent studies demonstrating that warmer/drier climatic conditions do not necessarily induce greater fire importance. …These results contradict the current understanding of modern fire–climate relationships. It is also inconsistent with model predictions that a drier and warmer climate, as a result of glasshouse warming, will lead to increased fire activity in boreal systems“ Gorte, (2006) is categorical: “Research information on causative factors and on the complex circumstances surrounding wildfire is limited. The value of wildfires as case studies for building predictive models is confined, because the a priori situation (e.g., fuel loads and distribution) and burning conditions (e.g., wind and moisture levels, patterns, and variations) are often unknown“. On basis of the researches showed in this study, we may conclude the following:


70

- in all cases the data were gathered for, up to several days earlier the coronary holes and energetic regions in geoeffective position on the Sun had preceded forest fires in Europe. In every concrete situation, the emission of strong electromagnetic and thermal corpuscular energy from these sources had preceded fires;

- basic ways of solar wind penetration into the magnetosphere are a) reconnection (in the area of geomagnetic poles) and b) direct solar wind penetration under the dominant effect of the kinetic energy (near geomagnetic anomalies);

- solar wind directed towards the Earth gets weaker with deeper and deeper penetration towards the topographic surface. The modifications happening above the Atlantic anomaly and over magnetosphere tropics also represent the border area modern science has come to.

- air masses seized by power stream of the solar wind particles, are subject to the magnetic field laws and their moving is on the account of particles’ energy of the power stream;

- geomagnetic coordinates can represent the base for mathematical equation usage, which describe the trajectories of air mass movements;

- direction of air mass movements is determined by the polarization of the solar wind charged particles. In the northern hemisphere, the movement of winds made on the account of the proton solar wind energetic particles has the left direction. Wind speed increases with the height increase and it is directly proportional to the kinetic energy of the solar wind particles’ increase;

- cloudiness represents one of the most important factors, determining whether charged particles will be deposited to the topographic surface;

- on the basis of the preliminary results, there are indications that the cosmic radiation (especially in period of reduced solar activity) may also cause fire phenomenon. As already said, the cosmic radiation in certain situations may be characterized by far higher temperatures, speeds, particle density, that is, by far stronger electromagnetic waves than ever measured for the solar wind. “However, the physical mechanism of solar activity effects on weather phenomena remains unclear. It is suggested that a significant part in the transfer of the solar variability to the lower atmosphere may be played by charged particles of solar and galactic origin, mainly protons, with energies from ~100 MeV to several GeV“ (Veretenenko, Thejll, 2004).

- research at what conditions the charged particle dispersion on vegetation may cause the initial phase of burning require experimental testing. Due to impossibility of precise prognosticating at which locations it may concretely happen, necessary simulation of the similar conditions in laboratory is considered as the first step.

It is well known that a minimum of 300 °C is necessary for the mentioned initial phase. It

is not necessary to point that so high air temperature has never been measured on the Earth by standard meteorological measures, even when we talk about soil temperature.

Brief notes on the recent experiences of meteorologists and climatologists are certainly related to the ingratitude of the long-term forecasting. What could be concluded, when it is about the processes on the Sun, is that in the following several years the Sun should come into relatively calmer phase, so we should expect the reduction in the number of fires. It certainly does not mean that we won’t have them (it is first of all meant on those fires with “unknown” cause). However, for now we cannot conclude with certainty how it will effect


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the cosmic radiation and what, in fact, it will bring us in future. “Magnetic reconnection, turbulence and shocks are three fundamental ingredients of the plasma Universe. The detailed understanding of these key processes and their associated multi-scale physics is a challenge for the future of space physics. One of the lessons learned from Cluster is the need for new space missions equipped with instruments of higher sensitivity and better time resolution together with a larger number of satellites“

References

Adler N. O, Elías A. G. (2000): Solar variability associated to ionospheric, stratospheric, and tropospheric parameters. In: Vázquez M, Schmieder B: The solar cycle and terrestrial climate. ESA, Special Publication, 463, 509-512.

Agee J, Krusemark F. (2001): Forest Fire Regime of the Bull Run Watershed, Oregon. Northwest Science, Vol. 75, No. 3, p. 292-306.

Agee J. (2004): The Role of Fire in Forest Restoration. 2004 Starker Lecture Transcripts, (http://www.cof.orst.edu/starkerlectures/

transcripts/2004/fire.php#top). Agerup М. (2004): Is Kyoto a Good Idea? Adapt or Die: The science, politics and economics

of climate change, Profile Books, London. Agerup М, Ayodele T, Cordeiro J, Cudjoe F, Fernandez J. R, Hidalgo J. C, Krause M, Louw

L, Mitra B, Morris J, Okonski K, Oluwatuyi M. (2004): Climate change and sustainable. A blueprint from the Sustainable Development Network. International Policy Network, London.

Amiro D. B, Flannigan D. M, Stocks J. B, Todd B. J, Wotton M. B. (2003): Boreal forest fires: an increasing issue in a changing climate.

(http://www.fao.org/DOCREP/ARTICLE/WFC/XII/0207-B3.HTM). Andreae O. M. (1999): Biomass Burning: Its History, Use, and Distribution and its Impact on

Environmental Quality and Global Climate. Global Biomass Burning: Atmospheric, Climatic, and Biospheric Implications (J. S. Levine, Ed). The MIT Press, Cambridge, Massachusetts, 1991, quoted in J. Levine, T. Bobbe, N. Ray, A. Singh, R. G. Witt, Wildland Fires and the Environment: A Global Synthesis, Division of Environmental Information, Assessment and Early Warning, United Nations Environment Programme, p. 2-3.

Arking A, Hopkins J, Cooper R, Happer W, Legates D, Lindzen R, Nichols R, O’Keefe W, Schlesinger J, Sedjo R, Sproull R, (2001): Climate Science and Policy: Making the Connection. George C. Marshall Institute, Washington, D. C.

Auclair A. N. D. (1992): Forest wildfire, atmospheric CO2, and solar irradiance periodicity.

The role of the Sun in Climate Change by Hoyt and Schatten, EOS 73, 70, chapter 8 (http://www.amazon.com/gp/reader

/019509414X/ref=sib_dp_pt/002-0508150-1026466#reader-link). 135 Baliunas S, Soon W. (2000): The Sun Also Warms. Presented at the GCMI/CEI Cooler Heads

Coalition, Washington, DC. (http://www. marshall.org/article.php?id=96).


72

Barron J. E. (1995): Global Change Researchers Assess Projections of Climate Change. Eos Vol. 76, No. 18, p. 185, 189-90. American Geophysical Union.

Beniston M. (2004): The 2003 heat wave in Europe: A shape of things to come? An analysis based on Swiss climatological data and model simulations. Geophisical Research Letters, vol. 31, L02202.

Beniston M, Diaz H. F. (2004): The 2003 heat wave as an example of summers in a greenhouse climate? Observations and climate model simulations for Basel, Switzerland. Global and planetary change, 44, p. 73-81.

Bhattacharyya S, Narasimha R. (2005): Possible association between Indian monsoon rainfall and sola activity. Geophisical Research Letters, vol. 32, L05813, AGU.

Bond P. (2004): The Sun’s influence – and beyond. Astronomy &Geophysics, vol. 45, Issue 1, p. 1.30.

Brown J. T, Hall B. L, Westerling A. L. (2004): The Impact of Twenty-first Century Climate Change on Widland Fire Danger in the Western United States: an Applications Perspective. Climatic Change, 62, p. 365–388.

Bushby P, Mason J. (2004): Solar dynamo, Understanding the solar dynamo. Astronomy & Geophysics, Volume 45 p. 4.07.

Chisham G. (2005): New proxy for reconnection. Astronomy & Geophysics, vol. 46, Issue 4, p. 4.23.

Climate Change (1995): The Science of Climate Change, Summary for Policymakers, Geneve.

Climate Change (2001): The Science of Climate Change, Summary for Policymakers: Geneve.

Conard G. S, Sukhinin I. A, Stocks J. B, Cahoon R. D, Davidenko P. E, Ivanova A. G. (2002): Determining Effects of Area Burned and Fire Severity on Carbon

136 Cycling and Emissions in Siberia. Climatic Change, Vol. 55, No. 1-2, p. 197-211. Cowen R. (2001): Stormy Weather - When the sun's fury maxes out, Earth may take a hit.

Stormy Weather Science News Online, Jan_ 13, 2001.htm. (http://www.sciencenews.org/articles/20010113/bob9.asp)

Cranmer R. S. (2000): Coronal holes and the high-speed solar wind. Space Science Reviews, 101, p. 229–294.

Csiszar I, Denis L, Giglio L, Justice O. C, Hewson J. (2005): Global fire activity from two years of MODIS data. International Journal of Widland Fire, 14(2), p. 117-130.

Cumming S. G. (2001): Forest type and wildfire in the Alberta boreal mixedwood: What do fires burn? Ecological Applications 11(1) p. 97-110.

Dale H. V, Joyce A. L, McNulty S, Neilson P. R, Ayres P. M, Flannigan D. M, Hanson J. P, Irland C. L, Lugo E. A, Peterson J. C, Simberloff D, Swanson J. F, Stocks J. B, Wotton B. M. (2001): Climate Change and Forest Disturbances. BioScience, Vol. 51 No. 9, p. 723-734.

Dmitriev N. A. (1997): Planetophysical state of the Earth and life. IICA Transactions, Volume 4, (http://www.tmgnow).

com/repository/global/planetophysical2.html), English Presentation Sponsored by: THE MILLENNIUM GROUP (http://www.tmgnow.com/) 1998.


73

Egorova V. L, Vovk Ya V, Troshichev A. O. (2000): Influence of variations of the cosmic rays on atmospheric pressure and temperature in the Southern geomagnetic pole region. Journal of Atmospheric and Solar-Terrestrial Physics Volume 62, Issue 11, p. 955-966.

Erdelyi R. (2004): Heating in the solar atmosphere. Astronomy &Geophysics, vol. 45, p. 4.34-4.37.

FAO (2001): Global Forest Resources Assessment 2000. FAO Forestry Paper 140. Rome, Food and Agriculture Organization (http://www.fao.org/forestry/fo/fra/) [Geo-2-397].

137 FAO (2002): Forestry Country Profiles: Iceland. Food and Agriculture Organization

http://www.fao.org/forestry/fo/country/index.jsp?lang_id=1&geo_id=127, 6 March 2002 [Geo-2-417].

Farr D, Kennett S, Ross M. M, Stelfox B, Weber M. (2004): Conserving Canada’s natural capital: the boreal forest; Al-Pac Case Study Report – Part 1, Management Objectives. Prepared for the National Round Table on the Environment and the Economy (http://ilm.law.uvic.ca/PDF/Boreal_Futures_E.pdf).

Flannigan M. D, Logan K. D, Stocks B. J, Wotton B. M, Amiro B. D, Todd J. B. (2002): Projections of future fire activity and area burned in Canada. In: Forest fire research and wildland fire safety (ed. Viegas D. X), Millpress, Rotterdam, Netherlands.

Frey U. H, Phan D. T, Fuselier A. S, Mende B. S. (2003): Continuous magnetic reconnection at Earth’s magnetopause. Nature, 426, p. 533-537.

Galand M. (2001): Introduction to special section: Proton precipitation into the atmosphere. Journal of Geophysical Research, 106, p. 1-6.

Girardin M. P, Tardif J, Flannigan M. D. (2006): Temporal variability in area burned for the province of Ontario, Canada, during the past 200 years inferred from tree rings. Journal of Geophyical Research, 111, D17108, doi: 10.1029/2005JD006815.

Gedalof Z, Peterson D. L, Mantua N. J. (2005): Atmospheric, climatic, and ecological controls on extreme wildfire years in the northwestern United States. Ecological Applications, vol. 15, No. 1, p. 154-174.

Goldammer G. J. (2002): Towards International Cooperation in Managing Forest Fire Disasters in the Mediterranean Region. International Forest Fire News/GFMC No. 27, p. 81-89 (http://www.fire.uni-freiburg.de

/GlobalNetworks/Mediterrania/Security%20Environment%20Ch50%20Fire.pdf) Gomes F. P. J. (2006): Forest fires in Portugal: How it happened and why it happened.

International Journal of Environmental Studies, Vol. 63, No. 02, p. 109–119. Gomes F. P. J, Radovanovic M. (2008): Solar activity as a possible cause of large forest fires

— A case study: Analysis of the Portuguese forest fires. 138 Science of the total environment 394, p. 197–205, doi:10.1016/j.scitotenv.2008.01.040.

Gonzales R. J, Palahi M, Trasobares A, Pukkala T. (2006): A fire probability model for forest stands in Catalonia (north-east Spain). Annals of Forest Science, 63, p. 169-176.

Gorte W. R. (2000): Forest Fire Protection. CRS Report for Congress (Received through the CRS Web), Congressional Research Service, The Library of Congress, Order Code RL30755.

Gorte W. R. (2006): Forest Fire/Wildfire Protection. CRS Report for Congress (Received through the CRS Web), Congressional Research Service, The Library of Congress, Order Code RL30755.

Gray V. (2000): The cause of global warming (http://www.john-daly.com/cause/cause.htm).


74

Habbal R. S, Woo R. (2004): The solar wind and the Sun-Earth link. Astronomy &Geophysics, vol. 45, p. 4.38-4.43.

Hall L. B. (2007): Precipitation associated with lightning-ignited wildfires in Arizona and New Mexico. International Journal of Wildland Fire 16(2) 242–254, DOI: 10.1071/WF06075.

Hallett J. D, Mathewes W. R, Walker C. R. (2003): A 1000-year record of forest fire, drought and lake-level change in southeastern British Columbia, Canada. The Holocene 13,5 (2003) p. 751–761.

Hardy C. C, Hardy E. C. (2007): Fire danger rating in the United States of America: an evolution since 1916. International Journal of Wildland Fire 16(2) 217–231, DOI: 10.1071/WF06076.

Hathaway H. D, Wilson M. R. (2006): Geomagnetic activity indicates large amplitude for sunspot cycle 24. Geophysical Research Letters 33, L18101, doi:10.1029/2006GL027053, (http://solarscience.msfc.nasa.gov/papers/hathadh/HathawayWilson2006.pdf).

Iucci N, Dorman I. L, Levitin E. A, Belov V. A, Eroshenko A. E, Ptitsyna G. N, Villoresi G, Chizhenkov V. G, Gromova I. L, Parisi M, Tyasto I. M, Yanke G. 139 V. (2006): Spacecraft operational anomalies and space weather impact hazards. Advances in Space Research, Vol. 37, Issue 1, p. 184-190.

Komitov B. (2005): The Sun, Climate and Their Changes in Time. Nauka, Year XV, Issues 1, No. 6, p. 28-39, (www.astro.bas.bg/~komitov/).

Kourtz P. H, Todd J. B. (1991): Predicting the daily occurrence of lightning-caused forest fires. Forestry Canada Information Report PI-X-112. Petawawa National Forestry Institute.

Krawchuk A. M, Cumming G. S, Flannigan D. M, Wein W. R. (2006): Biotic and abiotic regulation of lightning fire initiation in the mixedwood boreal forest. Ecology, 87(2), p. 458-468.

Krstic N, Hope P, Jovanovic B. (2004): From the middle Pliocene drought to the extant “green house”. Milutin Milankovich Anniversary Symposium: Paleoclimate and the Earth climate system. Serbian Academy of Sciences and Arts, 30 August – 2 Septemer 2004, Belgrade, p. 193-187.

Kristjansson E. J, Staple A, Kristiansen J. (2002): A new look at possible connections between solar activity, clouds and climate. Geophysical Research Letters, 29(23), 2107.

Kristjansson E. J, Kristiansen J, Kaas E. (2004): Solar activity, cosmic rays, clouds and climate – an update. Advances in space research, 34, p. 407-415.

Landscheidt T. (1998): Solar activity - A dominant factor in climate dynamics. (http://www.john-daly.com/solar/solar.htm).

Landschieidt T. (2000 а): Solar wind near Earth: indicator of variations in global temperature. European Space Agency Special Publication 463, p. 497 – 500, (http://adsabs.harvard.edu/abs/2000sctc.proc..497L).

Landschieidt T. (2000 b): Solar forcing of ЕlNino and LaNina. European Space Agency Special Publication, 463, p. 135-140,

(http://mitosyfraudes.8k.com/Calen/NinoLand.html). Landschieidt T. (2000 c): Linked to Solar Motion Cycle (http://www.john-

daly.com/topevnts.htm). 140


75

Landscheidt T. (2003 a): Long-range forecast of U. S. drought based on solar activity (http://www.john-daly.com/solar/US-drought.htm).

Landscheidt, T. (2003 b): New Little Ice Age instead of global warming. Energy and Environment, 14, 327-350, (http://mitosyfraudes.8k.com/Calen/Landscheidt-1.html).

Langematz U, Matthes K; Grenfell L. J. (2005): Solar impact on climate: modeling the coupling between the middle and the lower atmosphere. Memorie della Società Astronomica Italiana, Vol. 76 MontePorzio Catone, June 27-July 1, p. 868-875.

Lepidi S, Santarelli L, Cafarella L, Palangio P. (2005): The Earth's passage of coronal mass ejecta on october 29-31, 2003: ULF geomagnetic field fluctuations at very high latitude. Memorie della Società Astronomica Italiana, Vol. 76, MontePorzio Catone, June 27-July 1, 2005, p. 998-1001.

Levine J. S, Bobbe T, Ray N, Singh A, Witt G. R. (1999): Wildland Fires and the Environment: a Global Synthesis. UNEP/DEIAEW/TR.99-1 (http://grid2.cr.usgs.gov/publications/wildfire.pdf).

Lilensten J, Bornarel J. (2006): Space Weather, Environment and Societies, Springer Ltd. Linn R. R. (2007): Numerical simulations of grass fires using a coupled atmosphere-fire

model: Dynamics of fire spread. Journal of geophysical research, vol. 112, D05108, doi:10.1029/2006JD007638, 2007.

Lockwood M, Stamper R, Wild N. M. (1999): A doubling of the Sun’s coronal magnetic field during the past 100 years. Nature, vol. 399, p. 437-439.

Lockwood M, Lanchester B. S, Frey H. U, Throp K, Morley S. K, Milan S. E, Lester M. (2003): IMF control of cusp proton emission intensity and dayside convection: implications for component and anti-parallel reconnection. Annales Geophysicae 21, p. 955–982.

Lucio S. P. (2005): Can Solar Activities Influence ExtremeWeather over Continental Portugal? Stochastic Contrasts of Temperature and Precipitation with Sunspots and Cosmic Ray Intensity. Geophysical Research Abstracts, Vol. 7, 00129, SRef-ID: 1607-7962/gra/EGU05-A-00129, E G U (http://www.cosis.net/abstracts/EGU05/00129/EGU05-A-00129-1.pdf).

Lynch A. J, Hollis L. J, Hu S. F. (2004): Climatic and landscape controls of the boreal forest fire regime: Holocene records from Alaska. Journal of Ecology 92, p. 477–489.

Mann M. E, Bradley R. S, Hughes M. K. (1998): Global-Scale Temperature Patterns and Climate Forcing Over the Past Six Centuries, Nature, 392, p. 779-787.

Marhavilas P. K, Sarris E. T. and Anagnostopoulos G. C. (2004): Elaboration and analysis of Ulysses' observations, in the vicinity of a magnetohydrodynamic shock. The-eggs_org NewsLetter & Information Service of the E_G_U.htm, Issue #08 30 June 2004.

Marsh N, Svensmark H. (2000): Cosmic Rays, Clouds, and Climate. Space Science Reviews, 00: p. 1–16.

Mauas P, Flamenco E. (2005): Solar activity and the streamflow of the Parana River Memorie della Società Astronomica Italiana, Vol. 76, MontePorzio Catone, June 27-July 1, 2005, p. 1002-1003.

McGuffie K, Henderson-Sellers A. (1997): A climate modeling primer. John Eiley & Sons Ltd.

McGuire B. (2004): Climate Change. Technical paper 02, Benfield Hazard Research Centrre.


76

McIntyre S, McKitrick R. (2003): Corrections to the Mann et al (1998) Proxy Data Base and Northern Hemisphere Average Temperature Series. Energy and Environment, 14(6) p. 751-772. (http://www.climate2003.com/)

McIntyre S, McKitrick R. (2005): The M&M critique the MBH98 northern hemisphere climate index: update and implications. Energy and Environment, 16(1) p. 69-100.

McKenzie D, Hessl A. E, Peterson L. D, Agee K. J, Lehmkuhl F. J, Kellogg B. L-K, Kernan J. (2004): Fire and climatic Variability in the Inland Pacific Northwest: Integrating Science and Management. Final report to the Joint Fire Science Program on Project #01-1-6-01.

McKenzie D, Gedalof Z, Peterson L. D, Mote P. (2004): Climatic Change, Wildfire, and Conservation. Conservation Biology, vol. 18(4), p. 890-902.

McLean S, Macmillan S, Maus S, Lesur V, Thomson A, Dater D. (2004): The US/UK World Magnetic Model for 2005-2010. NOAA Technical Report NESDIS/NGDC-1, (http://www.ngdc.noaa.gov/seg/WMM/data/TRWMM_2005.pdf).

Meloni P, De Michelis A, Tozzi R. (2005): Geomagnetic storms, dependence on solar and interplanetary phenomena: a review. Memorie della Società Astronomica Italiana, Vol. 76 n. 4, MontePorzio Catone, June 27-July 1, 2005, p. 882-887.

Michaels J. P. (1998): Long hot year - Latest Science Debunks - Global Warming Hysteria. Policy Analysis, No. 329.

Monbiot G, Lynas M, Marshall G, Juniper T, Tindale S. (2005): Time to speak up for climate-change science. If debate is left to greens and sceptics, people think the evidence is equal on each side. Nature, vol. 434, p. 559.

MoNP Russian Federation (1996): National Report on the State of the Environment in the Russian Federation in 1995. Ministry of Nature Protection of the Russian Federation. Moscow, Center for International Projects (in Russian).

Moore P, Haase N, Hoffmann A. (2002): Burning Questions about Fire. Burning Issues 4, (http://www.asiaforests.org/doc/resources/fire/BI_4.pdf).

Mukherjee S. (2006): Influence of a Star flare on the Sun-Earth environment and its possible relationship with snowfall. The-Eggs NewsLetter & Information Service of the E_G_U.htm Issue #15 19 April 2006.

Naitamor S. (2005): Coronal Mass Ejection: theirs sources and geomagnetic disturbances, Memorie della Società Astronomica Italiana, Vol. 76, MontePorzio Catone, June 27-July 1, 2005, p. 1011-1014.

Neugebauer M, Smith J. E, Ruzmaikin A, Feynman J, Vaughan H. A. (2000): The solar magnetic field and the solar wind: Existence of preferred longitudes. Journal of Geophysical Research, American Geophysical Union, Volume 105, p. 2315-2324.

Nikolov N. (2006): Global Forest Resources Assessment 2005 – Report on fires in the Balkan Region. Forestry Department, Food and Agriculture Organization of the United Nations, Fire Management Working Papers, Working Paper FM/11/E, Rome (www.fao.org/forestry/site/fire-alerts/en).

Nunes C. S. M, Vasconcelos J. M, Pereira M. C. J, Dasgupta N, Alldredge J. R, Rego C. F. (2005): Land cover type and fire in Portugal: do fires burn land cover selectively? Landscape Ecology, 20, p. 661-673.

Palamara R. D, Bryant A. E. (2004): Geomagnetic activity forcing of the Northern Annular Mode via the stratosphere. Annales Geophysicae, 22, p. 725-731.


77

Palle E. (2005): Possible satellite perspective effects on the reported correlations between solar activity and clouds. Geophysical Research Letters, 32, L03802.

Ponyavin D. I, Barliaeva T. V, Zolotova N. V. (2005): Hypersensitivity of climate response to solar activity output during the last 60 years. Memorie della Società Astronomica Italiana, Vol. 76, MontePorzio Catone, June 27-July 1, 2005, p. 1026-1029.

Przybylak R. (2002): Variability of air temperature in the Arctic in the 20th

century. Man and

climate in the 20th

century. International conference 13-15 June 2002, Wroclaw, abstract book, p. 84-85.

Quassim M. S, Attia A. F. (2005): Forecasting the global temperature trend according to the predicted solar activity during the next decades. Memorie della Società Astronomica Italiana, Vol. 76, MontePorzio Catone, June 27-July 1, 2005, p. 1030-1033.

Radovanovic M, Stevancevic M, Strbac D. (2003 a): Influence of the Solar wind energy on the atmospheric processes. Geophysical Research Abstracts, Vol. 5, 13963.

Radovanovic M, Stevancevic M, Strbac D. (2003 b): Прилог проучавању утицаја енергије сунчевог ветра на атмосферске процесе (A contribution to the study of the influence of the energy of solar wind upon the atmospheric processes). Зборник радова, Географски институт „Јован Цвијић” САНУ, бр. 52, Београд, р. 1-18.

Radovanovic M, Ducic V. (2004): Колебање температуре ваздуха у Србији у другој половини XX века. (Temperature variability in Serbia in the second half of XX century) Гласник Српског географског друштва, св. LXXXIV бр. 1, Београд, р. 19-28.

Radovanovic M, Lukic V, Todorovic N. (2005): Heliocentric electromagnetic long-term weather forecast and its applicable significance. Collection of papers, No 54, Geographical institute ”Jovan Cvijic” SASA Belgrade, p. 5-18.

Radovanović M, Stevančević M, Marković D. (2005): Repetition of the Regional Magnetic Fields on the Sun and Their Importance for the development of the Weather Circumstances on Earth. The Sixth European Meeting on Environmental Chemistry,

Belgrade, December 6-10th

, Programme and The Book of Abstracts, Belgrade, p. 277. Riano D, Moreno Ruiz A. J, Isidoro D, USTIN L. S. (2007): Global spatial patterns and

temporal trends of burned area between 1981 and 2000 using NOAA-NASA Pathfinder. Global Change Biology 13, p. 40 – 50, doi: 10.1111/j.1365-2486.2006.01268.x

Rowell A, Moore F. P. (2000): Global Review of Forest Fires. (http://www.wwf.de/fileadmin/fm-wwf/pdf-alt/waelder/brnde/Forest_Fires_Report.pdf).

Ryu S-R, Chen J, Crow T, Saunders C. S. (2004): Available Fuel Dynamics in Nine Contrasting Forest Ecosystems in North America. Environmental Management, Vol. 33, Supplement 1, Springer-Verlag New York, LLC, p. S87–S107, DOI: 10.1007/s00267-003-9120-7.

Santer B. D, Wigley T. M. L, Gaffen D. J, Bengtsson L, Doutriaux C, Boyle J. S, Esch M, Hnilo J. J, Jones P. D, Meehl G. A, Roeckner E, Taylor K. E, Wehner M. F. (2000): Interpreting Differential Temperature Trends at the Surface and in the Lower Troposphere. Science, vol. 287, p. 1227-1232.

Schär C, Vidale P. L, Luthi D, Frei C, Haberli C, Liniger M. A, Appenzeller C. (2004): The role of increasing temperature variability in European summer heat waves. Nature, 427, p. 332-336.

Schuurmans C. J. E. (1991): Changes of the coupled troposphere and lower stratosphere after solar activity events. Journal of Geomagnetism and Geoelectricity, 43, p. 767-773.


78

Shaviv J. N. (2005): On climate response to changes in the cosmic ray flux and radiative budget. Journal of geophysical research, vol. 110, A08105.

145 Shnidell D, Rind D, Balachandran N, Lean J, Lonergan P. (1999): Solar Cycle Variablity,

Ozone, and Climate. Science, vol. 284 no. 5412, p. 305-308. Solanki K. S, Schüssler M, Fligge M. (2000): Evolution of the Sun's large-scale magnetic

field since the Maunder minimum. Nature, vol. 408, p. 445-447. Solanki K. S. (2002): Solar variability and climate change: is there a link?, Astronomy

&Geophysics, Vol 43, p. 5.9-5.13. Soon W, Baliunas S. L, Robinson A. B, Robinson Z. W. (2001): Global Warming A Guide to

the Science. Risc Controversy Series 1, The Fraser Institute Centre for Studies in Risk and Regulation Vancouver British Columbia Canada 2001 Risk Controversy Series 1.

Stevancevic M. (2004): Тајне Сунчевог ветра (Secrets of the Solar Wind). Београд. Стеванчевић М, Радовановић М, Тодоровић Н. (2004): Могућност примене

електромагнетне методе за средњорочне временске прогнозе (The possibility of application of electromagnetic method in mid-term weather forecasting). Зборник радова EkoIst’04 Еколошка истина, 30. 05. – 02. 06. 2004, Бор, стр. 396-399.

Stevancevic M. (2006): Теоријске основе хелиоцентричне електромагнетне метеорологије. (Theoretic Elements of Heliocentric Electromagnetic Meteorolgy). Београд.

Stevancevic M, Radovanovic M, Strbac D. (2006): Solar Wind and the Magnetospheric Door as Factor of Atmospheric Processes. Second International Conference ''Global Changes

and New Chellenges of 21st

Century, 22-23 April 2005. Sofia, Bulgaria, p. 88-94. Sun B, Bradly R. S. (2004): Reply to comment by N. D. Marsh and H. Svensmark on “Solar

influences on cosmic rays and cloud formation: A reassessment”. Journal of geophysical research, vol. 109, DI4206.

Svensmark H, Friis-Christensen E, (1997): Variation of cosmic ray flux and cloud coverage: a missing link in solar-climate relationships. Jоurnal of Atmospheric and Solar Terrestrial Physics, 59, p. 1225-1232.

Tinsley A. B, Yu F. (2004): Atmospheric Ionization and Clouds as Links between Solar Activity and Climate. in press in forthcoming AGU monograph: Solar Variability and Its Effects on the Earth's Atmospheric and Climate System. AGU press, Washington, DC, p. 321-340, (http://www.utdallas.edu/physics/pdf/Atmos_060302.pdf).

Todorovic N, Stevancevic M, Radovanovic M. (2005): Solar activity – possible cause of large forest fires. The Sixth European Meeting on Environmental Chemistry, Belgrade,

December 6-10th

, Programme and The Book of Abstracts, Belgrade, p. 139. Troshichev O, Egorova L, Janzhura A, Vovk V. (2005): Inuence of the disturbed solar wind

on atmospheric processes in Antarctica and El-Nino Southern Oscillation (ENSO). Memorie della Società Astronomica Italiana, Vol. 76, 2005 MontePorzio Catone, June 27-July 1, 2005, p. 890-898.

Ubysz B, Szczygiel R. (2002): Fire Situation in Poland. International Forest Fire News, No. 27, p. 38-64 (http://www.fire.uni-freiburg.de/iffn/country/pl/pl_5.htm).

Udelhofen P. M, Cess R. D. (2001): Cloud cover variations over the United States: An influence of cosmic rays or solar variability?, Geophisical Research Letters, 28, 13, 2617-26-20.


79

Usoskin G. I, Marsh N, Kovaltsov A. G, Mursula K, Gladysheva G. O. (2004): Latitudinal dependence of low cloud amount on cosmic ray induced ionization. Geophysical Research Letters, 31, L16109.

Vaughn D. G. (2005): How does the Antarctic ice sheet affect sea level rise? Science, 308, 1877-1878.

van Geel B, Raspopov M. O, Renssen H, van der Plicht J, Dergachev A. V, Meijer J. A. H. (1999): The role of solar forcing upon climate change. Quaternary Science Reviews 18 p. 331-338.

Verdon C. D, Kiem S. A, Franks W. S. (2004): Multi-decadal variability of forest fire risk - eastern Australia. International Journal of Wildland Fire 13(2) p. 165–171.

Veretenenko S, Thejll P. (2004): Effects of energetic solar proton events on the cyclone development in the North Atlantic, Journal of Atmospheric and Solar-Terrestrial Physics, 66, p. 393-405.

Veselovsky S. I. (2005): Similarity and diversity of solar extreme events. Memorie della Società Astronomica Italiana, Vol. 76, MontePorzio Catone, June 27-July 1, 2005, p. 1056-1059.

Wang J. (2005): Magnetic fields of Solar Active Regions. Proceedings of the International Astronomical Union, Volume 2004, Issue IAUS223, No. 223, p. 3-12.

Wheeler D. (2001): A verification of UK gale forecasts by the ‘solar weather technique’: October 1995–September 1997. Journal of Atmospheric and Solar-Terrestrial Physics, Volume 63, Issue 1 p. 29-34.

Wiin-Neilsen A. (1997): A note on hemispheric and global temperature changes. Atmosphera, p. 125-135.

WMO (1999) WMO Statment on the Status of the Global Climate in 1998, WMO – No 896. Wotton M, B, Stocks J. B, Martell L. D. (2005): An index for tracking sheltered forest floor

moisture within the Canadian Forest Fire Weather Index System. International Journal of Widlendfire, 14, p. 169-182.

Zherebtsov G, Kovalenko V, Molodykh S. (2005): The effect of solar activity on the Earth’s climate changes. Memorie della Società Astronomica Italiana, Vol. 76 MontePorzio Catone, June 27-July 1, 2005, p. 1076-1079.


Chapter 2

STATISTICAL CHARACTERISTICS OF THE HELIOSPHERIC PLASMA

AND MAGNETIC FIELD AT THE EARTH'S ORBIT DURING FOUR SOLAR CYCLES 20-23

A.V. Dmitriev1, 2, A.V. Suvorova2 and I.S. Veselovsky2, 3 1Institute of Space Science, National Central University, Taiwan

2Skobeltsyn Institute of Nuclear Physics, Moscow State University, Russian Federation 3Space Research Institute (IKI), Russian Academy of Sciences,

Moscow, Russian Federation

Abstract

The review presents analysis and physical interpretation of available statistical data about solar wind plasma and interplanetary magnetic field (IMF) properties as measured in-situ at 1 A.U. by numerous space experiments during time period from 1964 to 2007. The experimental information have been collected in the OMNI Web/NSSDC data set of hourly averaged heliospheric parameters for last four solar cycles from 20th to 23rd. We studied statistical characteristics of such key heliospheric parameters as solar wind proton number density, temperature, bulk velocity, and IMF vector as well as dimensionless parameters. From harmonic analysis of the variations of key parameters we found basic periods of 13.5 days, 27 days, 1 year, and ~11 years, which correspond to rotation of the Sun, Earth and to the solar cycle. We also revealed other periodicities such as specific five-year plasma density and temperature variations, which origin is a subject of discussion. We have found that the distribution of solar wind proton density, temperature and IMF is very close to a log-normal function, while the solar wind velocity is characterized by a very broad statistical distribution. Detailed study of the variability of statistical distributions with solar activity was performed using a method of running histograms. In general, the distributions of heliospheric parameters are wider during maximum and declining phase of the solar cycle. More complicated behavior was revealed for the solar wind velocity and temperature, which distribution is characterized by two- or even tree-peak structure in dependence on the phase of solar cycle. Our findings support the concepts of solar wind sources in the open, closed and intermittent magnetic regions on the Sun.

A.V. Dmitriev, A.V. Suvorova and I.S. Veselovsky

82

1. Introduction

Solar wind (SW) plasma and interplanetary magnetic field (IMF) parameters are measured in situ during space era nearly continuously onboard many spacecraft and satellites. The physical processes on the Sun and in the heliosphere leading to observed SW and IMF parameters and their variations are now rather well investigated and understood, though some unsolved problems still remaining [Schwenn and Marsch, 1990; Burlaga, 2005]. Namely, heating of the solar corona and generation of the solar wind and heliospheric magnetic field are still unresolved subjects of very intense investigations during last decades.

The SW and IMF data are processed and compiled in data bases, which contain hundreds of thousand hourly averages of the solar wind plasma and IMF parameters measured near Earth’s orbit in 1964-2007 by the IMP, HEOS, VELA, OGO, ISEE, Prognoz, Wind and ACE satellites [King, 1981, King and Papitashvili, 2005]. The estimation of errors in those data is difficult because direct measurements were made with different instruments on different satellites and at different orbits. The data obtained are rather nonuniform in both spacing and relative and absolute accuracy. The procedure of relative intercalibration of detectors and introduction of correction is not complete [King, 1977; Couzens and King, 1986; Freeman et at al., 1993; Russell and Petrinec, 1993; Zwickl, 1993; Dmitriev et al., 2005a; King and Papitashvili, 2005]. Detailed description of the data intercalibrations and corrections are presented at web site http://omniweb.gsfc.nasa.gov/html/omni2_doc.html.

The average values of SW and IMF parameters at the Earth orbit were calculated in a number of papers based on the analysis of these growing data sets [Veselovsky et al., 1998a; 1999; 2000a, 2001]. In mentioned papers, long-term variations of the averaged density and other parameters of the solar wind and interplanetary magnetic field were analyzed using the data obtained from direct measurements at the Earth orbit from 1964 to 1996. A general trend was revealed for the entire period along with quite pronounced but comparatively small variations during solar cycles 20, 21, and 22. The results obtained highlighted the important role of different sources of the solar wind. At different phases of the solar cycle, open, closed, and intermittent magnetic-field configurations are typical of these sources [Veselovsky et al., 1998a].

The variability and the periodicity of heliospheric parameters are of interest from the point of view of plasma dynamics on the Sun and in the interplanetary space as well as for the solar-terrestrial physics. The long-term and large-scale variations are described in numerous studies [e.g. Crooker, 1983; Veselovsky, 1984; Schwenn, 1990; Zhang and Xu, 1993; Gazis, 1996; El-Borie et аl., 1997]. The variability of the Sun as a star was traced in its integrated solar-wind mass and energy fluxes [Veselovsky et al., 1999]. Direct plasma measurements in the heliosphere over more than the last thirty years indicated that these quantities have experienced relative variations by factors of 1.5-2, approximately in antiphase with the last three eleven-year solar cycles. A rising trend was noted over this time, with a similar relative-variation scale. This trend may be a manifestation of a "secular" cycle with duration of 60-70 years or longer.

The methods of the Fourier transform, spectrum-time analysis, and wavelet analysis were used to study the structure and dynamics of rhythmic and non-rythmic variations of the main SW and IMF parameters at time scales from days to tens of years. A large variety of the observed regular and irregular variations in the near-Earth heliosphere is explained by a

Statistical Characteristics of the Heliospheric Plasma and Magnetic Field…

83

number of reasons: (1) the variability of unstable processes in the region of solar wind formation, (2) the rotation of Sun and the associated inhomogeneities in its corona, (3) and the Earth's orbital motion. Irregular, a-periodic variations are present for all parameters and at all time scales. The most prominent regular variations are related to cyclic processes on the Sun and its rotation [Veselovsky et al., 2000b; Dmitriev et al., 2000].

The time-epoch analysis and hysteresis curves of the heliospheric parameters show some general and specific properties of the cycles [Veselovsky et al., 2000b; 2001; Dmitriev et al., 2002a; 2002b; 2005b]. Based on these results and using measured heliospheric parameters during the rising phase of the 23-rd solar cycle we were able to present some semi-quantitative estimations of the expected solar wind energy flux and the induced electric field for the time period after the solar maximum. The similarity between the rising phases of the 23-rd and 20-th solar cycles presented additional grounds for correct expectations of the lower maximum of the 23-rd solar cycle and the geomagnetic activity as compared with the 21-st and 22-nd solar cycles [Dmitriev et al., 2002b].

The purpose of this paper is an extension of our statistical studies of SW and IMF parameters based on growing amount of direct in-situ measurements near the Earth orbit during space era. Common statistical properties are considered in a form of statistical distributions in Section 2. “Basic Statistical Properties”. Some characteristic periods in variations of heliospheric parameters derived by a method of Fourier transform for unequally-spaced data are discussed in Section 3. “Characteristic periodicities”. Variations of the parameters with solar cycle are studied by a method of running histograms in Section 4. “Solar cycle variations”. Section 5. is “Summary and Conclusions”.

2. Basic Statistical Properties

Sunspot Number

In the first turn we consider sunspot numbers represented by the Wolf number (W) as a key heliospheric parameter related to the variations of solar activity. The Wolf number is measured continuously with 1-day step for many decades. It is a simple and robust parameter for comparisons and ordering of data in its regular and irregular behavior. Figure 1 shows 27-day running annual Wolf number for the time interval from 1963 to 2007. The smoothed time profile has four prominent maxima of solar cycles 20th to 23rd, respectively, in 1969, 1980, 1989 and 2000. We can also indicate five solar minima in 1964, 1976, 1986, 1996 and about 2007, which allow easy estimation of the cycle duration: 12 years for the 20th cycle, 10 years for the cycles 21st and 22nd, and ~11 to 12 years for the 23rd cycle. Those time intervals are in good agreement with empirical fact that large solar cycles (21st and 22nd) have shorter duration of ~10 years than small cycles (20th and 23rd) having duration of ~12 years. It is a manifestation of the well-known Waldmeier’s rule [Veselovsky and Tarsina, 2002a]. Hence the last four solar cycles exhibit two periods of 10 years and of 12 years, i.e. around 11-year cycle.


84

1965 1970 1975 1980 1985 1990 1995 2000 2005Year

0

50

100

150Su

nspo

t Num

ber W

20th 21st 22nd 23rd

Figure 1. Time profile of the 27-day running annual Wolf number W from 1963 to 2007.

Further analysis of the dynamics of sunspot number requires a study of its statistical properties. Statistical distributions of the W are presented in Figure 2. The daily value of sunspot number varies in very wide range from 0 to 302. In the linear scale, the distribution is smooth and decreases fast from maximum at W=0. There is a little plateau at W of ~100. Hence in the linear representation the dominant contribution to the distribution function is produced by relatively small sunspot number of W<100.

The situation changes dramatically when we represent the sunspot number in logarithmic scale. Namely, instead of values W we consider their decimal logarithms lg(W). The statistical distribution of lg(W) has two maxima. The first one is formed by small values of W<10 and the second peak with amplitude of ~1400 at W~100 is wide and most prominent. Apparently the values of W=0 are not accounted in this distribution. From 1963 to 2007 the number of days with W=0 is 1300. That is much smaller than the number of days forming the wide second maximum. As we can see in Figure 1, that peak is mainly contributed by long-lasting solar maxima of the moderate 20th and 23rd cycles. Hence the logarithmic representation of sunspot number allows grouping the vast majority of solar active days in a wide peak around W=100. As a result, considering the lg(W) we get ability to study in detail the sunspot number enhancements, rather than sunspot number decreases in vicinities of the solar minima, which are mostly prominent in the linear scale.


85

0 100 200 300Sunspot Number W

0

500

1000

1500

2000

2500

Occ

urre

nce

num

ber

a)

10 100Sunspot Number W

200

400

600

800

1000

1200

1400

Occ

urre

nce

num

ber

median = 62mean = 51most prob. = 97~117RMSD=4.67Xo = 100SD = 1.88

b)

Figure 2. Statistical distribution of the daily Wolf numbers for time interval 1963 to 2007: (a) linear and (b) logarithmic scale. In the latter case, the distribution contains two maxima: at small W (from 0 to 7) and at large W~100. The dotted line is a lognormal distribution with mode X0=100 and standard deviation σ=1.88 (see Formulae 6).

Data Coverage

Hourly averaged data on heliospheric parameters for time period from 1963 to 2007 contains about 400,000 consequent hours of measurements. However, about one third of the data is occupied by gaps. Figure 3 shows the data coverage for SW and IMF data at each year from 1963 to 2007. The poor coverage (below 50%) of data takes place during early years of interplanetary measurements in 1963 to 1972 and during interval of 1983 to 1993, when single satellite IMP-8 was operating in the interplanetary medium. Though there are many data gaps occur during the other years, especially for the plasma parameters.


86

1970 1980 1990 2000Year

0

50

100

Dat

a co

vera

ge (%

)

SW Density

a)

1970 1980 1990 2000Year

0

50

100

Dat

a co

vera

ge (%

)

IMF B

b)

1970 1980 1990 2000Year

0

50

100

Dat

a co

vera

ge (%

)

He/p ratio

c)

Figure 3. Annual data coverage for the datasets of: (a) solar wind density, (b) IMF strength, and (c) helium to proton ratio.


87

Duration of the data gaps varies in a wide range from 1 hour to more than 10 days as shown in Figure 4. There are various reasons causing the gaps. Before 1996, the near-earth interplanetary measurements were conducted by high apogee satellites, which spent a large portion of time inside the magnetosphere and magnetosheath. Data gaps were caused also by restricted volume of onboard data storages and infrequent sessions of data transmission. Measurements of modern interplanetary monitors such as Wind and ACE have many data gaps due to malfunctions of onboard equipment.

1 10 100Data gap duration, hours

1E+0

1E+1

1E+2

1E+3

Occ

urre

nce

num

ber

SWP Density

a)

1 10 100Data gap duration, hours

1E+0

1E+1

1E+2

1E+3

Occ

urre

nce

num

ber

IMF B

b)

Figure 4. Occurrence number distribution for the duration of data gaps in the data sets of: (a) solar wind density and (b) IMF strength.


88

Most serious and long-lasting malfunctions are caused by radiation damage during intense solar proton events, which duration can achieve up to several days [e.g. Dmitriev et al., 2005b]. Because of specific of experimental methodic, the solar energetic particles impinging upon the plasma detectors affect mostly the data on density and temperature. The measurements of IMF and plasma velocity are less sensitive to the radiation effects. Apparently, studying of such “full of holes” data sets requires using specific methods of statistical analysis.

Probability Distribution Functions

Statistical study of a heliospheric parameter is aimed determination of two basic statistical moments: most probable value, or mode, and dispersion, i.e. variability of the parameter around its mode. One of mostly common approaches for the statistical distributions is a normal probability distribution function (PDF). An assumption that the measured parameter is distributed normally is prevalent in many studies of the space physics.

The normal PDF of a random variable x is expressed by a Gaussian function:

⎥⎦

⎤⎢⎣

⎡ −−= 2

20

2)(exp)(

σXxAxP (1)

where A is amplitude of the Gaussian, X0 is mode or most probable value, and σ is standard deviation (SD), a measure of the dispersion of distribution. An interval within one standard deviation around the mode accounts for ~68% of the dataset, while two and three standard deviations account 95% and 99.7%, respectively. A half width at middle height (hwmh) of the

normal distribution is simply related to the SD as hwmh= )2ln(2σ . Here ln means a function of natural logarithm.

In experiment, statistical distributions of measured parameters are usually characterized by median and first four moments: mean, root mean square deviation (RMSD), skewness and kurtosis. The median is a middle number separating the higher half of statistical distribution from the lower half. The Gaussian function is symmetric relative to the X0. Hence its mode and median are equal. The mean of N independent measurements of the random variable xi is defined as follow:

∑=

=N

iix

NX

1

1 (2)

Very important property of the normal distribution is that the mean is equal to mode and

median. Apparently, the number N should be as more as possible. The proof of equality between the X0 and <X> as well as proofs of other important properties of the normal distribution can be found in many books devoted to statistics [e.g. Mood et al., 1974].

The RMSD is calculated from the following expression:


89

∑=

−−

=N

ii Xx

NRMSD

1

2)(1

1 (3)

Because the set of measurements xi has been already used for determination of the

average <X>, the number of independent measurements in calculation of the RMSD becomes N-1 as represented in the denominator. The RMSD of normal distribution is equal to one standard deviation σ. That is another important property of the normal PDF.

The third moment of a statistical distribution is skewness:

∑=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

N

i

i

RMSDXx

Nk

1

3

31

. (4)

The skewness is a measure of the lack of symmetry of the distribution. A positive

(negative) number indicates a higher number of large (small) values of the parameter than would be expected for the normal PDF, which has zero skewness.

The fourth statistical moment, kurtosis, is defined as follow:

311

4

4 −⎟⎟⎠

⎞⎜⎜⎝

⎛ −= ∑

=

N

i

i

RMSDXx

Nk (5)

The kurtosis is a measure of the flatness (negative value of k4) or peakedness (positive

value of k4) of the distribution relative to the normal PDF with the same mean and dispersion. Note that normal distribution has zero kurtosis.

Thus, under the assumption of normal distribution the determination of mode and standard deviation can be simply substituted by calculation of mean and RMSD. Actually those moments can be calculated for any variable, which statistical distribution might differ from the normal, i.e. have non-zero skeweness and/or kurtosis. However in such a case the first two statistical moment have lost their important statistical sense. Namely, the mean might be different from the mode, i.e. we lost information about the most probable value of measured parameter. The RMSD is not equal to the standard deviation σ, i.e. the variation of parameter can not be determined in standard manner. In this case it might be possible to find such a represnetation of the parameter that allows approaching its statistical distribution to the normal PDF.

The logarithmic scale is one of very useful representations. Here we can introduce a lognormal PDF as follow [e.g. Hartlep et al., 2000]:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−≡

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=

20

20

)ln()/ln(

21exp

)ln()ln()ln(

21exp)(

σσXxAXxAxP (6)

The lognormal PDF has the same properties as normal distribution but in logarithmic

scale. Indeed, replacing ln(x) by z, ln(X0) by Z0 and ln(σ) by δ we can rewrite Equation 4 as:


90

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−=2

0

21exp)(

δZzAzP (6a)

This Equation is exactly the same as Equation 1. Taking the exponent we can simply

convert numbers from logarithm to linear scale. The exponent of most probable of lognormal distribution is equal to mode X0. In other words, the lognormal distribution reaches the maximum at X0. However, the dispersion of lognormal PDF has a different meaning such that the hwmh should be redefined as a ratio of x/X0 at middle height (rmh), which is equal to

)2ln(2σ=rmh . Therefore, the standard deviation σ in the logarithmic scale has a meaning of standard relative deviation, i.e. a standard ratio relative to mode. In the lognormal distribution the parameter σ is dimensionless. In linear scale, the lognormal distribution is asymmetric and its dispersion is characterized by upper SDup and lower SDlo standard deviations:

SDup= X0 σ - X0 = X0(σ-1) (7a) SDlo= X0 - X0/σ= X0(1-1/σ) (7b),

which are not equal, because of σ is always more than 1. Indeed, the logarithmic dispersion δ=ln(σ) should be always positive.

In the logarithmic scale we can also introduce the first four statistical moments of the distribution of random variable. Namely, the mean value <X>ln can be defined as follow:

))ln(exp(

lnxX = (8)

where

∑=

=N

iix

Nx

1)ln(1)ln( (8a)

It is very easy to show that the mean in logarithmic scale is equal to the geometric mean:

NN

iixX

1

1ln ⎟⎟

⎠

⎞⎜⎜⎝

⎛= ∏

=

(8b)

The lognormal distribution has the same achievement as the normal one: mean <X>ln is

equal to mode X0 and to median of logarithms. The second moment RMSDln is introduced as follow:


91

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−−

= ∑=

N

ii Xx

NRMSD

1

2lnln )ln)(ln(

11exp (9)

For large number of independent measurements N the RMSDln approaches to the standard

deviation σ of lognormal PDF. Note that the RMSDln is also dimensionless and has a meaning of relative deviation from the mean <X>ln. Hence in linear scale, the upper and lower deviations from the mean are calculated as <X>ln RMSDln and <X>ln/RMSDln, respectively.

The third and fourth statistical parameters can be defined in logarithmic scale as follows:

skewness ∑=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

N

i

i

RMSDXx

Nk

1

3

ln

ln3 )ln(

ln)ln(1 (10)

and

kurtosis 3)ln(

ln)ln(11

4

ln

ln4 −⎟⎟

⎠

⎞⎜⎜⎝

⎛ −= ∑

=

N

i

i

RMSDXx

Nk (11)

The skewness and kurtosis calculated in the logarithmic scale have the same properties as

those in the linear scale. Hence they can be used as a measure of similarity of the statistical distribution to lognormal PDF. For a log-normally distributed parameter the skewness and kurtosis are equal to zero, and the most probable and standard deviation can be easily calculated, respectively, as mean <X>ln and RMSDln.

In practice however, the number N is not infinitely large and statistical distributions may have various shapes, which in general differ from the normal PDF. The mode, i.e. most probable value, is different from mean and median, and may be very different for strongly skewed distributions. As an example we demonstrate the statistical distribution of sunspot number (see Figure 2). Direct determination of the most probable of statistical distribution is not very accurate because of the following circumstances. The statistical distribution of empirical parameter is discrete with finite size of bins, because of limited number of measurements N. Very small size of the bins leads to appearance of many subsidiary peaks with low statistical significance, such that the most probable is hidden by noise. Hence the size of bins is selected in such a way as to provide a smooth shape of statistical distribution. As a result the accuracy of mode and dispersion are limited by the width of bin, which might be pretty wide and, thus, the accuracy becomes very poor. Another way of fitting the statistical distribution by standard, say normal, PDF is also unreliable, because in general the distributions are different from the normal.

In such situation, as a first step we compare the mode, mean and median in order to verify the normality of distribution. As a second step, the statistical distribution is approached, if possible, to the normal shape. Namely we choose such a representation (linear or logarithmic), which provides minimal difference between the mode, median and mean. Hence in the new representation the statistical distribution becomes more symmetric and its most probable is close to average. Our choice is based on a very important property of median: it is invariant in transformations between the linear and logarithmic scales. The quality of our approach is expressed numerically by the skewness and kurtosis.


92

In the following sections we will show that the logarithmic representation allows symmetrization of the statistical distributions for many heliospheric parameters. The number of bins is chosen to achieve a smooth shape of statistical distribution. For most of parameters that number is about 30. Using the statistical distribution, we estimate the most probable value of parameter. The median, mean and RMSD are calculated in the most appropriate scale, where the distribution is mostly close to the normal PDF.

The distribution is fitted by normal or lognormal PDF in the following way. The mode X0 of PDF is supposed to be equal to median. The standard deviation SD is calculated by fitting the shape of statistical distribution by a PDF. The results are presented in Table 1. There we also indicate a type of PDF and percentage of data covered by that PDF.

Table 1. Main statistical numbers of key heliospheric parameters at the Earth orbit

during 1963-2007. statistics min max median mean mode RMSD SD k3 k4 PDF %

W 16437* 0 302 62 51 97~117 4.66 1.88 two-peak - V, km/s 265699 156 1200 420 430 370~390 1.25 1.26 .42 -.32 flatten - T, 103 K 227883 2.9 7000 85 83 72~94 2.3 2.43 -.14 -.31 lognormal 94n, cm-3 244625 0.1 118. 5.3 5.4 4.3~5.3 2.0 2.0 .008 .59 lognormal 95He/p 163052 0.001 0.4 0.037 0.034 0.03~0.05 2.0 1.7 -.79 1.4 skewed -

Pd, nPa 244625 0.01 79 2. 2. 1.8~2.25 1.86 1.74 -.01 1.7 lognormal 95Sk,

erg/cm2⋅s 244625 .0015 30 0.43 0.44 0.37~0.49 2.0 1.92 .08 1.3 lognormal 98

B, nT 271938 0.4 55.8 5.9 6.0 5.5~6.5 1.55 1.48 .12 .85 lognormal 95Bxy, nT 271938 0.14 52. 4.6 4.5 4.3~4.7 1.74 1.55 -.78 2.8 lognormal 82Bx, nT 271938 -40.1 29.4 0. 0. ±3 3.90 - - - two-peak - By, nT 271938 -38.8 46.1 0. 0. ±3 4.30 - - - two-peak - Bz, nT 271938 -46.3 36.8 0. 0. -0.6~1.5 3.1 2.09 -.01 9.1 normal 88

Ey, mV/m 242155 -34 30 0 0 -0.4~0.2 1.55 1.0 -0.1 23. normal 88Ma 228053 1.1 93. 8.4 8.4 8.~9.4 1.54 1.44 .025 1.7 lognormal 95Ms 227171 2.6 72. 12.7 13. 11.~13.8 1.35 1.30 0.57 1.3 lognormal 92β 212221 0.001 87. 0.48 0.43 0.44~0.65 2.61 2.12 -.92 2.5 lognormal 89

* Number of days

Solar Wind Plasma

There are many indications that SW parameters have lognormal distribution. Veselovsky et al. [1998b] revealed that statistical distributions of hourly averages of SW proton density and temperature during three solar cycles from 20 to 22 are well fitted by the lognormal PDF. Statistical analysis of SW data acquired from the Wind satellite in 1995 to 1998 also reveal that hourly averages of solar wind velocity, density and temperature have lognormal distribution [Burlaga and Szabo, 1999, Burlaga and Lazarus, 2000]. King and Papitashvili [2005] studying the hourly averaged SW plasma data during the 23rd solar cycle, use also logarithmic representation of the proton density and temperature and mention that the distribution of density is close to the lognormal.

Statistical distributions of the SW parameters are shown in Figure 5. All the parameters are represented in the logarithmic scale. In Figures 5a and 5b we find that the distributions of


93

proton density n and temperature T are very close to lognormal PDF with the mode, respectively, 5.3 cm-3 and 85 103 K and standard relative deviation, respectively, 2 and 2.43. They have pretty small skewness and kurtosis. In contrast, the distributions of SW velocity and He/p ratio are different from lognormal (Figure 5c and 5d). The statistical distributions of n and T are fitted very well by the lognormal PDF within 2-σ interval that corresponds to ~95% of the total statistics, which contain 244625 and 227883 hourly averaged measurements, respectively, of the density and temperature.

1E-1 1E+0 1E+1 1E+2SWP Density, 1/cc

1E+1

1E+2

1E+3

1E+4

1E+5

Occ

urre

nce

num

ber

median = 5.3mean = 5.4mode = 4.3~5.3RMSD = 2. SD = 2.skewness = 0.008kurtosis = 0.59

−2σ +2σ

a)

1E+3 1E+4 1E+5 1E+6 1E+7SWP Temperature, K

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

Occ

urre

nce

num

ber

median = 85000mean = 83000mode = 72000 ~ 94000RMSD = 2.3SD = 2.43skewness = -0.14kurtosis = -0.31

+2σ−2σ

b)

Figure 5. (Continued)


94

100 1000SWP Velocity, km/s

1E+0

1E+1

1E+2

1E+3

1E+4O

ccur

renc

e nu

mbe

r

median = 420mean = 430mode = 370 ~ 390RMSD = 1.25SD = 1.26skewness = 0.42kurtosis = -0.32

c)

1E-3 1E-2 1E-1 1E+0He/p ratio

1E+1

1E+2

1E+3

1E+4

Occ

urre

nce

num

ber

median = 0.037mean = 0.034mode = 0.03 ~ 0.05RMSD = 1.97SD = 1.72skewness = -0.8kurtosis = 1.4

d)



95

1E-2 1E-1 1E+0 1E+1Pd, nPa

1E+0

1E+1

1E+2

1E+3

1E+4

Occ

urre

nce

num

ber

median = 2.mean = 2.mode = 1.8~2.2RMSD = 1.85SD = 1.74skewness = -0.01kurtosis = 1.7

−2σ +2σ

e)

1E-3 1E-2 1E-1 1E+0 1E+1

Sk, erg/cm2s

1E+0

1E+1

1E+2

1E+3

1E+4

Occ

urre

nce

num

ber

median = 0.43mean = 0.44mode = 0.37~0.49RMSD = 2.0SD = 1.92skewness = 0.08kurtosis = 1.3

−3σ +3σ

f)

Figure 5. Statistical distributions of the solar wind parameters represented in logarithmic scale for time interval from 1963 to 2007: (a) proton density, (b) proton temperature, (c) SW velocity, (d) He/p ratio, (e) dynamic pressure Pd, and (f) kinetic energy flux density Sk. Fitting by lognormal distribution function is shown by dashed line for good fit or by dotted line for poor fit. Vertical thin dashed lines restrict the best-fit intervals.


96

A characteristic feature of the solar wind density within the 2-σ interval is an anticorrelation with the SW velocity such that fast streams originating mainly in coronal holes in average have lower density than dense slow SW originating around coronal streamers [Ipavich et al., 1998]. Beyond of the 2-σ interval, the proton density distribution deviates from the lognormal PDF such that the wings of distribution become less steep. At small values, the 2-σ level restricts densities smaller than 1 cm-3. Interplanetary structures with very small proton density are associated with transient SW structures, in particular, expanding ejecta and post-shock flows [Richardson et al., 2000].

Most prominent deviation from the lognormal PDF is revealed at extremely small densities of n<0.4 cm-3. Note that the proton density can be less than 0.1 cm-3 for several hours [Usmanov et al., 2005], but the OMNI dataset has no information about such events, because the density is recorded only with one position after decimal point. Time intervals of extremely low densities, so-called SW disappearance events [Lazarus, 2000], are accompanied with stable unipolar magnetic field and highly nonradial SW flow, which is not associated with any transient structures [Crooker et al., 2000]. These density anomalies are caused by a rarefaction at the trailing edge of relatively fast flow that formed as a result of suppression of coronal outflow from a region that earlier provided fast wind flow [Usmanov et al., 2005]. The solar sources of the density anomalies are found as either active region open fields or small coronal hole boundaries embedded in or near large active region located close to central meridian [Janardhan et al., 2008].

The proton density distribution is slightly deviated from the PDF at densities above 20 cm-3. High densities are usually formed in the strongly compressed leading regions associated with CIRs and sheaths of CMEs, and in particular with interplanetary shocks [e.g. Borrini, et al., 1982a; Crooker et al., 2000]. Strongly compressed regions of high proton density can be also formed as a result of interaction between the leading or rear edges of ICME with the ambient SW [Bothmer and Schwenn, 1995; Dal Lago et al., 2001]. Extremely high densities (up to n~100 cm-3) are observed in solar eruptive filaments/prominences, which have characteristics of the chromosphere, i.e. consist of dense, cold material with abundance of He [Burlaga et al., 1998]. Note that the SW structures with extremely high densities have relatively short duration and, thus, the hourly averaged density reaches only maximum of 118 cm-3.

The distribution of SW proton temperature is fitted very well by the lognormal PDF in the range from ~10000 K to ~400000 K. Inside that range the temperature correlates with the SW velocity [Lopez, 1987] such that fast SW is much hotter than the slow one. Outside the 2-σ range, the wings of distribution turn down and go lower than the lognormal PDF, demonstrating a deficiency of extremely low and high temperatures. The deficiency can be also revealed from the comparison of the temperature dispersions: the calculated RMSD of 2.3 is less than standard deviation of 2.43 derived from the fitting.

Previous studies showed that the intervals of cold SW with proton temperature T<15000 K are often sustained for substantial periods, up to several days, accompanying a very slow SW propagating with speeds of 200 to 350 km/s [Freeman and Lopez, 1985]. It is claimed that the cold SW is not a separate component of the SW, but rather part of the continuum of the SW below 500 km/s, which satisfies a continuous linear relationship between the temperature and velocity [Lopez and Freeman, 1986]. In addition, plasma structures with very low proton temperature occur inside the ICME and in solar eruptive


97

filaments/prominences [Richardson and Cane, 1995; Burlaga et al., 1998]. Hence there should be no natural reasons for the deficiency of low-temperature events. To explain this discrepancy we can assume that the contribution of cold and slow SW to the total statistics might be reduced due to interaction with hot and fast SW streams, which sweep-away the slow solar wind.

In Figure 5b more prominent deficiency is found at very high temperatures of >400000 K. Those temperatures are associated mainly with the fast SW streams expanding from coronal holes at middle and high heliographic latitudes as revealed by Ulysses [McComas et al., 2003]. Because of curved heliospheric streamer belt, a portion of fast and hot SW streams can penetrate to the ecliptic plane. The deficiency of very high temperatures might indicate to restricted contribution of that portion of fast SW to the total statistics of temperature.

It is interesting to note a far tail of the statistical distribution at extremely high temperatures of >2 106 K. Such high temperatures are observed downstream of very strong interplanetary shocks [Skoug et al., 2004]. They are far exceed those predicted from empirical relationship between the temperature and speed [Lopez and Freeman, 1986]. The extremely high temperature is a result of conversion of the kinetic energy of the interplanetary disturbance into thermal energy of the shocked gas. Hence they are generated by such extremely fast SW transients as ICMEs.

From the above we can see that the thermodynamic properties of SW plasma are related with the SW velocity V. The statistical distribution of the SW velocity is different from the lognormal PDFs (see Figure 5c). The distribution has a relatively large positive skewness. The most probable of ~380 km/s is shifted toward lower velocities relative to the median of 420 km/s. In the linear scale (not shown), the distribution is even far from the normal PDF, because in that representation the mean value of 443 km/s differs very much from the median of 420 km/s and from the most probable of 360 ~ 380 km/s.

In the range from 300 km/s to ~700 km/s the statistical distribution has a very wide peak, which contains more than 95% of the total statistics of 265699 hourly averages. That wide peak is formed by various kinds of the solar wind from slow plasma streams in the heliospheric current sheet to fast streams from the coronal holes [e.g. Smith, 2001; McComas et al., 2003]. Note that the speed of fast streams correlates well with the size of coronal holes located near the central solar meridian [Veselovsky et al., 2006; Vrsnak et al., 2007].

It is interesting that the distribution extends smoothly from the peak of most probable to very high speeds of >800 km/s. Those fast SW streams are related to fast interplanetary transients, such as ICME and other eruptive events. Note that the highest SW speed of more than 2000 km/s was observed in the interplanetary sheath region leading by extremely fast ICME [Skoug et al., 2004].

The number of events with slow SW decreases abruptly at velocities below 300 km/s. That deficiency of very slow SW might be due the “sweep-away” effect, which was discussed above in regard to deficiency of very low SW temperatures. It is difficult to interpret the extremely slow SW speeds of ~200 km/s. Some of those events correspond to intervals of extremely low SW density. Others might be due to unaccounted encounters to the magnetosheath or comet tails [Baker et al., 1986; Oyama et al., 1986]. Further studies of that subject are required.


98

Table 2. Average values of the fluxes for the solar wind at the Earth orbit during 1963-2007.

Physical quantity

Formula

Mean value

Mass flux density

DVmJ p= 4.0⋅10-16

g/cm2⋅s

Momentum flux density (dynamic pressure)

2DVmP pd = 2.0⋅10-8

erg/cm3 (nPa)

Kinetic energy flux density

3

21 DVmS pk =

0.44 erg/cm2⋅s

Potential energy flux density

DVVmS gpp2

21

= ,

where skmVg /618=

1.7 erg/cm2⋅s

Enthalpy flux density for protons nTVSt 2

5= 6.8⋅10-1

erg/cm2⋅s

Magnetic energy flux density

π8

2BVSm = 6.1⋅10-3 erg/cm2⋅s

Based on the key plasma parameters, we calculate average physical numbers

characterizing the SW plasma flow at the Earth orbit (see Table 2). As we have found, most of the SW parameters have better representation in logarithmic scale, where their statistical distributions are very close to the lognormal PDF. The average values of physical numbers from the Table 2 have been also calculated in the logarithmic scale, i.e. those are geometric mean. In calculation we take into account that the SW density D is contributed by both protons with atom mass A=1 and helium ions with atom mass A=4.

)/41( pHenD ⋅+= , (12)

where n is concentration of protons per cubic centimeter and He/p is a ratio of helium content to proton concentration. Here we suppose that the speed of helium ions is equal to the speed


99

of protons. That assumption is reasonable because the average difference between the He and proton speeds was found in the SW observations of only about 10 km/s [Ogilvie et al., 1982].

Statistical distribution of the He to proton ratio is presented in Figure 5d. The shape of distribution is different from both lognormal and normal PDF. The skewness and kurtosis are relatively large. Helium to proton ratio is averaged about 0.04 and varies from 10-3 to ~0.3. In Figure 3c we can see that the data coverage for the He/p is poor. There are no data before 1970. More-less regular measurements started only in 1998. As a result, the He/p is known only for less than 50% of measurements in 1963 to 2007 and, thus, the statistics is not very representative. Usually the data gaps are filled by the average value of 0.04. This assumption is very rough. The statistical distribution of He/p ratio has a long tail toward very small values of ~10-3. Note that the ratio can be even smaller but in the OMNI dataset, only three positions after decimal point were used to record that value. In average, the He/p ratio correlates with the SW velocity [Aellig et al., 2001]. Smaller He/p ratio is characteristic of the slow SW in the heliospheric current sheet and the ratio of >0.04 corresponds to fast streams from coronal holes [Borrini et al., 1981; McComas et al., 2003]. Very high ratios of >0.1 occur within the ICMEs and eruptive filaments [Borrini et al., 1982b; Burlaga et al., 1998; Skoug et al., 2004].

Interaction of the SW plasma with planetary atmospheres and magnetospheres as well as with interstellar gas is controlled mainly by such important parameter as SW dynamic pressure Pd. The dynamic pressure is contributed by both proton and helium ion population, and, hence it is calculated as follow

251067.1 DVPd

−⋅= (13), The pressure Pd and velocity V are expressed, respectively, in nPa and km/s. Figure 5e shows the statistical distribution of SW dynamic pressure. The distribution is

fitted very well by the lognormal PDF within 2-σ vicinity of the median of 2 nPa, i.e. about 95% of statistics satisfy to lognormal distribution. The same properties of the dynamic pressure were revealed in previous studies of ~1 min averages of SW parameters measured by the ACE and Wind satellites, and of hourly averages from the OMNI data base [Dmitriev et al., 2002a; 2004; 2005c].

The distribution of Pd has zero skewness. However, pretty large positive kurtosis indicates to excess peakedness due to long tails of the distribution at small and high pressures. The tail at low pressures of <0.5 nPa is contributed mainly by low-density plasma structures. Small amount of slow SW streams is characterized by relatively high density, and hence does not contribute to the low-pressure tail. In contrast, the redundant statistics at high pressures of >7 nPa is mostly associated with fast SW transient events, which are often accompanied with dense regions of plasma compression. We should emphasize that SW structures with very low and very high dynamic pressure occupy only less than 5% of total statistics.

Statistical distribution of the kinetic energy flux density Sk presented in Figure 5f is very similar to the distribution of dynamic pressure. The distribution is fitted by the lognormal PDF within 3-σ vicinity of the median of 0.43 erg/cm2s, i.e. more than 98% of statistics are distributed lognormally. The skewness of distribution is zero and the kurtosis is relatively small. The moderate peakedness is due to excess of statistics at very small and very large magnitudes, which contribute only to less than 2% of statistics.


100

Interplanetary Magnetic Field

Numerous studies are devoted to statistical properties of the IMF at various heliocentric distances and in various time scales. Most of studies note that statistical distribution of IMF intensity B is different from the normal PDF. Some authors consider the lognormal PDF as the best fit for the distribution of B [Burlaga and King, 1979; Burlaga and Ness, 1998; Veselovsky et al., 1998b; 2000a; Burlaga, 2001b; Dmitriev et al., 2005c]. However, Feynman and Ruzmaikin [1994] considering 3-hour averages, found that the statistical distribution of B is different from the log-normal, because of non-zero skewness toward the small values, and relatively large positive kurtosis, corresponding to larger peakedness relative to a normal distribution. Hartlep et al. [2000] propose another approach of the IMF distribution in a form of fixed mean and normally distributed components. In particular, they reveal very good correspondence with the observed IMF statistical distribution when the normal component magnitude distribution is axisymmetric about the mean field (which is mainly aligned with the Archimedean spiral) but admits a high degree of variance anisotropy, with parallel variance much less than perpendicular variance. On the other hand, Bieber et al. [1993] revealed that the amplitudes of the spectra of variations are comparable for the IMF components, respectively, in the north-south direction, perpendicular to the Archimedean spiral in the ecliptic plane, and parallel to the Archimede spiral.

Figure 6a shows statistical distribution of the IMF intensity B represented in logarithmic scale. The distribution is very close to lognormal PDF within 2-σ and 1.5-σ deviations, respectively, toward low and high intensities relative to the average of 6 nT. So more than 95% of the statistics satisfy to the lognormal distribution. There are no any well-defined correlations of the magnetic field with other heliospheric parameters in that range. The skewness of distribution is relatively small. The positive non-zero kurtosis is due to pretty prominent wings, which exceed the lognormal PDF at very low and very high magnitudes and contribute less than 5% of total statistics.

The range of very weak IMF intensities of <2 nT contains less that 1% of the total statistics. Zurbuchen et al. [2001] studying the magnetic field depletions, or so-called magnetic holes, reveal that they can last for up to several hours. The magnetic holes are associated with increases in the SW density and temperature and large magnetic field rotations. However, they are not associated with large-scale magnetic field polarity changes. From analysis of the chemical composition, the authors conclude that the magnetic holes very likely develop in the heliosphere and are not of direct solar origin.

Very strong IMF of >13 nT is observed in 4% of cases, which are characterized by wide variability of the SW parameters from very small to very large values. An excess of strong fields relative to the lognormal distribution was reported in several studies [e.g. Burlaga and Szabo, 1999]. There are various physical processes contributing to the long tail at large IMF magnitudes. It is well known that the magnetic field can be enhanced significantly inside the ICMEs [Burlaga et al., 1987; 2001; Owens et al., 2005]. It was found that the IMF intensity correlates well with the speed of ICME [Owens and Cargill, 2002]. The IMF is also enforced in the interplanetary sheath and other compressed regions formed due to interaction of high speed structures with the ambient SW [Burlaga and King, 1979; Borrini et al., 1982a; Bothmer and Schwenn, 1995; Dal Lago et al., 2001; Owens et al., 2005].


101

1 10IMF B, nT

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

Occ

urre

nce

num

ber

median = 5.9mean = 6.0mode = 5.5~6.6RMSD = 1.55SD = 1.48skewness = 0.12kurtosis = 0.85

−2σ +1.5σ

a)

1 10IMF Bxy, nT

1E+0

1E+1

1E+2

1E+3

1E+4

Occ

urre

nce

num

ber

median = 4.6mean = 4.5mode = 4.3~4.7RMSD = 1.74SD = 1.55skewness = -0.78kurtosis = 2.8

−1.2σ +1.4σ

b)

Figure 6. Statistical distributions of the IMF for time interval from 1963 to 2007 in logarithmic scale: (a) strength B, (b) projection of the IMF vector onto the ecliptic plane Bxy. Dashed curves depict the best fit of the B and Bxy by the lognormal PDF. Vertical thin dashed lines restrict the best-fit intervals.


102

The vector of IMF can be presented as a sum of three orthogonal components Bx, By, and Bz. In the GSE coordinate system, X-axis is pointed to the Sun, Y-axis lies in the ecliptic plane and directed duskward, and Z-axis is perpendicular to the ecliptic plane and directed northward. Projection of the IMF vector to the ecliptic plane Bxy is simply presented as the vector sum of Bx and By components: yxxy BBB

rrr+= , and the magnitude of Bxy is equal to

22yxxy BBB +=

r.

Statistical distribution of the Bxy magnitude is presented in Figure 6b. It is close to the

lognormal PDF with average of 4.6 nT within a narrow interval from –1.2 to 1.4 standard deviations, i.e. ~80% of the total statistics of Bxy satisfy to lognormal distribution. The distribution is slightly skewed toward small values. That skewness is mainly due to very prominent tail extending to small magnitudes. The tail together with excess of large values of Bxy leads to a pretty large positive kurtosis and large RMSD=1.74 relative to the standard deviation of 1.55. The tail at large magnitudes of Bxy (>10 nT) has apparently the same nature as the tail of high IMF intensities. The abundant statistics at small values of Bxy (<2 nT) is mainly contributed by the variations of IMF orientation in Alfvén waves and will be discussed later.

We find that the problem of lognormal distribution of IMF intensity comes to a problem of lognormal distribution of the component Bxy in the ecliptic plane. The statistical distribution of Bxy has been studied in detail by Luhmann et al. [1993] on the base of an ideal Archimedean spiral model of IMF. In that model the solar magnetic field is stretched out to a spiral by the expanding SW plasma from the rotating Sun. As a result, the radial Bx component decreases as a square of distance from the Sun and the tangential By component is formed due to rotation of the Sun. The Bx and By components decrease inversely proportional with distance. In this model the changes in SW velocity should anticorrelate with the changes in magnitude of Bxy. Luhmann et al. [1993] found that the IMF vector is indeed oriented along the Archimedean spiral but they did not find distinct anticorrelation between the velocity and Bxy magnitude. Following to King et al. [1981] the authors concluded that the solar source field variation must play an important role in the observed variability of IMF at the Earth orbit.

In Figure 7 we show statistical distributions of the IMF components Bx and By as well as two-dimensional probability distribution P(Bx, By). The distributions of Bx and By have a typical two-peak shape with long tails as reported in previous studies [Luhmann et al., 1993; Dmitriev et al., 2004]. The peaks are situated at about 3 nT. Apparently, those peaks correspond to the average value of Bxy =4.5 nT. The long tails correspond to the excess of large values in the Bxy statistical distribution.


103

-10 -5 0 5 10

Bx, nT

-10

-5

0

5

10

By, n

T

0E+0

1E+4

2E+4

3E+4O

ccur

renc

e nu

mbe

r

Bx

0E+0 2E+4 4E+4Occurrence number

By

Figure 7. Statistical distribution of the IMF Bx and By components in GSE coordinate system. Two-dimensional distribution is presented in rainbow color scale: from small occurrence numbers of a few counts (violet) to maximum statistics of >500 counts (red). The top and right histograms represent statistical distributions of the Bx and By component, respectively. The distributions of Bx and By components correspond to predominant orientation of the IMF vector along the Archimedean spiral, which has an angle of ~135° relative to the sunward direction (pointed by positive Bx).

The two-dimensional distribution of the components Bx and By has a long ridge corresponding to a predominant orientation of the Bxy vector along a line, which is inclined on ~-45° relative the X-axis. The same predominant orientation of the IMF was reported earlier [e.g. Luhmann et al., 1993; Veselovsky and Tarsina, 2001]. This orientation is very close to the Archimedean spiral. In the solar equatorial plane the angle α between the Archimedean spiral and the X-axis is calculated as follow:

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

Vr

sτπα 2tan 1 , (14)


104

where r is heliocentric distance, V is the SW velocity and τs=25.4 days is the sidereal rotation period of the Sun at the equator. Taking distance r=1.5 108 km and median SW velocity of 420 km/s directed antiparallel to the X-axis, we obtain α=-45° at the Earth orbit.

We should emphasize that the predominant orientation along the Archimedean spiral is revealed even at very large Bxy magnitudes of >15 nT. Such strong magnetic field in the ecliptic plane can not be only the result of field line stretching. The ecliptic magnetic field described by the ideal Parker spiral model is given by

22212

0 /VrraBBxy Ω+= −− (15)

were a is the radius of the solar source surface. Using this equation we simply estimate that variations of the solar wind velocity with average of 420 km/s and dispersion of ~1.25 (see Table 1) cause the relative variation of ~1.24 in the Bxy magnitude. That variation is apparently smaller than logarithmic RMSD of 1.74 and standard deviation of 1.55, which we find from the statistical distribution of the Bxy (Figure 6b).

Hence it is rather possible that significant part of the Bxy variations is originated from solar sources. Variations of the Archimedean spiral angle from α~-55° in slow SW (V=300 km/s) to α~-31° in the fast SW (V=700 km/s) also contribute to a pretty large dispersion of the ridge of most probable values in the two-dimensional distribution P(Bx,By) presented in Figure 7.

Another important heliospheric phenomenon contributing to the dispersion of magnetic field components is large-amplitude Alfvén waves propagating outward from the Sun [Belcher and Davis, 1971; Tsurutani and Gonzalez, 1987; Tsurutani et al., 1995]. They have a broad wavelength range up to 5 106 km and beyond, which corresponds to period of hours. Most Alfvén waves in the interplanetary medium are likely the undamped remnants of waves generated at the Sun. They occur mainly in high-speed SW streams and on their trailing edges where the velocity slowly decreases. In the Alfvén waves, the magnetic field orientation varies such that one IMF component increases and another decreases. As a result, those variations can contribute a lot to the statistics at both very small and large values of Bxand By. The largest amplitude Alfvénic fluctuations of ~10 nT in the IMF component are observed in the compression regions at the leading edges of high-velocity streams, i.e. in the CIR region.

The Alfvén waves are one of the sources of IMF fluctuations perpendicular to the ecliptic plane, i.e. variations of the Bz component, which statistical distribution is presented in Figure 8a. The distribution has a zero skewness and can be fitted well by a normal PDF within 2-σ interval (i.e. ±4.18 nT) around the average of 0 nT. However the RMSD of 3.1 nT is much larger than the standard deviation SD of 2.1 nT, because of presence of very prominent tails, which contain about 13% of the total statistics. Because of those tails the kurtosis is positive and very large. The large peakedness of the Bz distribution is also reported by [Feynman and Ruzmaikin, 1994]. The excess of large Bz magnitudes can be explained by the Alfvén waves only partially. Large Bz is generated due to compression in the CIR regions and in the interplanetary sheaths. In the latter case the Bz can achieve extremely high values but for a short time. The long-duration large and extremely large Bz occurs in the ICME and as a result of interaction between the ICME and other SW structures [Bothmer and Schwenn, 1995; Dal Lago et al., 2001].


105

-40 -20 0 20IMF Bz, nT

1E+0

1E+1

1E+2

1E+3

1E+4O

ccur

renc

e nu

mbe

rmedian = 0.mean = 0.mode = -0.6~1.5RMSD = 3.10SD = 2.09skewness = -0.01kurtosis = 9.1

+2σ−2σ

a)

-30 -20 -10 0 10 20 30Ey, mV/m

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

Occ

urre

nce

num

ber

median = 0.mean = 0.mode = -0.4~0.2RMSD = 1.6SD = 1.0skewness = -0.1kurtosis = 23

+2σ−2σ

b)

Figure 8. Statistical distributions of (a) IMF Bz component and (b) Y-component of induced interplanetary electric field Ey for time interval 1963 to 2007. Dashed curve depicts the fitting by normal PDF. Vertical thin dashed lines restrict the best-fit intervals.


106

The IMF Bz and induced interplanetary electric field V×B play a key role in transmission of the SW energy into the Earth’s magnetosphere and hence control the system of magnetospheric currents [Burton et al., 1975; Akasofu, 1979; Iijima and Potemra, 1982; Tsyganenko, 2002a,b; Tsurutani et al., 2004]. Geoeffective Ey component of the induced electric field is defined as follow:

zxy BVE ⋅= −310 (16)

Here the radial component of the velocity V is negative and expressed in km/s, Bz in nT

and Ey in mV/m. Note that in this case the IMF component Bz is represented in the GSM coordinate system, which is related to the orientation of the Earth dipole axis projection to YZ plane. In the GSM system the Z component is contributed mainly by the IMF Bz and partially by the By components represented in the GSE coordinate system.

Statistical distribution of the induced electric field Ey is presented in Figure 8b. The distribution is similar to one of the Bz (Figure 8a). It is well fitted by the normal PDF within 2-σ interval from –2 to 2 mV/m around the zero average. The distribution is symmetrical relative to the mode (skewness k3=0). The kurtosis is large because of great excess of large Ey magnitudes, which form prominent wings extending up to extremely high values of ~30 mV/m. As a result only 88% of the statistics at relatively low Ey magnitudes are distributed normally. The wings are contributed by both the excess of large intensities of the IMF Bz (see Figure 8a) and the abundant statistics of the fast SW streams (see Figure 5c). Note that the strongest magnitudes of Ey occur in extremely fast interplanetary transients (ICME and related sheath regions), which often contain very strong IMF Bz.

Burton et al. [1975] found a criterion for the onset of geomagnetic storms: a storm starts when the Ey is larger than 0.5 mV/m. Using the statistical distribution of Ey we can find that the criterion is satisfied in 30% of cases. So about one third of time the magnetosphere stays under magnetic storm conditions.

Relevant Physical Quantities

Using the measured parameters of SW and IMF, we calculated various quantities characterizing average physical properties of the interplanetary medium at the Earth orbit and listed them in Tables 2, 3 and 4. In the previous sections we found that statistical distributions of all measured parameters of the solar wind and IMF intensity are very close to lognormal PDF. It is easy to show that the lognormal distribution is multiplicative, i.e. multiplication/division of two random variables distributed log-normally has also lognormal distribution. As an example we can indicate the log-normally distributed SW dynamic pressure Pd. Hence physical quantities being a multiplication of log-normally distributed measured parameters should be represented in the logarithm scale. So we calculate average logarithms of the physical quantities (Equation 8).


107

Table 3. Mean heliospheric plasma conditions at the Earth orbit during 1963-2007.

Physical quantity Formula Mean value

Alfvèn velocity

pA nm

BVπ4

= 56.8 km/s

Sonic velocity for protons

pS m

Tc35

= 33.7 km/s

Alfvèn-Mach number

AA V

VM = 7.7

Sonic Mach number for protons

SS c

VM = 13.

Gas-kinetic proton pressure (Thermal proton pressure)

nTPt = .62⋅10-10 erg/cm3

(10-2 nPa) Magnetic pressure

π8

2BPm = 1.4⋅10-10 erg/cm3

(10-2 nPa) Proton gas-kinetic to magnetic pressure ratio

2

8B

nTp

πβ = 0.43

Coulomb collision time for electrons

12/3210 −−≅ nTeeτ ~9.9⋅104 s

Coulomb collision time for protons

12/36.0 −≅ nTppτ ~2.9⋅106 s


108

Table 4. Main plasma characteristics calculated for mean heliospheric parameters at the Earth orbit during 1963-2007.

Physical quantity Formula Mean value

Plasma frequency

emne2

04πω =

1.30⋅105 s-1

Electron cyclotron frequency

cmeB

ece =ω

1.04⋅103 s-1

Proton cyclotron frequency

cmeB

pcp =ω

0.56 s-1

Upper hybrid frequency

( ) 0

2/12201 ωωωω ≈+= ceh

1.30⋅105 s-1

Lower hybrid frequency

( ) 2/12 cecph ωωω =

24.1 s-1

Mean thermal speed of protons

pp m

TV 3=

45.8 km/s

Larmor radius for protons

cp

pp

Vr

ω=

81.8 km

Average values of the energy, momentum and mass fluxes for the SW are shown in Table

2. Note that here we consider SW density D which accounts the helium contribution (Equation 12). One can see that the largest energy flux density is carried in the shape of potential and kinetic energies of the solar wind. The density of enthalpy (thermal) and magnetic energy fluxes are smaller on about 2 orders of magnitude. The total energy flux density of ~2.3 erg cm-2 s-1 amounts only a small portion of the total energy flux density emitted by the Sun in the form of electromagnetic radiation [Veselovsky et al., 1999].

Mean heliospheric plasma and IMF quantities are listed in Table 3. In the present case we use only proton concentration n and temperature T in the solar wind. The neglect of helium contribution leads to ~10% overestimation of the Alfvèn speed, while the Alfvèn Mach number is underestimated on ~10%. Other plasma quantities such as the sonic speed cs, sonic Mach number Ms, gas-kinetic pressure Pt and plasma β depend strongly on electron temperature, which is not available in most cases.


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The electron temperature Te varies in very wide range from ~5 104 to ~106 K, and it has only very weak correlation with the proton temperature [Newbury et al., 1998; Salem et al., 2003]. It was found that in average the electron to proton ratio Te/T varies from 0.5 in the fast wind with velocities of ~700 km/s to ~4 in the slow solar wind. The average electron temperature is ~1.4 105 K, i.e. almost two-time higher than the average proton temperature of 8.5 104 K (see Table 1). Hence neglect of the electron temperature may lead to ~50% underestimation of the sonic speed cs and 50% overestimation of the sonic Mach number Ms. The magnitudes of gas-kinetic pressure Pt and plasma β might be about two-time underestimated. That is only rough estimation, because of the absence of electron temperature data.

From Table 3 we can conclude that in average the SW flow at the Earth orbit is supersonic (Ms>1) and superalfvènic (Ma>1). Interaction of such SW with the magnetosphere obstacle causes generation of fast magnetosonic wave enveloping the magnetosphere, or so-called bow shock [e.g. Spreiter et al., 1966]. The Alfvènic and sonic Mach numbers and plasma β are the key parameters controlling the bow shock formation, i.e. conditions for SW flow about the magnetosphere [e.g. Dmitriev et al., 2003]. Statistical distributions of dimensionless quantities Ma, Ms and β are presented in Figure 9. As one can see, those distributions can be well fitted by a lognormal PDF as reported before by Dmitriev et al. [2003]. Similar behavior was found with 1 min data [Mullan and Smith, 2006].

1E+0 1E+1 1E+2Ma

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

Occ

urre

nce

num

ber

median = 8.4mean = 8.4mode = 8.~9.4RMSD = 1.54SD = 1.44skewness = 0.03kurtosis = 1.7

−1.7σ +1.7σ

a)



110

1E+1Ms

1E+0

1E+1

1E+2

1E+3

1E+4O

ccur

renc

e nu

mbe

r median = 12.7mean = 13.mode = 11.~13.8RMSD = 1.35SD = 1.3skewness = 0.57kurtosis = 1.3

−2σ +1.2σ

b)

1E-3 1E-2 1E-1 1E+0 1E+1beta

1E+0

1E+1

1E+2

1E+3

1E+4

Occ

urre

nce

num

ber

median = 0.48mean = 0.43mode = 0.44~0.65RMSD = 2.61SD = 2.12skewness = -0.92kurtosis = 2.5

−1.75 σ +4 σ

c)

Figure 9. Statistical distributions of the dimensionless quantities in logarithmic scale for time interval 1963 to 2007: (a) Alfvén-Mach number Ma, (b) Sonic Mach number Ms, and (c) thermal to magnetic pressure ratio β. The distributions are fitted well by the lognormal PDF shown by dashed line. Vertical thin dashed lines restrict the best-fit intervals.


111

The distribution of Alfvèn Mach number (Figure 9a) is very close to the lognormal PDF within 1.7-σ interval around the average of 8.4 that contains ~95% of total statistics. The distribution has zero skewness and relatively large positive kurtosis, which is caused by abundant statistics at small and large Ma values. From analysis of statistical distributions of the SW velocity, density and IMF intensity, we can find that the tail of relatively small values of Ma can be contributed by relatively small SW densities and/or strong IMF. Such conditions often occur inside ICMEs. It is important to note the excess of extremely small values of Ma, which can be sometimes less than 1. Correction to the He abundance helps a little. Hence in some very rare cases the SW can be subalfvènic. Usmanov et al. [2005] have studied this problem and find that events of very low Alfvèn Mach number at the Earth orbit are associated mainly with extremely low SW density (<0.3 cm-3) and only few events are due to very high IMF intensity of >10 nT. On the other hand, the extremely high Ma can occur inside the magnetic holes [Zurbuchen et al., 2001].

Contrary to the Ma, the sonic Mach number Ms is always larger than 1, as we can see from its statistical distribution in Figure 9b. About 92% of the Ms statistics is fitted well by the lognormal PDF in the range from 5 to 20 with average of ~13. The events with very low Ms of <4 are very rare. The positive skewness and relatively large positive kurtosis are due to the excess of large values of Ms. The tail of large Ms can be contributed by fast and cold SW structures, such as fast ICMEs.

Figure 9c shows statistical distribution of the thermal to magnetic pressure ratio (plasma β). The distribution is close to the lognormal PDF with mode of 0.48 and standard deviation of σ=2.12 within interval restricted by lower limit of -1.75σ (β~0.1) and upper limit of 4σ (β~4). About 89% of the statistics are covered by the lognormal distribution. The skewness of statistical distribution is large negative and the kurtosis is relatively large positive because of significant excess of small values, which form a long tail extending to very small β of <10-3. In that region the magnetic pressure Pm is dominant and exceeds the gas-kinetic pressure Pt on orders of magnitude. This tail is contributed by cold plasma structures of SW with strong magnetic field, such as ICMEs and heliospheric current sheet. It is important to note that accounting the electron temperature leads to increase of the average value of β up to 1 and even more and can modify the tail of low β because the slow SW streams in the heliospheric current sheet are characterized by very high electron temperature contribution (Te/T~4). Hence the problem of very low β is a subject of future studies.

Considering statistical distribution of β we find that the thermal energy of the SW plasma Pt is comparable or even less than the energy of interplanetary magnetic field, Pm. Both of them amount of about 10-10 erg/cm3 (see Table 3). That is at least two orders of magnitude less than the SW plasma momentum flux density (or dynamic pressure, Pd), which amounts of 2•10-8 erg/cm3 at the Earth orbit (see Table 2). Note that under some circumstances inside the ICMEs the dynamic pressure Pd can be reduced by several times because of low density, and becomes comparable with significantly enhanced pressure of very intense magnetic field.

3. Characteristic Periodicities

Study of periodicities in dynamics of the heliospheric parameters is difficult because of very large amount (~30%) of data gaps having a wide range of durations (see Figures 3 and 4).


112

This problem is solved using various methods for sparse data processing from simple averaging and smoothing to interpolation by polynomials and splines. Also various techniques are applied for studying of periodicities in long time profiles of the heliospheric parameters containing hundreds of thousand data points such as widely used fast Fourier transform (FFT), wavelet techniques, spectral wave analysis (SWAN diagrams) and sophisticated methods of maximum entropy and singular spectrum analysis [e.g. Szabo et al., 1995; Rangarajan, and Barreto, 2000; Veselovsky and Tarsina, 2002b; Mursula and Vilppola, 2004; Kane, 2005].

In the present study we use a method of Fourier transform for unequally-spaced data proposed by Deeming [1975]. That method does not need any specific data processing for elimination of the data gaps. Only linear detrending of the data is desirable. Obviously, the spectrum derived by that method suffers from frequency interference, which is caused by both the finite data length and data spacing. The interference produces numerous subsidiary peaks. In this situation it is rather difficult to distinguish between the meaningful and spurious peaks. One of the ways to resolve this problem is a method of reducing statistics [Dmitriev et al., 2000]. Namely, the initial data set is reduced chaotically by increasing the number of data gaps with a random duration and spacing. The meaningful peaks survive even after the statistics reduction on several tens of percent (up to 85%). The subsidiary peaks change fast with the reduction, i.e. their amplitudes and locations vary and new peaks occur.

We should note that ‘meaningful’ in this context does not mean any quantitative, but only some qualitative characterization and indication for future more rigorous and complete studies. The method of integral Fourier transforms and all its modifications as applied for finite, non-complete non-stationary data sets obtained with a finite time resolution and accuracy of noisy data has its own limitations and restricts correct interpretation of obtained ‘periodicities’ with non-defined reservations from the side of high (Nyquist sampling) and low (finite data set length) frequencies as well as spurious harmonics. We caution the reader against straight applications of results without notification of accuracy and stress their illustrative and very preliminary nature only. The same can be said also about subsequent periodicities described below.

One can easily reveal by using all these methods the robust signatures of the presence of the solar cycle, the Earth rotation and the Sun rotation signals in the SW and IMF data obtained near the Earth. They are seen as a group of peaks in periodograms around corresponding characteristic durations of ten years, a year and a month, correspondingly. The accuracy and the reliability of numbers characterizing the positions and amplitudes of individual peaks is highly limited and not analyzed. Because of this, there is no big physical sense in all these details, which are not quantified in the present study, as well as in many similar works. Nevertheless, they are traditionally marked also in our study only for the purpose of further studies. As for eigenfrequecies of the solar oscillations manifested in the SW and IMF parameters [Thomson et al., 2002], there is no unique interpretation as yet in our opinion.

Solar Periodicities

Periodogram of daily sunspot number variations in 1963 to 2007 is presented in Figure 10. The periods are changed consequently from 3 days to 16437 days (45 years) with a step of 1-


113

day. In calculation of spectral amplitudes we use logarithm of the sunspot number W, because the lognormal scale is more representative, as we have demonstrated in the previous section (see Figure 2). The zero magnitudes of W are considered as data gaps. Hence this periodogram contains mainly information about the rising, maximum and declining phases of the four solar cycles 20 to 23.

Strongest amplitude is revealed for the solar cycle periodicity of 10.6 years. This period is a result of superposition of two strong 10-year cycles with two relatively weak 12-year cycles. As we can see in Figure 10, the four last solar cycles do not demonstrate 22-year period in sunspot number. This is because of weak 23rd solar cycle [e.g. Dmitriev et al., 2005c]. That cycle breaks a so-called “Gnevyshev-Ohl” empirical rule that the odd cycles are higher than the previous even cycles [Gnevyshev and Ohl, 1948]. Such violations happened also in more distant epochs. Tentatively they could be associated with longer secular cycles and trends. Physical origins of solar cycles are not known. They can be the internal property of the Sun as a star and its dynamo action as mostly believed now. Otherwise, planetary influences and interstellar causes could be involved. For example, it is believed sometimes that orbital rotation of giant planets (Jupiter, Saturn, Uranus and Neptune) is a natural source of the solar activity north-south asymmetries, and decadal and secular variations in the range of periods from ~11 years to ~165 years [e.g. Juckett, 2000].

1E+1 1E+2 1E+3 1E+4Period, Days

0.0

0.1

0.2

0.3

0.4

Am

plitu

de

Sunspot Number W

28 days

5.3 years

10.6 years

131 days

3.5 years

Figure 10. Periodogram of the sunspot number W for time interval 1963 to 2007. Some characteristic periods are indicated by vertical dashed lines.


114

Periods of 5.3 years and 3.5 years may correspond, respectively, to 1/2 and 1/3 of the 10.6-year solar cycle. Similar oscillations with 5.2-year and 3.2-year periods as well as ~2.5-year and ~1.9-year periodicities have been also found being meaningful from analysis of the sunspot number variations in 1975-2001 by a method of maximum entropy [Kane, 2005]. Recently different authors report those periodicities for various solar indices such as solar magnetic field, coronal index etc. [Kane, 2005; Mavromichalaki et al., 2005]. Using a basic wavelet technique for analysis of the solar magnetic flux, Valdés-Galicia et al. [2005] reveal periodicities of ~5, ~3, ~1.7, and ~1.3 years and demonstrate their alternating importance during consecutive odd 21st and even 22nd solar cycles. Mavromichalaki et al. [2005] also mention about variability of amplitudes and periods of the solar periodicities in the range from 0.5 year to 3 years. Note that the periods less than 3 years have relatively small amplitudes.

It is rather difficult to judge whether the periods of several years are sub-harmonics of the ~11-year solar cycle, i.e. correspond to double and triple etc. frequencies, or they are manifestations of physical processes driving the solar activity. In Figure 1 we can find that the smoothed sunspot number demonstrates various periodicities, which vary from cycle to cycle. For example, during maximum and declining phase of the 20th cycle we clearly see variations with ~2-year period. However during the 21st cycle a 1-year period prevails. The rising and declining phases of cycles 22nd and 23rd are smooth and have no any preferable periods. Prominent quasi-biennial variations during solar maxima are associated with so-called Gnevyshev gaps and the solar magnetic field reversal [Gnevyshev and Ohl, 1948]. Recently Charvátová [2007] has claimed that the period of 1.6, 2.13 and 6.4 years are associated with the solar interior motion due to disturbing effects from the rotation of terrestrial planets Mercury, Venus, Earths and Mars. Numerical estimation of the power and significance of the planetary effect to the solar variations is a subject for further investigations.

A periodicity around of 28 days in Figure 10 is apparently associated with the synodic period of the Sun rotation as seen from the Earth (27.3 days). The synodic period is also found in various solar indices [e.g. Mursula and Zieger, 1996; Mavromichalaki et al., 2005]. In Figure 10 we find a periodicity of ~131 days, which is related neither to the solar rotation nor to the solar cycle. The 131-day period is revealed in hard X-ray flare activity during declining phase of solar cycle 23 [Jain et al., 2008]. The nature of that period is still unclear.

SW Periodicities

The periodicities of heliospheric parameters having 1-hour time resolution are studied using quasi-logarithmic fragmentation of the periods. Namely, in the range of periods from 1 to 100 days we use 6-hour step, and further in ranges of 100 days ~ 1.1 year, 1.1 ~ 5.5 years, 5.5 ~ 11 years, and > 11 years we use respectively, 12-hour, 1-day, 10-day and 1-month steps. The fragmentation helps to reduce the calculation time. Note that changing the fragmentation does not affect significantly on the resultant periodicities.

Figure 11 demonstrates periodograms of the SW parameters. We analyse the logarithms of magnitudes of parameters. We do not consider periods longer than solar cycle because they are affected by interference with the finite length of data sets. As one can see in Figure 11a, the periodicities of solar wind proton velocity and temperature are very close.


115

1E+0 1E+1 1E+2 1E+3 1E+4Period, Days

0.000

0.005

0.010

0.015

0.020A

mpl

itude

SWP Velocity27.3 days

13.5 days

9.7 years

1.6 year

5 years

9 days

1.3 year

3.5 years

1 year

0.00

0.01

0.02

0.03

0.04

0.05

SWP Temperature0.48 year

a)


0.00

0.01

0.02

0.03

0.04

0.05

Am

plitu

de

SWP Density

27.3 days

13.5 days

5 years

10.2 years

1.5 years

9 days

0.49 year

2.6 years

6.3 years

0.0

0.0

0.0

0.0

0.0

0.0

1 year

SWP Pd

11.4 years

b)

Figure 11. Periodogram of the solar wind plasma parameters for time interval 1963 to 2007 (a) proton velocity (black curve) and temperature (grey curve, right axis); (b) density (grey curve, right axis) and dynamic pressure Pd (black curve). Characteristic periods are indicated by vertical dashed lines. The alternating period of 1.3 year is indicated by vertical dashed dotted line.


116

The periods of 27.3 days, 3.5 years and 5 years practically coincide with the characteristic periods in sunspot number. We can also find periods of 13.5 days and 9 days, which are observed for practically all heliospheric parameters and correspond, respectively, to 1/2 and 1/3 of the solar synodic period of 27.3 days [Mursula and Zieger, 1996; Dmitriev et al., 2000; Neugebauer et al., 2000; Burlaga and Forman, 2002; El-Borie, 2002; Bolzan et al., 2005]. Mursula and Zieger [1996] demonstrate that the ~9-day and 13.5-day sub-periods might be spurious due to the effect of interference with data gaps. On the other hand the periodicity of 13.5 days can be a manifestation of four-sector solar wind structure. Note, that this question needs more investigation in future with a more complete data set.

The period of 9.7 years is shorter than the 10.6-year solar cycle in sunspot number. The relatively short cycle in the solar wind velocity and temperature is also found in previous studies [Dmitriev et al., 2000; Neugebauer et al., 2000; Rangarajan and Barreto, 2000; El-Borie, 2002; Kane, 2005]. This period might be related to ~9.6 year periodicity of solar coronal-hole area [McIntosh et al., 1992]. As we know, the solar wind velocity correlates with the size of coronal holes [Veselovsky et al., 2006; Vrsnak et al., 2007].

In Figure 11a we find relatively strong variations with period of 1.3 years in the velocity and 1.6 years in the temperature. The latter one can be attributed to the effect of terrestrial planet [Charvátová, 2007]. Numerous studies regard the 1.3-year periodicity [Richardson et al., 1994; Gazis et al., 1995; Paularena et al., 1995]. A method of dynamic power spectrum [Szabo et al., 1995] and wavelet transform [Mursula and Vilppola, 2004] demonstrate the alternating importance of 1.3-year period, which is dominant during the 22nd cycle and vanishes in the 21st solar cycle. Rangarajan and Barreto [2000] show that the 1.3-year period alternates with 3.5-year and 5-year periodicities of the SW velocity. It is reasonable to assume that the 1.3-year period might be an 1/8 harmonic of the solar cycle.

In Figure 11 we also find periods of 1 year and ~0.5 year, which are apparently associated with the Earth’s orbital rotation. Note that the annual periodicity of solar wind velocity is revealed only in the near-Earth’s experiments, while the Voyager 2 and Pioneer 10 missions do not observe that periodicity in the outer heliosphere [Mursula and Vilppola, 2004]. The annual periodicity is originated from two geometric effects: 7° tilt of ecliptic plane relative to the solar equator, and nonzero eccentricity of the earth orbit with perihelion of 146•106 km and aphelion of 152•106. As a result, the Earth orbital rotation is characterized by annual variation of heliographic latitude within the range from -7° to 7°, and ~4% variation of the heliocentric distance. The north-south asymmetry of the Sun can be involved for a tentative explanation of the annual variations. The annual variations have been found in the solar wind plasma velocity, density and temperature [Dmitriev et al., 2000; Neugebauer et al., 2000].

Periodicities of the SW density and dynamic pressure are presented in Figure 11b. They have similar solar synodic and annual periods. The SW density demonstrates the periods of 5 years, 6.3 years and 11.4 years. The 5-year period corresponds to the sunspot number periodicity of 5.1 years, while the 6.3-year period might be associated with the effect of terrestrial planets [Charvátová, 2007]. Note that the sunspot period of 3.5 years is absent in the solar wind density.

The amplitudes of 5-year and ~6.3-year variations in the density are comparable with the 11.4-year peak. Unexpected and high significance of the five-year wave in the proton density


117

variations was reported for solar cycles 20th to 22nd [Dmitriev et al., 2000] and also partially for the 23rd solar cycle [Kane, 2005].

The solar wind dynamic pressure (Figure 11b) is characterized by periods of 1.5 years, 2.6 years, 6.3 years and 10.2 years. Note that the pressure is a multiplicative parameter of the solar wind velocity and density. In this context the 1.5-year and 6.3-year periods are inherited, respectively, from the velocity and density. The period of 2.6 years might be a meaningful result of interference between the 5-year periodicity in the density and 1.6-year periodicity in the velocity. By the same way the period of 10.2 years might be a superposition of the velocity and density cycles.

IMF Periodicities

Periodograms of the IMF intensity B and magnitude of Bxy component are presented in Figure 12a. As one can see, their profiles are practically identical. Hence the variation of magnetic field in the ecliptic plane is the major source of the IMF variations. They are represented by solar synodic harmonics and annual variations. Their cycle periodicities are very close to the sunspot number characteristic periods of 3.5 years, 5.3 years and 10.6 years. There are a number of reports about pretty strong 1.7-year periodicity observed in the IMF intensity at the Earth’s orbit during 20 to 23 solar cycles [Rouillard and Lockwood, 2004; Mursula and Vilppola, 2004]. Indeed, in Figure 10a one can distinguish a moderate intensification around the period of ~1.7 years (~600 days). This period can be probably attributed to the 1/6 harmonic of the IMF cycle, i.e. 10.3 / 6 ≈ 1.7 years.

The basic solar synodic period of 27.3 days is absent in the variations of magnetic field intensities. This fact is revealed in several studies but its origin is not clear [Mursula and Zieger, 1996; Dmitriev et al., 2000; Rouillard and Lockwood, 2004]. It is pretty possible that diminishing of the 27.3-day periodicity is related to substantial enhancements of the IMF intensity in the corotating interaction regions. Because of tilted and curved sector boundary, the CIRs pass the Earth at least two times per solar rotation, i.e. the period of 27.3 / 2 = 13.6 days should be dominant for the IMF B and Bxy intensities.

Figure 12b shows periodograms of the IMF Bx and By components. They have very similar periodicities, which however are different from those in IMF intensity. Note that the variable-polarity components are analyzed in linear scale, while the intensities are converted to logarithms. Variations of the Bx and By components are characterized by dominant periods of 27 days and 1 year. Neugebauer et al. [2000] obtain the same result for the Bx component. It is suggested that the 27-day period is most prominent because the Earth encounters two IMF sectors per solar rotation. The annual variation of the Earth’s heliographic latitude modulates the duration of encounters to the north or south IMF sector.

It is important to emphasize that the solar cycle period and its harmonics vanish in the periodograms of variable-polarity components as mentioned by Neugebauer et al. [2000]. Figure 12b illustrates this fact clearly. The amplitudes of ~3-year, ~5.9-year and 9.8-year periodicities diminish and only ~20-year cycle is still prominent. Note that the solar cycle in the Bx and By components is represented by the period of ~9.8 years. This period is close to the 9.7-year cycle in the solar wind plasma velocity and temperature that is attributed to variations of the size of unipolar solar coronal holes [McIntosh et al., 1992].


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Figure 12. Periodogram of the IMF parameters for time interval 1963 to 2007: (a) strength (black curve) and Bxy component (grey curve, right axis); (b) Bx (black curve) and By component (grey curve, right axis); (c) magnitudes of IMF components Bz (black curve) and Bx (grey curve, right axis), (d) Bz component (black curve) and Ey component of induced electric field (grey curve, right axis). Characteristic periods are indicated by vertical dashed lines.

The above effects disappear when we consider intensities (i.e. absolute values) of the IMF components. Figure 12c shows periodograms of the absolute values of IMF Bx and Bz. They are pretty similar one to other and they both very close to the periodograms of IMF B and Bxy intensities (see Figure 12a). Namely, the periodicities are represented by the cycle of 10.4 years, which is very close to the solar cycle of 10.6 years, and by harmonics of 10.4 / 2 = 5.2 years, 10.4 / 3 ≈ 3.4 years, 10.4 / 6 ≈ 1.7 years. There are two strong periodicities of 1 year and 13.5 days, while the solar synodic period of 27.3 days practically vanishes.


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Figure 13. Periodogram of the dimensionless parameters for time interval 1963 to 2007: (a) Sonic Mach number Ms (black curve) and thermal to magnetic pressure ratio β (grey curve, right axis); (b) Alfvén Mach number Ma. Characteristic periods are indicated by vertical dashed lines.


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Periodograms of the IMF Bz component and of the Ey component of induced interplanetary electric field (see Equation 16) are shown in Figure 15d. Similarly to the Bx and By components the periodograms of variable-polarity components Bz and Ey do not demonstrate prominent solar cycle periods of >2 years. In contrast to the Bx and By, there are no 27.3-day and 13.5-day periodicities in Bz component and only harmonics of 9.25 days and 5.75 days are presented [Mursula and Zieger, 1996]. That is a manifestation of very high variability of the IMF Bz within even half of the solar rotation.

The dominant periodicities of IMF Bz are 268 days (0.73 year) and 1.2 years. A broad peak near 250-285 days was revealed from power spectral analysis of cosmic-ray intensity during the period 1964-1995 [El-Borie and Al-Thoyaib, 2002]. The origin of 0.73-year periodicity is still unclear and hence that should be a subject of future investigations. The period of 1.2~1.4 years was revealed in the dynamics of Bz by different spectral methods [Paularena et al., 1995; Szabo et al., 1995]. This variable period was discussed above in the context of the solar wind velocity variations.

The Ey component is characterized mainly by periods of ~14 days, 28 days, 1 year 1.2 years, and 1.4 years, which inherit partially from the periodicities in solar wind velocity and IMF Bz. The dominant periodicity of Ey is characterized by a broad peak at ~28-day period, which is apparently associated with the solar synodic period. The solar cycle periodicities of >2 years vanish in the Ey variations because of high variability of the Bz.

Periodicities of Dimensionless Parameters

Periodograms of the plasma β, sonic and Alfvén Mach numbers are shown in Figure 13. The parameters β and Ms have very similar periods: solar synodic period with harmonics (27 days, 13.5 days and 9 days), annual and semiannual variations inherit from the dynamics of solar wind velocity and temperature (see Figure 11a). However the solar cycle variations (>2 years) in plasma β and Ms are slightly different. Comparing with Figure 11 we can find that the periodicities in the sonic Mach number are mostly related to the solar wind plasma variations with periods of 5-years and ~9.8 years. The periodicity of 2.5 years might be a harmonic of the 5-year period. The variations in plasma β are rather related to the dynamics of IMF intensity B (see Figure 12a) with periods of ~5.1 years and 10.3 years.

It is interesting that the periodicities of Alfvén Mach number Ma (see Figure 13b) are practically same as the characteristic periods of sunspot numbers (see Figure 10), excepting the period of 131 days. From Table 3 we can see that the number Ma is a complex parameter of solar wind velocity, proton density and IMF B. Comparing Figures 11a, 11b and 12a, we can see that those parameters have pretty different periodograms. Perhaps interference of different periodicities leads to degeneration of the variations into the basic harmonics of three main periodicities: solar synodic period, annual period of the Earth orbital rotation, and sunspot cycle.


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4. Solar Cycle Variations

Solar cycle variation of heliospheric parameters is a manifestation of various solar sources of the solar wind and IMF operating at different phases of the solar cycle [e.g. McComas et al., 2003]. It is widely accepted that the solar coronal holes is a main source of the solar wind during declining phases [e.g. Tsurutani et al., 1995]. Transient events form the solar wind at solar maximum [e.g. Cane and Richardson, 2003]. Slow and dense solar wind streams of heliospheric current sheet dominant in the ecliptic plane during solar minimum [e.g. Smith, 2001]. As a result, statistical properties of the heliospheric parameters vary within the cycle such that not only the average and dispersion but also the shape of statistical distributions can change [e.g. Dmitriev et al., 2000; 2005c].

We study solar-cycle variations using a method of running histogram [Dmitriev et al., 2002a; 2005c]. In this method a histogram of statistical distribution is accumulated within a relatively narrow time window, which is consequently shifted with a short time step. As result, a long time interval of measurements is represented by a sequence of running statistical distributions of the measured parameter. For each distribution we calculate running mode, mean and dispersion (RMSD). The choice of running time window and step depends mainly on data sampling. The variations of statistical distribution can be represented more brightly when we take into account the characteristic periodicities of analyzing parameter. In the previous section we find that practically all heliospheric parameters have prominent variation with solar synodic period of 27.3 and annual variation. We choose the step of 27 days and time window of 189 days. The time interval of 189 days is approximately equal to 7 solar synodic periods and also corresponds to the half-year period. By this way we eliminate short-time variations associated with solar rotation, but the annual and longer variations can be analyzed.

Figure 14 shows the running histogram of sunspot number. This parameter demonstrates very high variability during the four last solar cycles (Figure 14). The running mean varies in a wide range and during solar maxima and minima exceeds 1-σ deviation from the 40-year average of ~50. Large statistically significant variations during the cycle have been also found for the radio emission flux of the Sun at the wave length 10.7 cm and for the total solar irradiance [Dmitriev et al., 2005c]. The dispersion of sunspot number is lowest during solar maximum. A short-time enhancement of the dispersion coincides with decrease of sunspot number in the Gnevyshev gap, which corresponds to polarity reversal of the solar magnetic field in 1969, 1980, 1990 and 2001. The running dispersion is highest during rising and declining phases, while the solar cycle minima are characterized by moderate dispersion.

Solar Cycle in Plasma Parameters

Solar-cycle dynamics of the statistical distributions of SW plasma parameters is presented in Figure 15. All cyclic variations in the running mean are not very large and lie inside 1-σ corridor around the averages. Specific cyclic patterns of the variations can be discernible for all plasma parameters. Dmitriev et al. [2002b] demonstrate that the dynamics of solar wind plasma during rising and declining phases are systematically different such that the cycle variation in solar wind parameters represents hysteresis behavior in dependence on the sunspot number.


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Figure 14. Running histogram of statistical distribution of sunspot number W for time interval from 1963 to 2007. Occurrence number in the running histograms is indicated in rainbow palette from violet (minimum) to red (maximum). Top panel shows the running dispersion of distribution. Running mean and running 1-σ deviation are indicated, respectively, by thick and thin black curves. The average is indicated by horizontal black solid line. The 1-σ corridor is restricted by horizontal black dotted line.

Most prominent variations with pretty well organized pattern are revealed in the SW velocity (Figure 15a). Note that the statistical distribution of velocity is deviated from the lognormal PDF and hence the running averages can be different from running modes. One can clearly see that the variations in running average represent solar-cycle very roughly, because of very wide statistical distribution with long tails. Moreover, the running averages lose informative meaning because the running histogram often has two or even three peaks.

The running mode of solar wind velocity is more representative. In Figure 15a we can distinguish a clear pattern of the both 11-year and 22-year cycles. The 22nd cycle in velocity resembles the 20th cycle as reported before [e.g. Cliver et al., 1996]. Declining phases of both cycles contain long-duration intervals of fast solar wind with very high dispersion. Detailed comparison reveals that the cycles 21st and 23rd do not have so prominent velocity enhancements as the cycles 20th and 22nd. However, the common pattern of velocity variations repeats from cycle to cycle.

The slow solar wind streams with velocity <400 km/s are dominant during the minimum and beginning of rising phase of the solar cycle in 1965~1967, 1976~1977; 1985~1987, 1995~1998, and 2007. Relatively fast solar wind with velocity of 400 to 500 km/s appears in the late stage of rising phase (years 1967~1968, 1978~1979, 1988, and 1999). Solar maximum and beginning of declining phase are represented by pretty wide distribution with


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Figure 15. Running histograms of solar cycle variations in solar wind plasma parameters: (a) velocity; (b) temperature; (c) density; and (d) dynamic pressure. Occurrence number in the running histograms is indicated in rainbow palette from violet (minimum) to red (maximum). Running dispersion is expressed in RMSD and shown in the top panels. Running mean and running 1-σ deviation are indicated, respectively, by thick and thin black curves. The average is indicated by horizontal black solid line. The 1-σ and 3-σ corridors are restricted, respectively, by horizontal black dotted lines and white dotted lines.


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mode of ~400 km/s (years 1969~1972, 1989~1992, and 2000~2002). The maximum of 21st cycle demonstrates a little bit different behavior of the velocity with deep decrease to ~350 km/s in 1980 and strong enhancement to ~500 km/s in 1982. Note that in 1980 the solar wind velocity drops down to extremely low values of <200 km, while the other solar maxima are not accompanied by so slow solar wind. It is difficult to decide weather this effect real or experimental artefact.

Most significant variations in the solar wind velocity and substantial enhancements of the velocity dispersion are observed during the second half of declining phase in 1973~1976, 1983~1985, 1992~1995, and 2003~2006. During those time intervals we reveal two or three peaks in the velocity distribution at 600~700 km/s, at ~500 km/s and at ~350~400 km/s corresponding, respectively, to fast, intermediate and slow solar wind streams [Veselovsky et al., 1998c; Dmitriev et al., 2000]. Note that extremely fast solar wind with velocities of >1000 km/s occurs during declining phases. The fast and intermediate solar wind streams disappear abruptly after onset of solar minima.

In Figure 15b we find that solar wind temperature has very similar variations with the velocity, as indicated in many previous studies [e.g. Luhmann et al., 1993]. The statistical distribution of temperature is close to lognormal. Hence the running average is very close to running mode in most cases, excepting strong temperature enhancements during declining phase, when the mode exceeds 1-σ deviation from the average of 85000 K, similarly to the solar wind velocity. The most prominent temperature enhancements are revealed in the 20th and 22nd cycles, which have very similar patterns in the temperature variations.

Low temperatures of ~60000 K accompany solar minimum. During the rising phase and in solar maximum the temperature gradually grows up to ~100000 K. Short-time enhancements of the temperature in the late stage of rising phase in 1978 and 1999 correspond to fast solar wind streams appearing at that time. The declining phase is characterized by highest temperatures of about 2~3•105 K. At that time we can find statistical distributions with two peaks (see years 1975, 1994, and 2006), which correspond to very low temperatures of ~50000 K and very high temperatures of ~200000 K. There are no distributions with prominent 3-peak structure. Similarly to the solar wind velocity, the temperature drops down abruptly at the beginning of solar minimum.

From dynamics of running RMSD in Figure 15b we find that the rising and especially declining phases are characterized by largest variations in the temperature. Extremely high and extremely low temperatures are observed mainly around solar maximum. However, the highest temperatures in the cycle may occur in the beginning of rising phase and during late declining phase.

Solar cycle variations in the SW proton density are different from those in velocity and temperature as we can see in Figure 15d. The statistical distribution of density is very close to lognormal PDF. We do not reveal any multi-peak structure in the running histograms. However, very often the running distribution has large negative skewness, especially during declining phase, when the average becomes higher than the mode. At that time the running mode can be smaller than 1-σ lower deviation from the average. In contrast, the running average always lies within 1-σ corridor around the average of 5.3 cm-3. We do not find similarity between the 20th and 22nd cycles in the dynamics of average proton density. However, 22-year cycle can be revealed in the variations in running dispersion. For the running mean we can find only a pattern of variations inside the 11-year cycle.


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The running mode of solar wind density is highest (~7 cm-3) in the solar minimum. During rising phase, the density decreases and reaches minimum of <5 cm-3 in the solar maximum. Note that dispersion of density is maximal around the solar maximum. The density has a tendency to enhance in the beginning of declining phase and then decrease substantially to values of <5 cm-3 during the second half of the declining phase. The density grows fast with onset of the solar minimum. It is interesting that such pattern is very close to that in running dispersion of the sunspot number. In Figure 15c we can also find that the variation in running dispersion of the density anticorrelates with the running mean. This dynamic pattern with two minima preceding the solar maximum and minimum, has a clear 5-year periodicity. That periodicity is revealed very prominent in the periodogram of solar wind density (see Figure 11b).

It seems that the 23rd cycle in solar wind density is much different from the previous ones. Main distinguishing feature is significant negative trend in the density variations starting in 1998. The declining phase in 2002~2007 is enriched by very and extremely low densities. This fact is out of keeping with previous findings that the vast majority of tenuous solar wind streams are observed during rising phase and in maximum of solar cycle [Crooker et al., 2000; Richardson et al., 2000]. In Figure 15c we can clearly see this feature in the solar cycles 20th to 22nd.

Since 1998 the OMNI database is mostly replenished by the ACE data. Comparing the ACE proton density with data measured by the Wind and IMP-8 satellites we can find that the density measured by ACE is systematically lower [Dmitriev et al., 2002a]. Moreover this difference is growing with time probably because of ageing effect of about several percent per year [Dmitriev et al., 2005a]. Accurate accounting of this effect is a subject of future work. Currently it is difficult to interpret the data on solar wind density during the 23rd solar cycle.

We should also note that the occurrence of extremely high densities is distributed in solar cycle pretty randomly. They have a tendency to group around solar maximum. Though one can find such extreme events during other phases, including solar minimum. This is in agreement with a fact that the highest densities are generated in trailing edges of fast interplanetary transients and inside eruptive filaments [Burlaga et al., 1998; Crooker et al., 2000]. The former events group around the solar maximum, which is characterized by very high variability of the density [Cane and Richardson, 2003].

Figure 15d demonstrates solar cycle variations in the SW dynamic pressure. The running histograms of the dynamic pressure are fitted very well by lognormal PDF. Hence the running mean practically coincides with the running mode. Variation in the running average is not very high and restricted by 1-σ deviation from the average of 2 nPa. The running dispersion of dynamic pressure correlates very well with the sunspot number: it is lowest in the solar minima and highest around the solar maxima. Both extremely high and very low dynamic pressures occur around solar maximum.

The solar cycle variation in the dynamic pressure is remarkably regular and anticorrelates with sunspot number [Crooker and Gringauz, 1993; Luhmann et al., 1993]. Note that the dynamic pressure accounts the helium contribution, which correlates with sunspot number, i.e. it is highest (lowest) in solar maximum (minimum) [Feldman et al., 1978; Aellig et al., 2001]. However, the dynamic pressure variations are mainly contributed by the variations in proton density and velocity. As a result, the pressure is smallest in the solar maximum. In the beginning of declining phase the pressure enhances substantially up to ~3 times. This feature is reported by Richardson et al. [2001] for the 22nd solar cycle and by McComas et al. [2003]


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for the 23rd solar cycle. Apparently, that enhancement is due to the growth of solar wind density and velocity. The pressure remains high and decrease slowly during whole declining phase and in solar minimum. The rising phase is accompanied by relatively fast decrease of the dynamic pressure to the minimum value in solar maximum.

Note that this pattern is not well suitable for the 23rd solar cycle. The steep rising of the dynamic pressure observed in 2002 by McComas et al. [2003] is followed by pretty fast decrease to the values comparable with the pressure minimum in 2001, as we find in Figure 12d. Comparing with dynamics of the solar wind velocity and density, we find that the enhancement of dynamic pressure in 2002 is caused rather by strong jump of the velocity, while the density drops down at that time. In the previous cycles the dynamic pressure enhancements are produced by growth of the solar wind density.

Solar Cycle in IMF

Figure 16 represents running histograms of IMF statistical distribution. Similarly to the SW plasma parameters the solar cycle variation in IMF running mean is restricted by 1-σ corridor around the average.

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Figure 16. Running histograms of solar cycle variations in IMF parameters: (a) total intensity B; (b) Bx; (c) By; (d) Bz; and (e) induced interplanetary electric field Ey. Occurrence number in the running histograms is indicated in rainbow palette from violet (minimum) to red (maximum). Running dispersion of the total intensity B is expressed in RMSD and shown in the top panel of plot (a). Running mean and running 1-σ deviation are indicated, respectively, by thick and thin black curves. The average is indicated by horizontal black solid line. The 1-σ and 3-σ corridors are restricted, respectively, by horizontal black dotted lines and white dotted lines.


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The IMF also demonstrates hysteresis behavior consisting in the phase shifts between the variations in IMF parameters and sunspot number [Dmitriev et al., 2002b]. Slavin et al. [1986] mention about poor correlation of the IMF parameters with the sunspot number and find better correlation with the total solar magnetic flux. However a phase shift still persists between the IMF and solar magnetic flux variations.

Solar cycle dynamics of running histograms of the IMF intensity B is presented in Figure 16a. Running statistical distribution of the intensity can be well fitted by a lognormal PDF and hence the running mode and the running mean are very close. The IMF intensity is lowest in the solar minimum. During rising phase the intensity grows gradually. Solar maximum is characterized by a small local decrease of the IMF intensity. That decrease corresponds to the Gnevyshev gap and the polarity reversal of solar magnetic field when the sunspot number also has local minimum (see Figure 14). After solar maximum, the IMF intensity reaches highest values above the average of 6 nT and then gradually decreases during declining phase. Comparing Figure 16a with Figure 14 we can find that the running mean of IMF intensity correlates in general with the running mean of sunspot number, excepting IMF enhancements during the declining phase.

Similar pattern of the IMF dynamics is reported by Slavin et al. [1986]. They attribute the IMF enhancements at declining phase to the fast solar wind streams. Comparing Figure 16a with Figure 15a we can find that the maximum of IMF intensity indeed coincides with the peaks in solar wind velocity in the 20th, 21st and 23rd solar cycle, while in 1992 (22nd cycle) only moderate solar wind velocities of ~400 km/s correspond to the IMF maximum. Furthermore, we can find that the fast solar wind streams are not necessarily accompanied with the intense IMF.

Solar cycle variation in the IMF dispersion is intensively discussed in the context of IMF multifractal properties [Burlaga and Ness, 1998; Burlaga, 2001]. It is shown that the relative error of IMF strength is essentially invariant over 15-year period from 1979 to 1994. The RMSD in logarithmic scale has exactly the same meaning of relative error (see Equation 9). In Figure 16a (top panel) we can see that the variation in running RMSD is not very high (~20%) and pretty noisy. However, detailed analysis permits revealing some regular variations. Namely, the RMSD has local maximum during polarity reversal simultaneously with the maximum in running dispersion of sunspot number [see Figure 14]. The rising and declining phases of solar cycle are characterized by more-or less gradual decrease preceded by fast growth of the RMSD. The onset of solar minimum is accompanied with a short-time enhancement of the RMSD. Such dynamics of the running dispersion is different from the solar cycle variation in running averages.

Occurrence of extreme IMF intensities is more ordered in solar cycle. The extremely weak IMF occurs mainly during solar minimum and at beginning of rising and declining phases. Extremely strong IMF is observed usually around solar maximum. It is interesting that such dynamics of extremes resembles the dynamics of running average.

Another interesting feature is an absence of 22-year cycle in the IMF intensity. In the periodogram of IMF B (see Figure 12a) the ~22-year periodicity amplitude diminishes. The method of running histograms also demonstrates clearly that the IMF intensity variations in the 20th (21st) solar cycle does not much those in the cycle 22nd (23rd). Furthermore, the rising phase and maximum of 23rd solar cycle resembles mostly those in the 20th solar cycle [Dmitriev et al., 2002b; 2005c]. However, during declining phase, the 23rd cycle rather resembles the previous 22nd solar cycle, as we can see in Figure 16a. Note that the total solar


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magnetic flux SF also does not demonstrate the 22-year periodicity [Dmitriev et al., 2005c]. However, this result is very preliminary because of low quality of the SF data during the 20th solar cycle.

Solar cycle variations in the IMF components Bx and By in GSE coordinate system are presented in Figures 16b and 16c, respectively. The running histograms are characterized by 2-peak structure. The absolute value of peaks is situated at ~3 nT. The Bx and By demonstrate practically identical solar cycle variations. Dynamics of their running dispersion is very close to the solar cycle variation in IMF intensity. Namely, the dispersion is smallest during solar minimum. During rising phase, the dispersion grows gradually. The short-time decrease in the solar maximum corresponds to the time interval of polarity reversal. During declining phase, the running dispersion reaches the maximum and the gap between peaks at running histograms becomes most prominent. Then the dispersion decreases to the lowest values in solar minimum. Note that extremely large intensities of the Bx and By are characterized by the same dynamic pattern.

Interesting feature in dynamics of the Bx and By components is wave-like variations in running mean. They are characterized by anticorrelation between the Bx and By that is proper for the IMF orientation along the Archimedean spiral (see Figure 7). The variations are associated with consequent weakening of occurrence number peak at positive or negative branches of the running histogram. The period of variations varies from 1 to ~5 years. 1-year variations are originated from annual variation of the Earth’s heliographic latitude within a range of ±7°. They occur often in the minimum and at beginning of rising phase. That might indicate to very thing heliospheric current sheet separating magnetic field lines with opposite polarities. Longer periods are usually observed in the end of rising phase and during solar maximum. Those variations are associated with a global north-south asymmetry of the solar magnetic field such that plasma streams from north or south coronal hole prevail in the ecliptic plane for several years. We can indicate two intervals of most prominent solar asymmetry associated with dominant magnetic field from south coronal hole: from 1988 to 1991, when long-lasting positive Bx prevails, and from 1998 to 1999 with prevailing negative Bx.

Solar cycle variations in the IMF Bz component is shown in Figures 16d. The variations are very similar to those for the Bx and By components. The running dispersion is smallest in the solar minimum and increases gradually during the rising phase. The time-interval of polarity reversal in the solar maximum is accompanied with a short-time decease of the dispersion. During declining phase, the running dispersion reaches the maximum and then decreases to the lowest values in solar minimum. The extreme enhancements of IMF Bz group also around solar maximum. A good correlation of the components with IMF strength was reported by Slavin et al. [1986]. They attribute the IMF enhancements to fast solar wind streams. However this relationship is not obvious.

This fact can be clearly seen in dynamics of the induced electric field Ey presented in Figure 16e. Note that Ey is a direct multiplication of the Bz component with the SW velocity. We can see that variations in the electric field are slightly different from the dynamics of Bz. Several peaks corresponding to strong Bz component vanish in the Ey because of suppression by relatively small solar wind velocity. On the other hand, in the Ey variations we can find several enhancements, which are not coincident with the strong Bz intensities. Apparently, those enhancements are caused by very fast solar wind. Different solar cycle dynamics of the velocity and IMF is pointed out by Luhmann et al. [1993]. They conclude that the solar cycle


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in IMF is rather a variation of solar surface field than the changing contributions of coronal transients and stream interfaces.

Solar Cycle in Dimensionless Parameters

Solar cycle variations in Alfvén Mach number Ma, plasma β, and sonic Mach number Ms are presented in Figure 17. The running histograms of those parameters are close to a lognormal PDF. So the running mean is pretty close to the running mode, thought they can be slightly different due to non-zero skewness of the running statistical distributions. Similarly to the SW plasma and IMF parameters, the variations in running mode are not very strong and lie within 1-σ corridor around the average.

The Alfvén Mach number and plasma β demonstrate very similar solar cycle variations, which are close to those in the solar wind dynamic pressure (see Figure 15d). Namely, they anticorrelate with the sunspot number. Luhmann et al., [1993] also reported about the anticorrelation of the Ma with the sunspot number.

Variations in running dispersion of the Alfvén Mach number are more complex and different from those for the plasma β. That complexity is coming from the variations in IMF. Numerically, the dispersions of Ma and IMF B are comparable and vary in the same dynamic range. The dispersion of β varies in wider range. Despite of those differences, we can find common features in the variations. The running dispersion of both Ma and β is highest around solar maximum and small in the solar minimum, especially for the plasma β. Such pattern is apparently inherited from the solar cycle variation in proton density (see Figure 15c).

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Figure 17. Running histograms of solar cycle variations in dimensionless heliospheric numbers: (a) Alfvén Much number Ma; (b) proton plasma β; and (c) Sonic Mach number Ms. Occurrence number in the running histograms is indicated in rainbow palette from violet (minimum) to red (maximum). Running dispersion is expressed in RMSD and shown in the top panels. Running mean and running 1-σ deviation are indicated, respectively, by thick and thin black curves. The average is indicated by horizontal black solid line. The 1-σ and 3-σ corridors are restricted, respectively, by horizontal black dotted lines and white dotted lines.


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Extremely high magnitudes of Alfvén Mach number are distributed rather uniformly along the solar cycle, which reflects high variability of the IMF intensity. In contrast, extremely low Ma and plasma β occur around solar maximum that corresponds to high occurrence rate of very low proton density. Extremely high values of plasma β are observed during rising and declining phases that might be attributed to superposition of events with extremely high temperatures and weak IMF strength.

Solar cycle variations in the sonic Mach number are extremely weak, pretty gradual and totally non-regular (see Figure 17c). This degeneration indicates to very close relationship between the solar cycle variations in solar wind velocity and temperature. Indeed, we have found very close dynamics in running modes of those parameters (see Figure 15a and 15b). It is interesting that in contrast to solar wind velocity and temperature, the running dispersion of Ms demonstrates pretty well correlation with the sunspot number, while the extreme values of Ms are distributed practically uniformly along the solar cycle.

5. Summary and Conclusions

Based on the review of statistical properties we can indicate some general features in the dynamics of heliospheric parameters.

1. The IMF intensity B demonstrates pretty unique dynamics with solar cycles. The

intensity correlates with sunspot numbers. The periodogram of IMF B contains the periodicities, which are very close to the characteristic periods of sunspot number variations. Note that we don’t find any indications on the 22-year period in variability of this parameter in the data set under consideration. While the 21st and 22nd cycles in IMF intensity are similar, the 23rd solar cycle is different because of deeper decrease of the IMF intensity during the declining phase.

2. Solar wind proton density is also characterized by a specific dynamics. It seems that the running mean density correlates with running dispersion of the sunspot number. The periodogram of density is different from those for the sunspot number and for the IMF strength B. We can not find 22-periodicity in the solar wind density. Moreover, a 5-year periodicity is very prominent. This periodicity prevails in the solar cycle variation of running mean, which has two-wave structure with minima just before the solar maximum and minimum. That is not a case in the 23rd solar cycle, which demonstrates very deep gradual decrease of the SW density during recovery phase that is significantly different from the three previous cycles.

3. Statistical distributions of both IMF intensity and SW density are very close to lognormal in temporal scale of ~0.5 year and longer. Though dispersions of those parameters are slightly different. Running logarithmic dispersion of IMF B varies with solar cycle in the range from 1.4 to 1.6. The logarithmic dispersion of density is higher and varies from ~1.7 to ~2.2.

4. The solar wind velocity and temperature are characterized by common dynamics, which is different from the dynamics of IMF strength and SW density. The velocity and temperature have very similar periodograms and close solar cycle variations in running histograms. Their very similar dynamics leads to the disappearance of solar cycle variation in mean sonic Mach number. They demonstrate clearly the ~22-year


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variation. Statistical distributions of the velocity and temperature are close to lognormal PDF only in long time scale of tens of years. Within the solar cycle in short temporal scales of ~0.5 year, the distributions are skewed and can acquire two or three peaks.

The 3-peak structure of the velocity statistical distribution lends an additional support to

the concept of а three-component solar wind model [Schwenn, 1990]. Slow, fast and intermediate solar wind flows are statistically distinct especially during declining solar cycle phases because of the geometry conditions for the tilted rotator [Veselovsky et al., 1998c; Dmitriev, et al., 2000]. The slow solar wind of ~400 km/s, which occupies the heliospheric plasma sheet, originates somewhere inside coronal streamers. Coronal holes with their mostly open unipolar magnetic configuration are known to be the source of the fastest solar wind streams with speeds of >600 km/s. The transition region between slow and fast streams corresponds to the intermediate average flow velocities of ~500 km/s. The dominant magnetic topology here is not clear, but seems to be mixed and intermittent [e.g. Posner, et al., 2001].

Different dynamics of the IMF intensity, solar wind density at one side and solar wind velocity and temperature at other side indicates to different origin of those heliospheric parameters. Perhaps the velocity and temperature of the three-component solar wind are rather driven by magnetic topology of the source regions and geometry of the global magnetic field of the Sun, which varies substantially with solar cycle due to solar magnetic field reversal. The slow streams in the heliospheric plasma sheet and intermediate flows from extended transition region prevail during solar minimum and rising phase when the solar dipole is tilted only slightly. Large-scale coronal holes diminish during solar maximum, which is enriched by active regions with close configuration of magnetic field lines. At that time the slow solar wind dominates. After the reversal, the solar magnetic dipole is substantially tilted and, thus, during declining phase the fast streams from coronal holes concurrent with the intermediate and slow solar wind streams.

Origin of the lognormally distributed IMF intensity is still a subject of investigation. Considering the statistical distribution of Bxy we have found that variations of the magnetic field in the ecliptic plane can not be attributed to the variations of solar wind velocity only. Solar cycle variations and periodicities in the IMF intensity are different from those in solar wind velocity. Namely, the IMF enhancements are not necessarily accompanied with the fast solar wind streams enriched by strong Alfvén waves and compressed leading edges with enhanced magnetic field. And vice versa, the fast solar wind is characterized often by moderate and even weak IMF intensity.

Hence a significant portion of the IMF variations should be originated from the solar source. Solar eruptive events such as ICME and interplanetary sheath regions contribute mainly to the excess of statistics at very large IMF intensities. Perhaps they might cause the increase of the average magnetic field observed around the solar maximum. However that does not explain the lognormal shape of the variations in IMF strength as well as in solar wind density.

The lognormal shape of statistical distribution has a deep physical meaning. A parameter x with lognormal distribution can be originated from a specific multiplication generator. The coefficient of multiplication k=x/X0 of that generator can be represented as k=exp(ν), where ν is distributed normally with the mode ν0=0 and dispersion equal to the dispersion of


137

parameter x. In other words, the variable with lognormal distribution is a result of numerous multiplications of random variables.

The lognormal statistical distributions of the solar wind parameters and IMF might indirectly indicate to multiplicative transformation of local characteristics under alternating random amplification and weakening of waves, compression and rarefaction of inhomogeneities in turbulent processes of transfer of plasma mass, energy and momentum on the Sun and in the heliosphere. For example, in the downstream region of fast interplanetary shock, the values of plasma density and magnetic field are multiplied by compression. We can assume that the solar wind plasma density and IMF intensity might be generated and/or modulated in the regions of alternate compression/decompression in the solar atmosphere.

On the other hand the lognormal distribution itself is not sufficient for conclusions about predominantly random and irregular nature of a multiplicative process because regular processes with very high levels of complexity and multi-dimensions are rather difficult to distinguish from the random process. Both of those possibilities do not seem excluding each other in interpretation of observations. They rather supplement the interpretation from different points of view.

The fact that statistical properties of heliospheric parameters do not satisfy to normal distribution is not surprising. Normal statistics is proper for equilibrium and stationary processes. In contrast, the solar wind plasma and IMF are non-equilibrium and non-stationary. They change with distance and with heliographic latitude and longitude, i.e. they are characterized by various spatial gradients. Moreover, the heliosphere is populated by various kinds of large-scale transient events, interaction regions and waves. We have demonstrated that the key heliospheric parameters are transitional. They are characterized by meaningful temporal variations within solar cycle and from cycle to cycle. However, those variations are not totally random but reveal specific spatial and temporal patterns. Our results clearly show that the lognormal statistics is more-or-less proper for such non-equilibrium and non-stationary random processes with characteristic spatial and temporal scales.

Finally, we should comment that we investigated here only individual one-point, one-time and one-parameter statistical representations. Correlations between different parameters and higher order multi-point and multi-time structure functions were not considered, but remained mostly beyond the scope of our consideration. It is a next step for future analysis enabling visualization of physical nonlinearities, memory effects and non-local links on the Sun and in the heliosphere. Existing knowledge in this regard is also in its infant stage in spite of increasing information about turbulent processes in solar wind and interplanetary magnetic field [Bruno and Carbone, 2005].

We conclude that summary of statistical studies of individual SW and IMF parameters was presented. Growing amount of direct in-situ measurements near the Earth orbit during space era allowed a robust empirical modeling of average SW and IMF characteristics and variations. The resulting probability distribution functions together with their reliability and variability estimates given in formulae, Tables and simple graphs can be used for scientific and technical applications. The statistics up to now encompasses only four recent solar cycles. It is not sufficient for characterization of typical and a-typical solar cycle behavior of SW and IMF parameters contrary to premature claims in this respect found sometimes in literature. Nevertheless, the fundamental quantitative knowledge accumulates and fits rather well modern views and ideas based on MHD and kinetic plasma electromagnetic theories.


138

Acknowledgements

We thank Joe King and Natalia Papitashvili from NASA/NSSDC and QSS Group, Inc. for providing OMNI database. This study was supported by the RFBR grants 07-02-00147, 06-05-64500, INTAS 03-51-6202, MSU Interdisciplinary Scientific Project and grant NSC96-2923-M-008-001MY3/07-02-92004HHC_a from the National Science Council of Taiwan. It is also fulfilled as a part of the Programs of the Russian Academy of Sciences: “Origin and evolution of stars and galaxies” (P-04), “Solar activity and physical processes in the Sun-Earth system” (P-16, Part 3) and “Plasma processes in the Solar system (OFN-16).

References

Aellig, M., A. Lazarus, and J. Steinberg (2001), The Solar Wind Helium Abundance: Variation with Wind Speed and the Solar Cycle, Geophys. Res. Lett., 28(14), 2767-2770.

Akasofu, S.-I. (1979), Interplanetary energy flux associated with magnetospheric substorms, Planet. Space. Sci., 27, 425.

Baker, D., W. Feldman, S. Gary, D. McComas, and J. Middleditch (1986), Plasma Fluctuations and Large-Scale Mixing Near Comet Giacobini-Zinner, Geophys. Res. Lett., 13(3), 271-274.

Belcher, J., and L. Davis Jr. (1971), Large-Amplitude Alfvèn Waves in the Interplanetary Medium, 2, J. Geophys. Res., 76(16), 3534-3563.

Bieber, J., J. Chen, W. Matthaeus, C. Smith, and M. Pomerantz (1993), Long-Term Variations of Interplanetary Magnetic Field Spectra with Implications for Cosmic Ray Modulation, J. Geophys. Res., 98(A3), 3585-3603.

Bruno, R., and V. Carbone (2005), The Solar Wind as a Turbulence Laboratory, Living Rev. Solar Phys., 2, 4. http://www.livingreviews.org/lrsp-2005-4

Bolzan, M. J. A., R. R. Rosa, F. M. Ramos, P. R. Fagundes, Y. Sahai (2005), Generalized thermostatistics and wavelet analysis of solar wind and proton density variability, Journal of Atmospheric and Solar-Terrestrial Physics, 67, 1843-1851.

Borrini, G., J. Gosling, S. Bame, W. Feldman, and J. Wilcox (1981), Solar Wind Helium and Hydrogen Structure Near the Heliospheric Current Sheet: A Signal of Coronal Streamers at 1 AU, J. Geophys. Res., 86(A6), 4565-4573.

Borrini, G., J. Gosling, S. Bame, and W. Feldman (1982a), An Analysis of Shock Wave Disturbances Observed at 1 AU from 1971 Through 1978, J. Geophys. Res., 87(A6), 4365-4373.

Borrini, G., J. Gosling, S. Bame, and W. Feldman (1982b), Helium Abundance Enhancements in the Solar Wind, J. Geophys. Res., 87(A9), 7370-7378.

Bothmer, V. and R. Schwenn (1995), The interplanetary and solar causes of major geomagnetic storms, J. Geomag. Geoelectr., 47, 1127-1132.

Burlaga, L. F. (1992), Multifractal Structure of the Magnetic Field and Plasma in Recurrent Streams at 1 AU, J. Geophys. Res., 97(A4), 4283-4293.

Burlaga, L. F. (2001), Lognormal and multifractal distributions of the heliospheric magnetic field, J. Geophys. Res., 106(A8), 15,917-15,927.

Burlaga, L. F. (2005), Interplanetary magnetohydrodynamics, New York : Oxford University Press, 1995.


139

Burlaga, L. F., and M. A. Forman (2002), Large-scale speed fluctuations at 1 AU on scales from 1 hour to ~1 year: 1999 and 1995, J. Geophys. Res., 107(A11), 1403, doi:10.1029/2002JA009271.

Burlaga, L. F., and J. King (1979), Intense Interplanetary Magnetic Fields Observed by Geocentric Spacecraft During 1963-1975, J. Geophys. Res., 84(A11), 6633-6640.

Burlaga, L. F., and A. Lazarus (2000), Lognormal distributions and spectra of solar wind plasma fluctuations: Wind 1995-1998, J. Geophys. Res., 105(A2), 2357-2364.

Burlaga, L. F., and N. Ness (1998), Magnetic field strength distributions and spectra in the heliosphere and their significance for cosmic ray modulation: Voyager 1, 1980–1994, J. Geophys. Res., 103(A12), 29719-29732.

Burlaga, L. F., and A. Szabo (1999), Fast and slow flows in the solar wind near the ecliptic at 1 AU?, Space Science Reviews, 87, 137-140.

Burlaga, L. F., K. Behannon, and L. Klein (1987), Compound Streams, Magnetic Clouds, and Major Geomagnetic Storms, J. Geophys. Res., 92(A6), 5725-5734.

Burlaga, L. F., R. Fitzenreiter, R. Lepping, K. Ogilvie, A. Szabo, A. Lazarus, J. Steinberg, et al. (1998), A magnetic cloud containing prominence material: January 1997, J. Geophys. Res., 103(A1), 277-285.

Burlaga, L. F., R. Skoug, C. Smith, D. Webb, T. Zurbuchen, and A. Reinard (2001), Fast ejecta during the ascending phase of solar cycle 23: ACE observations, 1998-1999, J. Geophys. Res., 106(A10), 20957-20977.

Burton, R.K., R.L. McPherron, and C.T. Russell (1975), An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 80, 4204.

Cane H. V., and I. G. Richardson (2003), Interplanetary coronal mass ejections in the near-Earth solar wind during 1996-2002, J. Geophys. Res., 108 (A4), 1156, doi:10.1029/2002JA009817.

Charvátová, I. (2007), The prominent 1.6-year periodicity in solar motion due to the inner planets, Ann. Geophys., 25, 1227-1232.

Cliver, E., V. Boriakoff, and K. Bounar (1996), The 22-year cycle of geomagnetic and solar wind activity, J. Geophys. Res., 101(A12), 27091-27109.

Couzens, D. A., and J. H. King (1986), Interplanetary Medium Data Book, Suppl, 3, 1977-1985, Rep. NSSDC/WDC-A-R&S 86-04, NASA, 1986.

Crooker, N.U. (1983), Solar cycle variations of the solar wind, in Solar Wind Five edited by M. Neugebauer, NASA, CP-2280, 303-313.

Crooker, N., and K. Gringauz (1993), On the Low Correlation Between Long-Term Averages of Solar Wind Speed and Geomagnetic Activity After 1976, J. Geophys. Res., 98(A1), 59-62.

Crooker, N., S. Shodhan, J. Gosling, J. Simmerer, R. Lepping, J. Steinberg, and S. Kahler (2000), Density Extremes in the Solar Wind, Geophys. Res. Lett., 27(23), 3769-3772.

Dal Lago, A., W. D. Gonzalez, A. L. C. de Gonzalez, L.E. A. Vieira (2001), Compression of magnetic clouds in interplanetary space and increase in their geoeffectiveness, J. Atmosph. Solar Terrest Phys., 63, 451-455

Deeming, T. J. (1975), Fourier analysis with unequally-spaced data, Astrophysics and Space Science, 36, 137-158.

Dmitriev A. V., A. V. Suvorova, I. S. Veselovsky (2000), Solar Wind and Interplanetary Magnetic Field Parameters at the Earth's Orbit During Three Solar Cycles, Phys. Chem. of the Earth, Part C, 25(1-2), 125-128.


140

Dmitriev A. V., J. K. Chao, Y. H. Yang, C.-H. Lin, and D. J. Wu (2002a), Possible Sources of the Difference between a Model Prediction and Observations of Bow Shock Crossings, Terrestrial, Atmospheric and Oceanic Sciences (TAO), 13(4), 499-521.

Dmitriev, A. V., Suvorova, A. V., Veselovsky, I. S. (2002b), Expected hysteresis of the 23-rd solar cycle in the heliosphere, Adv. Space Res., 29(3), 475-479.

Dmitriev A., J.-K. Chao, D.-J. Wu (2003), Comparative study of bow shock models using Wind and Geotail observations, J. Geophys. Res., 108(A12), 1464, doi:10.1029/2003JA010027.

Dmitriev A. V., A. V. Suvorova, J.-K. Chao, Y.-H. Yang (2004), Dawn-dusk asymmetry of geosynchronous magnetopause crossings, J. Geophys. Res., 109, A05203 doi: 10.1029/2003JA010171.

Dmitriev, A. V., I. S. Veselovsky, O.S. Yakovchouk, (2005a), Problems of consistency in solar wind parameters between data sets OMNI and OMNI-2, “Solar activity as space weather factor”. Proceedings of the 9th International Conference on the Physics of the Sun, St Petersburg, July 4-9, 2005, VVM Publishers, pp. 51-56 (in Russian).

Dmitriev A. V., J.-K. Chao, A. V. Suvorova, K. Ackerson, K. Ishisaka, Y. Kasaba, H. Kojima, H. Matsumoto (2005b), Indirect estimation of the solar wind conditions in 29-31 October 2003, J. Geophys. Res., 110, A09S02, doi:10.1029/2004JA010806.

Dmitriev, A. V., I. S. Veselovsky, A. V. Suvorova, (2005c), Comparison of heliospheric conditions near the Earth during four recent solar maxima, Adv. Space Res., 36, 2339-2344.

El-Borie, M. A., Duldig, M.L., and Humble (1997), J.E., Interplanetary plasma and magnetic field observations at 1AU, 25th International Cosmic Ray Conference, Contributed Papers ,1, SH1-3, 317-320, 1997.

El-Borie, M. A. (2002), On long-term periodicities n the solar-wind ion density and speed measurements during the period 1973-2000, Solar Physics, 208(2), pp. 345-358.

El-Borie, M. A., and S. S. Al-Thoyaib (2002), Power spectrum of cosmic-ray fluctuations during consecutive solar minimum and maximum periods, Solar Physics, 209, 397-407.

Feldman, W., J. Asbridge, S. Bame, and J. Gosling (1978), Long-Term Variations of Selected Solar Wind Properties: Imp 6, 7, and 8 Results, J. Geophys. Res., 83(A5), 2177-2189.

Feynman, J., and A. Ruzmaikin (1994), Distributions of the Interplanetary Magnetic Field Revisited, J. Geophys. Res., 99(A9), 17645-17651.

Freeman, J., and R. Lopez (1985), The cold solar wind, J. Geophys. Res., 90(A10), 9885-9887.

Freeman, J., T. Tollen, and A. Arya (1993), Comparison between Helios data normalized to 1 AU and OMNI data, in Solar-Terrestrial Predictions-IV, Hruska, H., Shea, M. A., Smart, D. F., and Heckman, G., Eds., Boulder: NOAA/ERL, 2, 540-549.

Gazis, P.R. (1996), Solar cycle variation in the heliosphere, Rev. Geophys.,34, 379-402. Gazis, P. R., J. D. Richardson, and K. I. Paularena (1995), Long Term Periodicity in Solar

Wind Velocity During the Last Three Solar Cycles, Geophys. Res. Lett., 22(10), 1165-1168.

Gnevyshev, M. N., and A. I. Ohl (1948), 22-year solar activity cycle, Astronomicheskii Zhurnal, 25, 18-20 (in Russian).

Hartlep, T., W. Matthaeus, N. Padhye, and C. Smith (2000), Magnetic field strength distribution in interplanetary turbulence, J. Geophys. Res., 105(A3), 5135-5139.


141

Iijima, T., and T. A. Potemra (1982), The relationship between interplanetary quantities and Birkeland current densities, Geophys. Res. Lett., 9, 442.

Ipavich, F., A. B. Galvin, S. E. Lasley, J. A. Paquette, S. Hefti, K.-U. Reiche, M. A. Coplan, et al. (1998), Solar wind measurements with SOHO: The CELIAS/MTOF proton monitor, J. Geophys. Res., 103(A8), 17205-17213.

Jain, R, B. Chandel, M. Aggarwal1, R. Devi, and A. K. Gwal1 (2008), Periodicities Inferred from SOXS Mission in Soft and Hard X-ray Emission from the Solar Corona, Abs. on International Workshop Solar Variability, Earth's Climate & the Space Environment, Bozeman, Montana, June 1-6, 2008, 30.

Janardhan P., K. Fujiki, H. S. Sawant, M. Kojima, K. Hakamada, R. Krishnan (2008), Source regions of solar wind disappearance events, J. Geophys. Res., 113, A03102, doi:10.1029/2007JA012608.

Juckett, D. A. (2000), Solar activity cycles, north/south asymmetries, and differential rotation associated with solar spin-orbit variations, Solar Physics, 191, 201-226.

Kane, R. P. (2005), Differences in the quasi-biennial oscillation and quasi-triennial oscillation characteristics of the solar, interplanetary, and terrestrial parameters, J. Geophys. Res., 110, A01108, doi:10.1029/2004JA010606.

King, J. H. (1977), Ed. Interplanetary Medium Data Book, NSSDC/WDC-A-R/S 77-04. King, J. H. (1981), On the Enhancement of the IMF Magnitude During 1978-1979, J.

Geophys. Res., 86(A6), 4828-4830. King, J. H., N. E. Papitashvili (2005), Solar wind spatial scales in and comparisons of hourly

Wind and ACE plasma and magnetic field data, J. Geophys. Res., 110, A02104, doi:10.1029/2004JA010649.

Lazarus, A. J. (2000), The day the solar wind almost disappeared, Science, 287(5461), 2172-2173.

Lazarus, A. J., and K. I. Paularena (1993), Solar wind parameters from the MIT plasma experiment of IMP-8, Solar-Terrestrial Predictions-IV, Hruska, H., Shea, M. A., Smart, D. F., and Heckman, G., Eds., Boulder: NOAA/ERL, 2, 720.

Lopez, R. (1987), Solar Cycle Invariance in Solar Wind Proton Temperature Relationships, J. Geophys. Res., 92(A10), 11189-11194.

Lopez, R., and J. Freeman (1986), Solar Wind Proton Temperature-Velocity Relationship, J. Geophys. Res., 91(A2), 1701-1705.

Luhmann, J., T.-L. Zhang, S. Petrinec, C. Russell, P. Gazis, and A. Barnes (1993), Solar Cycle 21 Effects on the Interplanetary Magnetic Field and Related Parameters at 0.7 and 1.0 AU, J. Geophys. Res., 98(A4), 5559-5572.

Mavromichalaki, H., B. Petropoulos, C. Plainaki, O. Dionatos, I. Zouganeils (2005), Coronal index as a solar activity index applied to space weather, Adv. Space Res., 35, 410-415.

McComas D. J., H. A. Elliott, N. A. Schwadron, J. T. Gosling, R. M. Skoug, B. E. Goldstein (2003), The three-dimensional solar wind around solar maximum, Geophys. Res. Lett., 30 (10), 1517, doi:10.1029/2003GL017136.

McIntosh, P. S., R. J. Thompson, E. C. Willock (1992), A 600-day periodicity in solar coronal holes, Nature, 360, 322 - 324.

Mood, A. M., F. A. Graybill, D. C. Boes (1974), Introduction to the theory of statistics, McGraw-Hill, Singapore.

Mullan, D. J. , C. W. Smith (2006), Solar Wind Statistics at 1 AU: Alfven Speed and Plasma Beta, Solar Phys. 234 (2), 325-338.


142

Mursula, K., and J. H. Vilppola (2004), Fluctuations of the solar dynamo observed in the solar wind and interplanetary magnetic field at 1 AU and in the outer heliosphere, Solar Physics, 221, 337-349.

Mursula, K., and B. Zieger (1996), The 13.5-day periodicity in the Sun, solar wind, and geomagnetic activity: The last three solar cycles, J. Geophys. Res., 101(A12), 27077-27090.

Neugebauer, M., E. J. Smith, A. Ruzmaikin, J. Feynman, and A. H. Vaughan (2000), The solar magnetic field and the solar wind: Existence of preferred longitudes, J. Geophys. Res., 105(A2), 2315-2324.

Newbury, J. A., Russell, C. T., Phillips, J. L., Gary, S. P. (1998), "Electron temperature in the ambient solar wind: Typical properties and a lower bound at 1 AU", J. Geophys. Res., 103, 9553-9566.

Ogilvie, K., M. Coplan, and R. Zwickl (1982), Helium, Hydrogen, and Oxygen Velocities Observed on ISEE 3, J. Geophys. Res., 87(A9), 7363-7369.

Owens, M. J., and P. J. Cargill (2002), Correlation of magnetic field intensities and solar wind speeds of events observed by ACE, J. Geophys. Res., 107(A5), 1050, doi:10.1029/2001JA000238.

Owens M. J., P. J. Cargill, C. Pagel, G. L. Siscoe, N. U. Crooker (2005), Characteristic magnetic field and speed properties of interplanetary coronal mass ejections and their sheath regions, J. Geophys. Res., 110, A01105, doi:10.1029/2004JA010814.

Oyama, K., K. Hirao, T. Hirano, K. Yumoto, and T. Saito (1986), Was the solar wind decelerated by comet Halley? Nature, 321, 310-313.

Paularena, K., A. Szabo, and J. Richardson (1995), Coincident 1.3-Year Periodicities in the ap Geomagnetic Index and the Solar Wind, Geophys. Res. Lett., 22(21), 3001-3004.

Posner, A., T. Zurbuchen, N. Schwadron, L. Fisk, G. Gloeckler, J. Linker, Z. Mikić;, and P. Riley (2001), Nature of the boundary between open and closed magnetic field line regions at the Sun revealed by composition data and numerical models, J. Geophys. Res., 106(A8), 15869-15879.

Rangarajan, G. K., and L. M. Barreto (2000), Long term variability in solar wind velocity and IMF intensity and the relationship between solar wind parameters & geomagnetic activity, Earth Planets Space, 52, 121-132.

Richardson, I. G., and H. V. Cane (1995), Regions of Abnormally Low Proton Temperature in the Solar Wind (1965-1991) and their Association with Ejecta, J. Geophys. Res., 100(A12), 23,397–23,412.

Richardson, J., K. Paularena, J. Belcher, and A. Lazarus (1994), Solar Wind Oscillations with a 1.3 Year Period, Geophys. Res. Lett., 21(14), 1559-1560.

Richardson, I., D. Berdichevsky, M. Desch, and C. Farrugia (2000), Solar-Cycle Variation of Low Density Solar Wind during more than Three Solar Cycles, Geophys. Res. Lett., 27(23), 3761-3764.

Richardson, J. D., C. Wang, and K. I. Paularena (2001), The solar wind: from solar minimum to solar maximum, Advances in Space Research, 27(3), 471-479.

Rouillard, A., and M. Lockwood (2004), Oscillations in the open solar magnetic flux with a period of 1.68 years: imprint on galactic cosmic rays and implications for heliospheric shielding, Annales Geophysicae, 22, 4381-4395.


143

Russell, C. T., and S. M. Petrinec (1993), On the relative intercalibration of solar wind detectors, in Solar-Terrestrial Predictions-IV, Hruska, H., Shea, M. A., Smart, D. F., and Heckman, G., Eds., Boulder: NOAA/ERL, 2, 663-670.

Salem, C., S. Hoang, K. Issautier, M. Maksimovic and C. Perche (2003), Wind-Ulysses in situ thermal noise measurements of solar wind electron density and core temperature at solar maximum and minimum, Adv. Space Res., 32, 491-496.

Schwenn, R. (1990), Large-scale structure of the interplanetary medium, in Physics of the Inner Helioshpere, 2, edited by R. Schwenn and E. Marsch, Berlin-Heidelberg, Springer-Verlag, 99-133.

Schwenn, R., and E. Marsch (Eds.) (1990), Physics of the Inner Heliosphere I, Berlin, Germany, Springer-Verlag.

Skoug R. M., J. T. Gosling, J. T. Steinberg, D. J. McComas, C. W. Smith, N. F. Ness, Q. Hu, L. F. Burlaga (2004), Extremely high speed solar wind: 29-30 October 2003, J. Geophys. Res., 109, A09102, doi:10.1029/2004JA010494.

Slavin, J., G. Jungman, and E. Smith (1986), The Interplanetary Magnetic Field During Solar Cycle 21: ISEE-3/ICE Observations, Geophys. Res. Lett., 13(6), 513-516.

Smith, E. (2001), The heliospheric current sheet, J. Geophys. Res., 106(A8), 15819-15831. Spreiter, J.R., A.L. Summers, and A.Y. Alksne (1966), Hydromagnetic flow around the

magnetosphere, Planet. Space Sci., 14, 223. Szabo, A., R. Lepping, and J. King (1995), Magnetic Field Observations of the 1.3-Year

Solar Wind Oscillation, Geophys. Res. Lett., 22(14), 1845-1848. Thomson, D. J. C. G. Maclennan , L. J. Lanzerotti (2002), Propagation of solar oscillations

through the interplanetary medium, Nature, 376, 139 - 144; doi:10.1038/376139a0. Tsyganenko, N. A. (2000a), Solar wind control of the tail lobe magnetic field as deduced

from Geotail, AMPTE/IRM, and ISEE 2 data, J. Geophys. Res., 105, 5517. Tsyganenko, N. A. (2000b), Modeling the inner magnetosphere: The asymmetric ring current

and Region 2 Birkeland currents revisited, J. Geophys. Res., 105, 27,739. Tsurutani, B., and W. Gonzalez (1987), The cause of high-intensity long-duration continuous

AE activity (HILDCAAS): interplanetary Alfvén wave trains, Planet. Space Sci., 35(4), 405-412.

Tsurutani, B., W. Gonzalez, A. Gonzalez, F. Tang, J. Arballo, and M. Okada (1995), Interplanetary Origin of Geomagnetic Activity in the Declining Phase of the Solar Cycle, J. Geophys. Res., 100(A11), 21717-21733.

Tsurutani, B. T., Mannucci, A. J., Iijima, B., Abdu, M. A., Sobral, J. H. A., Gonzalez, W., Guarnieri, F., et al. (2004): Global dayside ionospheric uplift and enhancement associated with interplanetary electric fields, J. Geophys. Res., 109, A08302, doi:10.1029/2003JA010342.

Usmanov A. V., M. L. Goldstein, K. W. Ogilvie, W. M. Farrell, G. R. Lawrence (2005), Low-density anomalies and sub-Alfvènic solar wind, J. Geophys. Res., 110, A01106, doi:10.1029/2004JA010699.

Valdés-Galicia, J. F., A. Lara, B. Mendoza (2005), The solar magnetic .ux mid-term periodicities, and the solar dynamo, J. Atmosph. Solar-Terr. Phys., 67, 1697-1701.

Veselovsky, I.S., Physics of the interplanetary plasma (1984), Itogi Nauki i Tekhniki, "Issledovania Kosmicheskogo Prostranstva", 22, Moscow, VINITI, (in Russian).

Veselovsky, I. S., and M. V. Tarsina (2001), Angular Distribution of the Interplanetary Magnetic Field Vector , Geomag. and Aeron. 41(4), 452-456.


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Veselovsky, I. S., and M. V. Tarsina (2002a), Intrinsic nonlinearity of the solar cycles, Adv. Space Res., 29(3), 417-420.

Veselovsky, I. S., and M. V. Tarsina (2002b), Rhythmic and a-rhythmic variations in the heliosphere near the Earth, Atlas of Time Variations of Natural, Anthrop and Social Processes, V.3, 457-464, Moscow, Yanus Publishing Co., (in Russian).

Veselovsky, I.S., A.V. Dmitriev, and A.V. Suvorova (1998a), Average parameters of the solar wind and interplanetary magnetic field at the Earth's orbit for the last three solar cycles, Solar System Research, 32, 4, 310-315.

Veselovsky I.S., Dmitirev A.V., Suvorova A.V., Panassenko O.A. (1998b), Plasma and magnetic field parameters in the heliosphere at the Earth's orbit, Preprint of the Institute of Nuclear Physics, Moscow State University #98-18/519, Moscow, 17pp.

Veselovsky I.S., Dmitirev A.V., Suvorova A.V., Panassenko O.A. (1998c), Statistical and spectral properties of the heliospheric plasma and magnetic fields at the Earth's orbit, Preprint of the Institute of Nuclear Physics, Moscow State University #98-18/519, Moscow, 20pp.

Veselovsky I. S., A. V. Dmitriev, O. A. Panassenko, and A. V. Suvorova (1999), Solar cycles in the energy and mass outputs of the heliospheric plasma, Astronomy Reports, 43, 7, 485-486.

Veselovsky, I. S., Dmitriev, A. V., Suvorova, A. V., Minaeva, Yu. S. (2000a), Structure of Long-Term Variations of the Plasma Parameters and Magnetic Field in the Near-Earth Heliosphere, Solar System Res. 34(1), 75-85.

Veselovsky I.S., Dmitriev A.V., Suvorova A.V., Tarsina M.V. (2000b), Solar wind variation with the cycle, J. Astrophys. Astr., 21, p. 423-429.

Veselovsky I.S., Dmitriev A.V., Suvorova A.V. (2001), Plasma and magnetic fields in the heliosphere at the growth phase of solar cycle 23: comparison with previous solar cycles, Solar System Res., 35, 3, 262-266.

Veselovsky, I. S., I. G. Persiantsev, A. Yu. Ryazanov, Yu. S. Shugai (2006), One-parameter representation of the daily averaged solar-wind velocity, Solar System Research, 40(5), 427-431, DOI: 10.1134/S0038094606050078.

Vrsnak, B., M. Temmer, A. M. Veronig (2007), Coronal holes and solar wind high-speed streams: I. forecasting the solar wind parameters, Solar Phys., 240, 315-330, DOI 10.1007/s11207-007-0285-8

Zhang, G.-L. and Xu, Y.-F., An interplanetary view of solar cycle variations, in Solar-Terrestrial Predictions-IV, 2, edited by H. Hruska , M.A. Shea, D.F. Smart, and G. Heckman, NOAA/ERL, Boulder, 396-401, 1993.

Zurbuchen, T. H., S. Hefti, L. A. Fisk, G. Gloeckler, N. A. Schwadron, C. W. Smith, N. F. Ness, R. M. Skoug, D. J. McComas, and L. F. Burlaga (2001), On the origin of microscale magnetic holes in the solar wind, J. Geophys. Res., 106(A8), 16,001-16,010.

Zwickl, R. (1993), Comparison of Los Alamos plasma ion sensors: IMP-8 and ISEE-3, in Solar-Terrestrial Predictions-IV, Hruska, H., Shea, M. A., Smart, D. F., and Heckman, G., Eds., Boulder: NOAA/ERL, 2, 723.

In: Handbook on Solar Wind: Effects, Dynamics … ISBN: 978-1-60692-572-0 Editor: Hans E. Jahonnson © 2009 Nova Science Publishers, Inc.

Chapter 3

SOLAR ENERGY RESEARCH, SUSTAINABLE DEVELOPMENT AND APPLICATIONS

Abdeen Mustafa Omer1 Nottingham, UK

Abstract

People relay upon oil for primary energy and this for a few more decades. Other orthodox sources may be more enduring, but are not without serious disadvantages. Power from natural resources has always had great appeal. Coal is plentiful, though there is concern about despoliation in winning it and pollution in burning it. Nuclear power has been developed with remarkable timeliness, but is not universally welcomed, construction of the plant is energy-intensive and there is concern about the disposal of its long-lived active wastes. Barrels of oil, lumps of coal, even uranium come from nature but the possibilities of almost limitless power from the atmosphere and the oceans seem to have special attraction. The wind machine provided an early way of developing motive power. The massive increases in fuel prices over the last years have however, made any scheme not requiring fuel appear to be more attractive and to be worth reinvestigation. In considering the atmosphere and the oceans as energy sources the four main contenders are wind power, wave power, tidal and power from ocean thermal gradients. The renewable energy resources are particularly suited for the provision of rural power supplies and a major advantage is that equipment such as flat plate solar driers, wind machines, etc., can be constructed using local resources and without the advantage results from the feasibility of local maintenance and the general encouragement such local manufacture gives to the build up of small-scale rural based industry. This chapter gives some examples of small-scale energy converters, nevertheless it should be noted that small conventional i.e., engines are currently the major source of power in rural areas and will continue to be so for a long time to come. There is a need for some further development to suit local conditions, to minimise spares holdings, to maximise interchangeability both of engine parts and of the engine application. Emphasis should be placed on full local manufacture.

Keywords: Renewable energy technologies, energy efficiency, sustainable development, emissions, environment.

1 Correspondence to: 17 Juniper Court, Forest Road West, Nottingham NG7 4EU, UK

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Abbreviations

a annum ha hectares l litre

1. Introduction

The sources to alleviate the energy situation in the world are sufficient to supply all foreseeable needs. Conservation of energy and rationing in some form will however have to be practised by most countries, to reduce oil imports and redress balance of payments positions. Meanwhile development and application of nuclear power and some of the traditional solar, wind and water energy alternatives must be set in hand to supplement what remains of the fossil fuels.

The encouragement of greater energy use is an essential component of development. In the short term it requires mechanisms to enable the rapid increase in energy/capita, and in the long term we should be working towards a way of life, which makes use of energy efficiency and without the impairment of the environment or of causing safety problems. Such a programme should as far as possible be based on renewable energy resources.

Large scale, conventional, power plant such as hydropower, has an important part to play in development. It does not, however, provide a complete solution. There is an important complementary role for the greater use of small scale, rural based, power plant. Such plant can be used to assist development since it can be made locally using local resources, enabling a rapid built-up in total equipment to be made without a corresponding and unacceptably large demand on central funds. Renewable resources are particularly suitable for providing the energy for such equipment and its use is also compatible with the long-term aims. It is possible with relatively simple flat plate solar collectors (Figure 1) to provide warmed water and enable some space heating for homes and offices which is particularly useful when the buildings are well insulated and thermal capacity sufficient for the carry over of energy from day to night is arranged.

Absorber

Transparent shelter screen Solar radiation

Warm tank

Building or support

Cool out

Warm in

Figure 1. Solar water warmer

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In compiling energy consumption data one can categorise usage according to a number of different schemes:

• Traditional sector- industrial, transportation, etc. • End-use- space heating, process steam, etc. • Final demand- total energy consumption related to automobiles, to food, etc. • Energy source- oil, coal, etc. • Energy form at point of use- electric drive, low temperature heat, etc.

2. Renewable Energy

The renewable energy resources are particularly suited for the provision of rural power supplies and a major advantage is that equipment such as flat plate solar driers, wind machines, etc., can be constructed using local resources and without the high capital cost of more conventional equipment. Further advantage results from the feasibility of local maintenance and the general encouragement such local manufacture gives to the build up of small scale rural based industry. Table 1 lists the energy sources available.

Table 1. Sources of energy

Energy source Energy carrier Energy end-use Vegetation Fuel-wood Cooking

Water heating Building materials Animal fodder preparation

Oil Kerosene Lighting Ignition fires

Dry cells Dry cell batteries Lighting Small appliances

Muscle power Animal power Transport Land preparation for farming Food preparation (threshing)

Muscle power Human power Transport Land preparation for farming Food preparation (threshing)

Currently the ‘non-commercial’ fuels wood, crop residues and animal dung are used in

large amounts in the rural areas of developing countries, principally for heating and cooking; the method of use is highly inefficient. Table 2 presented some renewable applications. Renewable sources of energy are an essential part of an overall strategy of sustainable development. They help reduce dependence of energy imports, thereby ensuring a sustainable supply. Furthermore renewable energy sources can help improve the competitiveness of industries over the long run and have a positive impact on regional development and employment. Renewable energy technologies are suitable for off-grid services, serving those in remote areas of the world without requiring expensive and complicated grid infrastructure. Eventually renewable energies will dominate the world's energy supply system.

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Table 2. Renewable applications

Systems Applications Water supply Wastes disposal Cooking Food Electrical demands Space heating Water heating Control system Building fabric

Rain collection, purification, storage and recycling Anaerobic digestion (CH4) Methane Cultivate the 1 hectare plot and greenhouse for four people Wind generator Solar collectors Solar collectors and excess wind energy Ultimately hardware Integration of subsystems to cut costs

Table 3 lists the most important of energy needs.

Table 3. Energy needs in rural areas

Transport e.g., small vehicles and boats Agricultural machinery e.g., two-wheeled tractors Crop processing e.g., milling Water pumping Small industries e.g., workshop equipment Electricity generation e.g., hospitals and schools Domestic e.g., cooking, heating, lighting Water supply e.g., rain collection, purification, storage and recycling Building fabric e.g., integration of subsystems to cut costs Wastes disposal e.g., anaerobic digestion (CH4)

Considerations when selecting power plant include the following: • Power level- whether continuous or discontinuous. • Cost- initial cost, total running cost including fuel, maintenance and capital

amortised over life. • Complexity of operation. • Maintenance and availability of spares. • Life. • Suitability for local manufacture. Table 4 listed methods of energy conversion. There is no real alternative. Mankind cannot indefinitely continue to base its life on the

consumption of finite energy resources. Today, the world's energy supply is largely based on fossil fuels and nuclear power. These sources of energy will not last forever and have proven to be contributors to our environmental problems. The environmental impacts of energy use are not new but they are increasingly well known; they range from deforestation to local and global pollution. The predicted effects of global warming for the environment and for human life are numerous and varied.


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Table 4. Methods of energy conversion

Muscle power Internal combustion engines Reciprocating Rotating Heat engines Vapour (Rankine) Reciprocating Rotating Gas Stirling (Reciprocating) Gas Brayton (Rotating) Electron gas Electromagnetic radiation Hydraulic engines Wind engines (wind machines) Electrical/mechanical

Man, animals Petrol- spark ignition Diesel- compression ignition Humphrey water piston Gas turbines Steam engine Steam turbine Steam engine Steam turbine Thermionic, thermoelectric Photo devices Wheels, screws, buckets, turbines Vertical axis, horizontal axis Dynamo/alternator, motor

The human wastes (four people) would provide about 280 kWh/a of methane, but with

the addition of vegetable wastes from 0.2 ha or wastes from 1 ha growing a complete diet, about 1500 kWh/a may be obtained by anaerobic digestion. The sludge from the digester may be returned to the land. In hotter climates, this efficient could be used to set up a more productive cycle (Figure 2). There is a need for greater attention to be devoted to this field in the development of new designs, the dissemination of information and the encouragement of its use. International and government bodies and independent organisations all have a role to play in renewable energy technologies.

Society and industry in Europe and elsewhere are increasingly dependent on the availability of electricity supply and on the efficient operation of electricity systems. In the European Union (EU), the average rate of growth of electricity demand has been about 1.8% per year since 1990 and is projected to be at least 1.5% yearly up to 2030. Currently, distribution networks generally differ greatly from transmission networks, mainly in terms of role, structure (radial against meshed) and consequent planning and operation philosophies. The use of a heat engine or a power station to simultaneously generate both electricity and useful heat is known as combined heat and power (CHP), or cogeneration. Generally, a conventional power plant emits the heat created as a by-product of electricity generation into the environment through cooling towers, as flue gas, or by other means. CHP or a bottoming cycle captures the by-product heat for domestic or industrial heating purposes, either very close to the plant, or for distribution through pipes to heat local housing. In Europe, the use of CHP presents a substantial potential for increased energy efficiency and reduced environmental impacts. The efficient use of fuel, in simultaneous production of heat and power, can offer energy savings and avoid CO2 emissions compared with separate production of heat and power. In addition, development in the use of fuels used in CHP applications show a trend toward cleaner fuels. Nearly 40% of the electricity produced from cogeneration is produced for public supply purposes, often in connection with district heating (DH) networks.

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Digester Ultra-violet pond

Humans

Algae fish and duck pond Vegetable garden

Figure 2. Biomass energy utilisation cycle

3. Energy Use

Energy use is one of several essential components for developing countries: • The overall situation and the implications of increased energy use in the future. • The problem of the provision of power in rural areas, including the consideration of

energy resources and energy conversion. In addition to the drain on resources, such an increase in consumption consequences,

together with the increased hazards of pollution and the safety problems associated with a large nuclear fission programmes. This is a disturbing prospect. It would be equally unacceptable to suggest that the difference in energy between the developed and developing countries and prudent for the developed countries to move towards a way of life which, whilst maintaining or even increasing quality of life, reduce significantly the energy consumption per capita. Such savings can be achieved in a number of ways:

• Improved efficiency of energy use, for example better thermal insulation, energy

recovery and total energy. • Conservation of energy resources by design for long life and recycling rather than the

short life throwaway product. • Systematic replanning of our way of life, for example in the field of transport. Energy ratio is defined as the ratio of: Energy content of the food product/Energy input to produce the food (1) A review of the potential range of recyclables is presented in Table 5. Almost 60% of the

electricity produced from cogeneration is generated by auto producers, normally for industrial


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processes. Currently the non-commercial fuels wood, crop residues and animal dung are used in large amounts in the rural areas of developing countries, principally for heating and cooking, the method of use is highly inefficient. As in the developed countries, the fossil fuels are currently of great importance in the developing countries. Geothermal and tidal energy are less important though, of course, will have local significance where conditions are suitable. Nuclear energy sources are included for completeness, but are not likely to make any effective contribution in the rural areas.

Table 5. Summary of material recycling practices in the construction sector [1]

Construction and demolition material Recycling technology options Recycling product

Asphalt Brick Concrete Ferrous metal Glass Masonry Non-ferrous metal Paper and cardboard Plastic Timber

Cold recycling: heat generation; Minnesota process; parallel drum process; elongated drum; microwave asphalt recycling system; finfalt; surface regeneration Burn to ash, crush into aggregate Crush into aggregate Melt; reuse directly Reuse directly; grind to powder; polishing; crush into aggregate; burn to ash Crush into aggregate; heat to 900oC to ash Melt Purification Convert to powder by cryogenic milling; clopping; crush into aggregate; burn to ash Reuse directly; cut into aggregate; blast furnace deoxidisation; gasification or pyrolysis; chipping; moulding by pressurising timber chip under steam and water

Recycling asphalt; asphalt aggregate Slime burn ash; filling material; hardcore Recycling aggregate; cement replacement; protection of levee; backfilling; filter Recycled steel scrap Recycled window unit; glass fibre; filling material; tile; paving block; asphalt; recycled aggregate; cement replacement; manmade soil Thermal insulating concrete; traditional clay Recycled metal Recycled paper Panel; recycled plastic; plastic lumber; recycled aggregate; landfill drainage; asphalt; manmade soil Whole timber; furniture and kitchen utensils; lightweight recycled aggregate; source of energy; chemical production; wood-based panel; plastic lumber; geofibre; insulation board

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4. Biogas

Biogas is a generic term for gases generated from the decomposition of organic material. As the material breaks down, methane (CH4) is produced as shown in Figure 3. Sources that generate biogas are numerous and varied. These include landfill sites, wastewater treatment plants and anaerobic digesters. Landfills and wastewater treatment plants emit biogas from decaying waste. To date, the waste industry has focused on controlling these emissions to our environment and in some cases, tapping this potential source of fuel to power gas turbines, thus generating electricity. The primary components of landfill gas are methane (CH4), carbon dioxide (CO2), and nitrogen (N2). The average concentration of methane is ~45%, CO2 is ~36% and nitrogen is ~18% [2]. Other components in the gas are oxygen (O2), water vapour and trace amounts of a wide range of non-methane organic compounds (NMOCs). Landfill gas-to-cogeneration projects present a win-win-win situation. Emissions of particularly damaging pollutant are avoided, electricity is generated from a free fuel and heat is available for use locally.

Complex organics

Organic acids

Hydrolytic bacteria

H2, CO2, formate Acetate

CH4, CO2

Bacteria

Hydrogen producing Acetogenic bacteria

Homo Acetogenic

Methanogenic bacteria

Figure 3. Biogas production process


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5. Wave Power Conversion Devices

The patent literature is full of devices for extracting energy from waves i.e., floats, ramps and flaps, covering channels. Small generators driven from air trapped by the rising and falling water in the chamber of a buoy are in use around the world [3]. Wave power is one possibility that has been selected. Figure 4 shows the many other aspects that will need to be covered. A wave power programme would make a significant contribution to energy resources within a relatively short time and with existing technology.

Wave energy resource

Devices

Pump loading Floating factory- direct use on board

Direct electrical generation

Hydraulic system

Turbo-t

Manufacture secondary fuels e.g., H2 Electrical sub-

station

Transmission ashore- electrical

Transmission ashore- hydraulic

Storage

Turbo-generator

Electrical grid Storage or standby plant Manufacture

secondary fuels e.g., H2

Electricity consumer Fuel consumer

Figure 4. Possible systems for exploiting wave power, each element represents an essential link in the chain from sea waves to consumer

Turbo-generator

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Wave energy has also been in the news recently. There is about 140 megawatts per mile available round British coasts. It could make a useful contribution people needs, about twice that of the UK generating system is available provided. Although very large amounts of power are available in the waves, it is important to consider how much power can be extracted. A few years ago only a few percent efficiency had been achieved. Recently, however, several devices have been studied which have very high efficiencies. Some form of storage will be essential on a second-to-second and minute-to-minute basis to smooth the fluctuations of individual waves and wave’s packets but storage from one day to the next will certainly not be economic. This is why provision must be made for adequate standby capacity.

6. Ethanol Production

Alternative fuels were defined as methanol, ethanol, natural gas, propane, hydrogen, coal-derived liquids, biological material and electricity. The fuel pathways currently under development for alcohol fuels are shown in Figure 5. The production of agricultural biomass and its exploitation for energy purposes can contribute to alleviate several problems, such as the dependence on import of energy products, the production of food surpluses, the pollution provoked by the use of fossil fuels, the abandonment of land by farmers and the connected urbanisation. Biomass is not at the moment competitive with mineral oil, but, taking into account also indirect costs and giving a value to the aforementioned advantages, public authorities at national and international level can spur its production and use by incentives of different nature. In order to address the problem of inefficiency, research centres around the world have investigated the viability of converting the resource to a more useful form, namely solid briquettes and fuel gas (Figure 6).

Natural gas (methane)

Reforming Synthesis Purification

Recycle Purge

Synthesis gas Crude

(CO2, H2, CO) CH3OH + H2O Methanol + Water

(CH3OH) Methanol

Chemical

Overall reaction: CH4 + H2O = CH3OH + H2Steam

Figure 5. Schematic process flowsheet


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Biomass resource

Food, fibre and wood process

residues

Industry Agriculture Forestry Waste

Energy and short rotation crops,

crop residues and animal wastes

Forest harvesting and supply chain.

Forest and agroforest residues

Organic MSW to energy. Landfill.

Biogas

Bioenergy conversion plants Carbon capture and storage linked with

biomass

Traditional biomass- fuelwood, charcoal

and animal dung from agricultural production

Heat/electricity, solid gaseous and

liquid fuels exported off-site

Liquid gaseous biofuels for

transport

Heating/electricity and cooking fuels used

on site

Biorefining, biomaterials, bio-

chemicals and charcoal

Energy supply Transport Buildings industry Industry

Bioenergy utilisation

Figure 6. Biomass resources from several sources is converted into a range of products for use by transport, industry and building sectors [4]

The main advantages are related to energy, agriculture and environment problems, are foreseeable both at regional level and at worldwide level and can be summarised as follows:

• Reduction of dependence on import of energy and related products. • Reduction of environmental impact of energy production (greenhouse effect, air

pollution and waste degradation).

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• Substitution of food crops and reduction of food surpluses and of related economic burdens and utilisation of marginal lands and of set aside lands.

• Reduction of related socio-economic and environmental problems (soil erosion, urbanisation, landscape deterioration, etc.).

• Development of new know-how and production of technological innovation. Biomass resources play a significant role in energy supply in all developing countries.

Biomass resources should be divided into residues or dedicated resources, the latter including firewood and charcoal can also be produced from forest residues. Ozone (O3) is a naturally occurring molecule that consists of three oxygen atoms held together by the bonding of the oxygen atoms to each other. The effects of the chlorofluorocarbons (CFCs) molecule can last for over a century. This reaction is shown in Figure 7.

CFC enters stratosphere

CFC broken down by UV

radiation

Chlorine

Chlorine catalyses O3 breakdown

Breakdown releases

oxygen and chlorine

Chlorine catalyses

another O3 breakdown

Figure 7. The process of ozone depletion [5]


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It is a common misconception that the reason for recycling old fridge is to recover the liquid from the cooling circuit at the back of the unit. The insulating foams used inside some fridges act as sinks of CFCs- the gases having been used as blowing agents to expand the foam during fridge manufacture. Although the use of ozone depleting chemicals in the foam in fridges has declined in the West, recyclers must consider which strategy to adopt to deal with the disposal problem they still present each year. It is common practice to dispose of this waste wood in landfill where it slowly degraded and takes up valuable void space. This wood is a good source of energy and is an alternative to energy crops. Agricultural wastes are abundantly available globally and can be converted to energy and useful chemicals by a number of microorganisms. The success of promoting any technology depends on careful planning, management, implementation, training and monitoring. Main features of gasification project are:

• Networking and institutional development/strengthening. • Promotion and extension. • Construction of demonstration projects. • Research and development; and training and monitoring.

7. Biomass CHP

Combined heat and power (CHP) installations are quite common in greenhouses, which grow high-energy, input crops (e.g., salad vegetables, pot plants, etc.). Scientific assumptions for a short-term energy strategy suggest that the most economically efficient way to replace the thermal plants is to modernise existing power plants to increase their energy efficiency and to improve their environmental performance. However, utilisation of wind power and the conversion of gas-fired CHP plants to biomass would significantly reduce the dependence on imported fossil fuels. Although a lack of generating capacity is forecast in the long-term, utilisation of the existing renewable energy potential and the huge possibilities for increasing energy efficiency are sufficient to meet future energy demands in the short-term.

A total shift towards a sustainable energy system is a complex and long process, but is one that can be achieved within a period of about 20 years. Implementation will require initial investment, long-term national strategies and action plans. However, the changes will have a number of benefits including a more stable energy supply than at present and major improvement in the environmental performance of the energy sector and certain social benefits. A vision used a methodology and calculations based on computer modelling that utilised:

• Data from existing governmental programmes. • Potential renewable energy sources and energy efficiency improvements. • Assumptions for future economy growth. • Information from studies and surveys on the recent situation in the energy sector. In addition to realising the economic potential identified by the National Energy Savings

Programme, a long-term effort leading to a 3% reduction in specific electricity demand per

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year after 2020 is proposed. This will require further improvements in building codes and continued information on energy efficiency.

The environmental Non Governmental Organisations (NGOs) are urging the government

to adopt sustainable development of the energy sector by: • Diversifying of primary energy sources to increase the contribution of renewable and

local energy resources in the total energy balance. • Implementing measures for energy efficiency increase at the demand side and in the

energy transformation sector. The price of natural gas is set by a number of market and regulatory factors that include: Supply and demand balance and market fundamentals, weather, pipeline availability and

deliverability, storage inventory, new supply sources, prices of other energy alternatives and regulatory issues and uncertainty.

Classic management approaches to risk are well documented and used in many

industries. These include the following four broad approaches to risk: • Avoidance includes not performing an activity that could carry risk. Avoidance may

seem the answer to all risks, but avoiding risks also means losing out on potential gain.

• Mitigation/reduction involves methods that reduce the severity of potential loss. • Retention/acceptance involves accepting the loss when it occurs. Risk retention is a

viable strategy for small risks. All risks that are not avoided or transferred are retained by default.

• Transfer means causing another party to accept the risk, typically by contract. Methane is a primary constituent of landfill gas (LFG) and a potent greenhouse gas

(GHG) when released into the atmosphere. Globally, landfills are the third largest anthropogenic emission source, accounting for about 13% of methane emissions or over 818 million tones of carbon dioxide equivalent (MMTCO2e) [7] as shown in Figures 8-10.

0200400600800

10001200

1992

1994

1996

1998

2000

2002

Year

TW

h/ye

ar

OECDNon OECD

Figure 8. Global CHP trends from 1992-2003 [6]


159

0%

10%

20%

30%

40%

50%

1 2 3 4 5 6 7 8

USAEU=25

1 Food, 2 Textile, 3 Pulp & paper, 4 Chemicals, 5 Refining, 6 Minerals, 7 Primary metals, and 8 others

Figure 9. Distribution of industrial CHP capacity in the EU and USA [6]

26%

2%

3%

2%

5%

2%

1%

2%

1%

1%

37%

0%

11%3%2%2%

USA UK Ukraine South AfricaRussia Poland Nigeria MexicoJapan Italy Others ColombiaChina Canada Brazil Australia

Figure 10. World landfill methane emissions (MMTCO2e) [7]

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8. Geothermal Energy

Geothermal steam has been used in volcanic regions in many countries to generate electricity. The use of geothermal energy involves the extraction of heat from rocks in the outer part of the earth. It is relatively unusual for the rocks to be sufficiently hot at shallow depth for this to be economically attractive. Virtually all the areas of present geothermal interest are concentrated along the margins of the major tectonic plates, which form the surface of the earth. Heat is conventionally extracted by the forced or natural circulation of water through permeable hot rock.

There are various practical difficulties and disadvantages associated with the use of geothermal power:

Transmission: geothermal power has to be used where it is found. In Iceland it has proved feasible to pipe hot water 20 km in insulated pipes but much shorter distances are preferred.

Environmental problems: these are somewhat variable and are usually not great. Perhaps the most serious is the disposal of warm high salinity water where it cannot be reinjected or purified. Dry steam plants tend to be very noisy and there is releases of small amounts of methane, hydrogen, nitrogen, amonia and hydrogen sulphide and of these the latter presents the main problem.

The geothermal fluid is often highly chemically corrosive or physically abrassive as the result of the entrained solid matter it carries. This may entail special plant design problems and unusually short operational lives for both the holes and the installations they serve.

Because the useful rate of heat extraction from a geothermal field is in nearly all cases much higher than the rate of conduction into the field from the underlying rocks, the mean temperatures of the field is likely to fall during exploitation. In some low rainfall areas there may also be a problem of fluid depletion. Ideally, as much as possible of the geothermal fluid should be reinjected into the field. However, this may involve the heavy capital costs of large condensation installations. Occasionally, the salinity of the fluid available for reinjection may be so high (as a result of concentration by boiling) that is unsuitable for reinjection into ground. Ocasionally, the impurities can be precipitated and used but this has not generally proved commercially attractive.

World capacity of geothermal energy is growing at a rate of 2.5% per year from a 2005 level of 28.3 GW [8]. GSHPs account for approximately 54% of this capacity almost all of it in North America and Europe [8]. The involvement of the UK is minimal with less than 0.04% of world capacity and yet is committed to substantial reduction in carbon emission beyond the 12.5% Kyoto obligation to be achieved by 2012. GSHPs offer a significant potential for carbon reduction and it is therefore expected that the market for these systems will rise sharply in the UK in the immediate years ahead given to low capacity base at present.

There are numerous ways of harnessing low-grade heat from the ground for use as a heat pump source or air conditioning sink. For small applications (residences and small commercial buildings) horizontal ground loop heat exchangers buried typically at between 1 m and 1.8 m below the surface can be used provided that a significant availability of land surrounding the building can be exploited which tends to limit these applications to rural settings.


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Heat generation within the earth is approximately 2700 GW, roughly an order of magnitude greater than the energy associated with the tides but about four orders less than that received by the earth from the sun [9].

Temperature distributions within the earth depend on:

• The abundance and distribution of heat producing elements within the earth. • The mean surface temperature (which is controlled by the ocean/atmosphere

system). • The thermal properties of the earth’s interior and their lateral and radial

variation. • Any movements of fluid or solid rock materials occurring at rates of more than a

few millimetres per year. Of these four factors the first two are of less importance from the point of view of

geothermal energy. Mean surface temperatures range between 0-30oC and this variation has a small effect on the useable enthalpy of any flows of hot water. Although radiogenic heat production in rocks may vary by three orders of magnitude, there is much less variation from place to place in the integrated heat production with depth. The latter factors, however, are of great importance and show a wide range of variation. Their importance is clear from the relationship:

β = q/k (2)

Where: β is the thermal gradient for a steady state (oC/km), q is the heat flux (10-6 cal cm-2 sec-1) and k is the thermal conductivity (cal cm-1 sec-1 oC-1).

The first requirement of any potential geothermal source region is that β being large i.e., that high rock temperatures occur at shallow depth. Beta will be large if either q is large or k is small or both. By comparison with most everyday materials, rocks are poor conductors of heat and values of conductivity may vary from 2 x 10-3 to 10-2 cal cm-1 sec-1 oC-1. The mean surface heat flux from the earth is about 1.5 heat flow units (1 HFU = 10-6 cal cm-2 sec-1) [9]. Rocks are also very slow respond to any temperature change to which they are exposed i.e., they have a low thermal diffusivity:

K = k/ρCp (3)

Where: K is thermal diffusivity; ρ and Cp are density and specific heat respectively. These values are simple intended to give a general idea of the normal range of

geothermal parameters (Table 6). In volcanic regions, in particular, both q and β can vary considerably and the upper values given are somewhat nominal. It is important to determine the depth of soil cover, the type of soil or rock and the ground temperature. The depth of soil cover may determine the possible configuration of the ground coil. If bedrock is within 1.5 m of the surface or there are large boulders, it may not possible to install a horizontal ground loop. For a vertical borehole the depth of soil will influence the costs, in general, it is more expensive and time consuming to drill through overburden than rock as the borehole has to be cased. The future plan is to predict system operational performance at each observation point,

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based on the relationship between estimated soil thermal property and measured soil thermal conductivity.

Table 6. Values of geothermal parameters

Parameter Lower Average Upper q (HFU) k =cal cm-2 sec-1 oC-1 β =oC/km

0.8 2x10-3 8

1.5 6x10-3 20

3.0 (non volcanic) ≈100 (volcanic) 12x10-3 60 (non volcanic) ≈300 (volcanic)

9. Landfill Gas

Landfill gas (LFG) is currently extracted at over 1200 landfills worldwide for a variety of energy purposes (Table 7), such as:

• Creating pipeline quality gas or an alternative fuel for vehicles. • Processing the LFG to make it available as an alternative fuel to local industrial or

commercial customers. • Generation of electricity with engines, turbines, micro-turbines and other emerging

technologies.

Table 7. Types of LFG implemented recently worldwide

In terms of solid waste management policy, many NGOs have changed drastically in the

past ten years from a mass production and mass consumption society to ‘material-cycle society’. In addition to national legislation, municipalities are legally obliged to develop a plan for handling the municipal solid waste (MSW) generated in administrative areas. Such plans contain:

• Estimates of future waste volume. • Measures to reduce waste and measures to encourage source separation. • A framework for solid waste disposal and the construction and management of solid

waste management facilities.

Landfill caps Soil caps Clay caps Geo-membrane

caps LFG destruction

Flares - Candlestick - Enclosed

Electricity generation Reciprocating

engines Combustion

turbines Micro-turbines Steam turbines Fuel cells

CHP

Turbines Engines

Fuel production Medium BTU gas High BTU gas Liquefied methane

Thermal generation

Boilers Kilns Greenhouse heaters Leachate evaporators


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Landfilling is in the least referred tier of the hierarchy of waste management options: Waste minimisation, reuse and recycling, incineration with energy recovery and optimised final disposal. The key elements are as follows: construction impacts, atmospheric emissions, noise, water quality, landscape, visual impacts, socio economics, ecological impacts, traffic, solid waste disposal and cultural heritage.

10. Energy Efficiency

Energy efficiency is the most cost-effective way of cutting carbon dioxide emissions and improvements to households and businesses. It can also have many other additional social, economic and health benefits, such as warmer and healthier homes, lower fuel bills and company running costs and, indirectly, jobs. Britain wastes 20 per cent of its fossil fuel and electricity use. This implies that it would be cost-effective to cut £10 billion a year off the collective fuel bill and reduce CO2 emissions by some 120 million tones. Yet, due to lack of good information and advice on energy saving, along with the capital to finance energy efficiency improvements, this huge potential for reducing energy demand is not being realised. Traditionally, energy utilities have been essentially fuel providers and the industry has pursued profits from increased volume of sales. Institutional and market arrangements have favoured energy consumption rather than conservation. However, energy is at the centre of the sustainable development paradigm as few activities affect the environment as much as the continually increasing use of energy. Most of the used energy depends on finite resources, such as coal, oil, gas and uranium. In addition, more than three quarters of the world’s consumption of these fuels is used, often inefficiently, by only one quarter of the world’s population. Without even addressing these inequities or the precious, finite nature of these resources, the scale of environmental damage will force the reduction of the usage of these fuels long before they run out.

Throughout the energy generation process there are impacts on the environment on local, national and international levels, from opencast mining and oil exploration to emissions of the potent greenhouse gas carbon dioxide in ever increasing concentration. Recently, the world’s leading climate scientists reached an agreement that human activities, such as burning fossil fuels for energy and transport, are causing the world’s temperature to rise. The Intergovernmental Panel on Climate Change has concluded that ‘‘the balance of evidence suggests a discernible human influence on global climate’’. It predicts a rate of warming greater than any one seen in the last 10,000 years, in other words, throughout human history. The exact impact of climate change is difficult to predict and will vary regionally. It could, however, include sea level rise, disrupted agriculture and food supplies and the possibility of more freak weather events such as hurricanes and droughts. Indeed, people already are waking up to the financial and social, as well as the environmental, risks of unsustainable energy generation methods that represent the costs of the impacts of climate change, acid rain and oil spills. The insurance industry, for example, concerned about the billion dollar costs of hurricanes and floods, has joined sides with environmentalists to lobby for greenhouse gas emissions reduction. Friends of the earth are campaigning for a more sustainable energy policy, guided by the principal of environmental protection and with the objectives of sound natural resource management and long-term energy security. The key priorities of such an energy policy must be to reduce fossil fuel use, move away from nuclear power, improve the

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efficiency with which energy is used and increase the amount of energy obtainable from sustainable, renewable sources. Efficient energy use has never been more crucial than it is today, particularly with the prospect of the imminent introduction of the climate change levy (CCL). Establishing an energy use action plan is the essential foundation to the elimination of energy waste. A logical starting point is to carry out an energy audit that enables the assessment of the energy use and determine what actions to take. The actions are best categorised by splitting measures into the following three general groups:

1) High priority/low cost: These are normally measures, which require minimal investment and can be implemented

quickly. The followings are some examples of such measures: • Good housekeeping, monitoring energy use and targeting waste-fuel practices. • Adjusting controls to match requirements. • Improved greenhouse space utilisation. • Small capital item time switches, thermostats, etc. • Carrying out minor maintenance and repairs. • Staff education and training. • Ensuring that energy is being purchased through the most suitable tariff or contract

arrangements. 2) Medium priority/medium cost: Measures, which, although involve little or no design, involve greater expenditure and

can take longer to implement. Examples of such measures are listed below: • New or replacement controls. • Greenhouse component alteration e.g., insulation, sealing glass joints, etc. • Alternative equipment components e.g., energy efficient lamps in light fittings, etc. 3) Long term/high cost: These measures require detailed study and design. They can be best represented by the

followings: • Replacing or upgrading of plant and equipment. • Fundamental redesign of systems e.g., CHP installations. This process can often be a complex experience and therefore the most cost-effective

approach is to employ an energy specialist to help.


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11. Policy Recommendations for a Sustainable Energy Future

Sustainability is regarded as a major consideration for both urban and rural development. People have been exploiting the natural resources with no consideration to the effects, both short-term (environmental) and long-term (resources crunch). It is also felt that knowledge and technology have not been used effectively in utilising energy resources. Energy is the vital input for economic and social development of any country. Its sustainability is an important factor to be considered. The urban areas depend, to a large extent, on commercial energy sources. The rural areas use non-commercial sources like firewood and agricultural wastes. With the present day trends for improving the quality of life and sustenance of mankind, environmental issues are considered highly important. In this context, the term energy loss has no significant technical meaning. Instead, the exergy loss has to be considered, as destruction of exergy is possible. Hence, exergy loss minimisation will help in sustainability.

The development of a renewable energy in a country depends on many factors. Those important to success are listed below:

1) Motivation of the population The population should be motivated towards awareness of high environmental issues,

rational use of energy in order to reduce cost. Subsidy programme should be implemented as incentives to install biomass energy plants. In addition, image campaigns to raise awareness of renewable technology.

2) Technical product development To achieve technical development of biomass energy technologies the following should

be addressed: • Increasing the longevity and reliability of renewable technology. • Adapting renewable technology to household technology (hot water supply). • Integration of renewable technology in heating technology. • Integration of renewable technology in architecture, e.g., in the roof or façade. • Development of new applications, e.g., solar cooling. • Cost reduction. 3) Distribution and sales Commercialisation of biomass energy technology requires: • Inclusion of renewable technology in the product range of heating trades at all levels

of the distribution process (wholesale and retail). • Building distribution nets for renewable technology. • Training of personnel in distribution and sales. • Training of field sales force.

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4) Consumer consultation and installation To encourage all sectors of the population to participate in adoption of biomass energy

technologies, the following has to be realised: • Acceptance by craftspeople, marketing by them. • Technical training of craftspeople, initial and follow-up training programmes. • Sales training for craftspeople. • Information material to be made available to craftspeople for consumer consultation. 5) Projecting and planning Successful application of biomass technologies also require: • Acceptance by decision makers in the building sector (architects, house technology

planners, etc.). • Integration of renewable technology in training. • Demonstration projects/architecture competitions. • Biomass energy project developers should prepare to participate in the carbon market

by:

° Ensuring that renewable energy projects comply with Kyoto Protocol requirements.

° Quantifying the expected avoided emissions. ° Registering the project with the required offices. ° Contractually allocating the right to this revenue stream.

• Other ecological measures employed on the development include:

° Simplified building details. ° Reduced number of materials. ° Materials that can be recycled or reused. ° Materials easily maintained and repaired. ° Materials that do not have a bad influence on the indoor climate (i.e., non-toxic). ° Local cleaning of grey water. ° Collecting and use of rainwater for outdoor purposes and park elements. ° Building volumes designed to give maximum access to neighbouring park areas. ° All apartments have visual access to both backyard and park.

6) Energy saving measures The following energy saving measures should also be considered: • Building integrated solar PV system.


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• Day-lighting. • Ecological insulation materials. • Natural/hybrid ventilation. • Passive cooling. • Passive solar heating. • Solar heating of domestic hot water. • Utilisation of rainwater for flushing. Improving access for rural and urban low-income areas in developing countries must be

through energy efficiency and renewable energies. Sustainable energy is a prerequisite for development. Energy-based living standards in developing countries, however, are clearly below standards in developed countries. Low levels of access to affordable and environmentally sound energy in both rural and urban low-income areas are therefore a predominant issue in developing countries. In recent years many programmes for development aid or technical assistance have been focusing on improving access to sustainable energy, many of them with impressive results.

Apart from success stories, however, experience also shows that positive appraisals of many projects evaporate after completion and vanishing of the implementation expert team. Altogether, the diffusion of sustainable technologies such as energy efficiency and renewable energies for cooking, heating, lighting, electrical appliances and building insulation in developing countries has been slow.

Energy efficiency and renewable energy programmes could be more sustainable and pilot studies more effective and pulse releasing if the entire policy and implementation process was considered and redesigned from the outset. New financing and implementation processes are needed which allow reallocating financial resources and thus enabling countries themselves to achieve a sustainable energy infrastructure. The links between the energy policy framework, financing and implementation of renewable energy and energy efficiency projects have to be strengthened and capacity building efforts are required.

12. Environmental Aspects of Energy Conversion and Use

Environment has no prcise limits because it is in fact a part of everything. Indeed, environment is, as anyone probably already knows, not only flowers blossoming or birds singing in the spring, or a lake surrounded by beautiful mountains. It is also human settlements, the places where people live, work, rest, the quality of the food they eat, the noise or silence of the street they live in. Environment is not only the fact that our cars consume a good deal of energy and pollute the air, but also, that we often need them to go to work and for hoildays. Obviously man uses energy just as plants, bactria, mishrooms, bees, fish and rats do. Man largely uses solar energy- food, hydropower, wood- and thus participates harmoniously in the natural flow of energy through the environment. But man also uses oil, gas, coal and nuclear power. By using such sources of energy, man is thus modifying his environment.

The atmospheric emissions of fossil fuelled installations are mosty aldehydes, carbon monoxide, nitrogen oxides, sulpher oxides and particles (i.e., ash) as well as carbon dioxide.

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Table 8 shows estimates include not only the releases occuring at the power plant itself but also cover fuel extraction and treatment, as well as the storage of wastes and the area of land required for operations. Table 9 shows energy consumption in different regions of the world.

Table 8. Annual greenhouse emissions from different sources of power plants

Emissions Primary source of energy Atmosphere Water

Waste (x 103 metric tons)

Area (km2)

Coal Oil Gas Nuclear

380 70-160 24 6

7-41 3-6 1 21

60-3000 negligible - 2600

120 70-84 84 77

Table 9. Energy consumption in different continents

Region Population (millions) Energy (Watt/m2) Africa Asia Central America North America South America Western Europe Eastern Europe Oceania Russia

820 3780 180 335 475 445 130 35 330

0.54 2.74 1.44 0.34 0.52 2.24 2.57 0.08 0.29

13. Greenhouses Environment

Greenhouse cultivation is one of the most absorbing and rewarding forms of gardening for anyone who enjoys growing plants. The enthusiastic gardener can adapt the greenhouse climate to suit a particular group of plants, or raise flowers, fruit and vegetables out of their natural season. The greenhouse can also be used as an essential garden tool, enabling the keen amateur to expand the scope of plants grown in the garden, as well as save money by raising their own plants and vegetables. There was a decline in large private greenhouses during the two world wars due to a shortage of materials for their construction and fuel to heat them. However, in the 1950s mass-produced, small greenhouses became widely available at affordable prices and were used mainly for raising plants [10]. Also, in recent years, the popularity of conservatories attached to the house has soared. Modern double-glazing panels can provide as much insulation as a brick wall to create a comfortable living space, as well as provide an ideal environment in which to grow and display tender plants.

The comfort in a greenhouse depends on many environmental parameters. These include temperature, relative humidity, air quality and lighting. Although greenhouse and conservatory originally both meant a place to house or conserve greens (variegated hollies, cirrus, myrtles and oleanders), a greenhouse today implies a place in which plants are raised while conservatory usually describes a glazed room where plants may or may not play a significant role. Indeed, a greenhouse can be used for so many different purposes. It is,


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therefore, difficult to decide how to group the information about the plants that can be grown inside it.

Throughout the world urban areas have increased in size during recent decades. About 50% of the world’s population and approximately 76% in the more developed countries are urban dwellers [11]. Even though there is an evidence to suggest that in many ‘advanced’ industrialised countries there has been a reversal in the rural-to-urban shift of populations, virtually all population growth expected between 2000 and 2030 will be concentrated in urban areas of the world. With an expected annual growth of 1.8%, the world’s urban population will double in 38 years [11]. This represents a serious contributing to the potential problem of maintaining the required food supply. Inappropriate land use and management, often driven by intensification resulting from high population pressure and market forces, is also a threat to food availability for domestic, livestock and wildlife use. Conversion to cropland and urban-industrial establishments is threatening their integrity. Improved productivity of peri-urban agriculture can, therefore, make a very large contribution to meeting food security needs of cities as well as providing income to the peri-urban farmers. Hence, greenhouses agriculture can become an engine of pro-poor ‘trickle-up’ growth because of the synergistic effects of agricultural growth such as [11]:

• Increased productivity increases wealth. • Intensification by small farmers raises the demand for wage labour more than by

larger farmers. • Intensification drives rural non-farm enterprise and employment. • Alleviation of rural and peri-urban poverty is likely to have a knock-on decrease of

urban poverty. Despite arguments for continued large-scale collective schemes there is now an

increasingly compelling argument in favour of individual technologies for the development of controlled greenhouses. The main points constituting this argument are summarised by [11] as follows:

• Individual technologies enable the poorest of the poor to engage in intensified

agricultural production and to reduce their vulnerability. • Development is encouraged where it is needed most and reaches many more poor

households more quickly and at a lower cost. • Farmer-controlled greenhouses enable farmers to avoid the difficulties of joint

management. Such development brings the following challenges [11]: • The need to provide farmers with ready access to these individual technologies,

repair services and technical assistance. • Access to markets with worthwhile commodity prices, so that sufficient profitability

is realised. • This type of technology could be a solution to food security problems. For example,

in greenhouses, advances in biotechnology like the genetic engineering, tissue culture

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and market-aided selection have the potential to be applied for raising yields, reducing pesticide excesses and increasing the nutrient value of basic foods.

However, the overall goal is to improve the cities in accordance with the Brundtland

Report [12] and the investigation into how urban green could be protected. Indeed, greenhouses can improve the urban environment in multitude of ways. They shape the character of the town and its neighbourhoods, provide places for outdoor recreation, and have important environmental functions such as mitigating the heat island effect, reduce surface water runoff and creating habitats for wildlife. Following analysis of social, cultural and ecological values of urban green, six criteria in order to evaluate the role of green urban in towns and cities were prescribed [12]. These are as follows:

• Recreation, everyday life and public health. • Maintenance of biodiversity - preserving diversity within species, between species,

ecosystems, and of landscape types in the surrounding countryside. • City structure - as an important element of urban structure and urban life. • Cultural identity - enhancing awareness of the history of the city and its cultural

traditions. • Environmental quality of the urban sites - improvement of the local climate, air

quality and noise reduction. • Biological solutions to technical problems in urban areas - establishing close links

between technical infrastructure and green-spaces of a city. The main reasons why it is vital for greenhouses planners and designers to develop a

better understanding of greenhouses in high-density housing can be summarised as follows [12]:

• Pressures to return to a higher density form of housing. • The requirement to provide more sustainable food. • The urgent need to regenerate the existing and often decaying, houses built in the

higher density, high-rise form, much of which is now suffering from technical problems.

The connection between technical change, economic policies and the environment is of

primary importance as observed by most governments in developing countries, whose attempts to attain food self-sufficiency have led them to take the measures that provide incentives for adoption of the Green Revolution Technology [13]. Since, the Green Revolution Technologies were introduced in many countries actively supported by irrigation development, subsidised credit, fertiliser programmes, self-sufficiency was found to be not economically efficient and often adopted for political reasons creating excessive damage to natural resources. Also, many developing countries governments provided direct assistance to farmers to adopt soil conservation measures. They found that high costs of establishment and maintenance and the loss of land to hedgerows are the major constraints to adoption [13]. The soil erosion problem in developing countries reveals that a dynamic view of the problem is necessary to ensure that the important elements of the problem are understood for any


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remedial measures to be undertaken. The policy environment has, in the past, encouraged unsustainable use of land [13]. In many regions, government policies such as provision of credit facilities, subsidies, price support for certain crops, subsidies for erosion control and tariff protection, have exacerbated the erosion problem. This is because technological approaches to control soil erosion have often been promoted to the exclusion of other effective approaches. However, adoption of conservation measures and the return to conservation depend on the specific agro-ecological conditions, the technologies used and the prices of inputs and outputs of production.

13.1. Types of Greenhouses

Choosing a greenhouse and setting it up are important and often expensive, steps to take. Greenhouses are either freestanding or lean-to, that is, built against an existing wall. A freestanding greenhouse can be placed in the open, and, hence, take advantage of receiving the full sun throughout the day. It is, therefore, suitable for a wide range of plants. However, its main disadvantage when compared to a lean-to type is that more heat is lost through its larger surface area. This is mainly why lean-to greenhouses have long been used in the walled gardens of large country houses to grow Lapageria rosea and other plants requiring cool, constant temperature, such as half-hardly ferns. However, generally, good ventilation and shading in the spring and summer to prevent overheating are essential for any greenhouse. The high daytime temperatures will warm the back wall, which acts as a heat battery, releasing its accumulated heat at night. Therefore, plants in a greenhouse with this orientation will need the most attention, as they will dry out rapidly.

Also, greenhouses vary considerably in their shapes and internal dimensions. Traditional greenhouses have straight sides, which allow the maximum use of internal space and are ideal for climbers [13]. On the other hand, Greenhouses with sloping sides have the advantage of allowing the greatest penetration of sunlight, even during winter [13]. The low winter sun striking the glass at 90oC lets in the maximum amount of light. Where the sun strikes the glass at a greater or lesser angle, a proportion of the light is reflected away from greenhouse. Sloping sides, also, offer less wind resistance than straight sides and therefore, less likely to be damaged during windy weather. This type of greenhouse is most suitable for short winter crops, such as early spring lettuce and flowering annuals from seed, which do not require much headroom.

A typical greenhouse is shown schematically in Figure 11. However, there are several designs of greenhouses, based on dimensions, orientation and function. The following three options are the most widely used:

• A ready-made design. • A designed, which is constructed from a number of prefabricated modules. • A bespoke design. Of these, the prefabricated ready-made design, which is utilised to fit the site, is the

cheapest greenhouses and gives flexibility. It is, also, the most popular option [13]. The introduction of a reflecting wall at the back of a greenhouse considerably enhances the solar radiation that reaches the ground level at any particular time of the day.

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Specific examples of commercially available designs are numerous. Dutch light greenhouses, for example, have large panes of glass, which cast little shade on the plants inside. They are simple to erect, consisting of frames bolted together, which are supported on a steel framework for all but the smallest models. They are easy to move and extra sections can be added on to them, a useful attraction [13]. Curvilinear greenhouses, on the other hand, are designed primarily to let in the maximum amount of light throughout the year by presenting at least one side perpendicular to the sun. This attractive style of greenhouse tends to be expensive because of the number of different angles, which require more engineering [13]. Likewise, the uneven span greenhouses are designed for maximum light transmission on one side. These are generally taller than traditional greenhouses, making them suitable for tall, early season crops, such as cucumbers [13]. Also, the polygonal greenhouses are designed more as garden features than as practical growing houses and consequently, are expensive. Their internal space is somewhat limited and on smaller models over-heading can be a problem because of their small roof ventilations. They are suitable for growing smaller pot plants, such as pelargoniums and cacti [13]. Another example is the solar greenhouses. These are designed primarily for areas with very cold winters and poor winter light. They take the form of lean-to structures facing the sun, are well insulated to conserve heat and are sometimes partially sunk into the ground. They are suitable for winter vegetable crops and early-sown bedding plants, such as begonias and pelargoniums [13]. Mini lean-to greenhouses are suitable for small gardens where space is limited. They can, also, be used to create a separate environment within larger greenhouses. The space inside is large enough to grow two tomato or melon plants in growing bags, or can install shelves to provide a multi-layered growing environment, ideal for many small potted plants and raising summer bedding plants [13].

13.2 Construction Materials

Different materials are used for the different parts. However, wood and aluminium are the two most popular materials used for small greenhouses. Steel is used for larger structures and UPVC for conservatories [14]. The introduction of a reflecting wall at the back of a greenhouse considerably enhances the solar radiation that reaches the ground level at any particular time of the day. The energy yield of the greenhouse with any type of reflecting wall was also significantly increased. The increase in energy efficiency was obtained by calculating the ratio between the total energy received during the day in greenhouse with a reflecting wall, compared to that in a classical greenhouse. Hence, the energy balance was significantly shifted towards conservation of classical energy for heating or lighting. The four-fold greater amount of energy that can be captured by virtue of using a reflecting wall with an adjustable inclination and louvers during winter attracts special attention. When sky (diffuse) radiation that was received by the ground in amounts shown in Figure 12, were taken into account, the values of the enhancement coefficients were reduced to some extent: this was due to the fact that they added up to the direct radiation from the sun in both new and classical greenhouses. However, this is a useful effect as further increases overall energy gain. There is also an ironing out effect expressed in terms of the ratios between peak and average insolations. Air humidity is measured as a percentage of water vapour in the air on a scale from 0% to 100%, where 0% being dry and 100% being full saturation level.


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1.879m

1.928m 2.568m

1.214m

Figure 11. Greenhouse and base with horticultural glass

13.3. Ground Radiation

Reflection of sunrays is mostly used for concentrating them onto reactors of solar power plants. Enhancing the insolation for other purposes has, so far, scarcely been used. Several years ago, application of this principle for increasing the ground irradiance in greenhouses, glass covered extensions in buildings and for illuminating northward facing walls of buildings was proposed [15]. Application of reflection of sun’s rays was motivated by the fact that ground illuminance/irradiance from direct sunlight is of very low intensity in winter months, even when skies are clear, due to the low incident angle of incoming radiation during most of the day. This is even more pronounced at greater latitudes. As can be seen in Figure 12, which depicts a sunbeam split into its vertical and horizontal components, nearly all of the radiation passes through a greenhouse during most of the day.

The comfort in a greenhouse depends on many environmental parameters. These include temperature, relative humidity, air quality and lighting. Although greenhouse and conservatory originally both meant a place to house or conserve greens (variegated hollies, cirrus, myrtles and oleanders), a greenhouse today implies a place in which plants are raised while conservatory usually describes a glazed room where plants may or may not play a significant role. Indeed, a greenhouse can be used for so many different purposes. It is, therefore, difficult to decide how to group the information about the plants that can be grown inside it. Whereas heat loss in winter a problem, it can be a positive advantage when greenhouse temperatures soar considerably above outside temperatures in summer. Indoor relative humidity control is one of the most effective long-term mite control measures. There

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are many ways in which the internal relative humidity can be controlled including the use of appropriate ventilation, the reduction of internal moisture production and maintenance of adequate internal temperatures through the use of efficient heating and insulation.

The main environmental control factor for dust mites is relative humidity. The followings are the practical methods of controlling measures available for reducing dust mite populations:

Chemical control. Cleaning and vacuuming. Use of electric blankets, and Indoor humidity.

Figure 12. Relative horizontal and vertical components of solar radiation

Conclusions

Two of the most essential natural resources for all life on the earth and for man’s survival are sunlight and water. Sunlight is the driving force behind many of the renewable energy technologies. The worldwide potential for utilising this resource, both directly by means of the solar technologies and indirectly by means of biofuels, wind and hydro technologies is vast. During the last decade interest has been refocused on renewable energy sources due to the increasing prices and fore-seeable exhaustion of presently used commercial energy sources. Plants, like human beings, need tender loving care in the form of optimum settings of light, sunshine, nourishment and water. Hence, the control of sunlight, air humidity and temperatures in greenhouses are the key to successful greenhouse gardening. The mop fan is a simple and novel air humidifier; which is capable of removing particulate and gaseous pollutants while providing ventilation. It is a device ideally suited to greenhouse applications, which require robustness, low cost, minimum maintenance and high efficiency. A device meeting these requirements is not yet available to the farming community. Hence, implementing mop fans aides sustainable development through using a clean, environmentally friendly device that decreases load in the greenhouse and reduces energy consumption.


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References

[1] Robinson, G. Changes in construction waste management. Waste Management World p. 43-49. May-June 2007.

[2] Omer, A.M., and Yemen, D. Biogas an appropriate technology. Proceedings of the 7th Arab International Solar Energy Conference, p.417, Sharjah, UAE, 19-22 February 2001.

[3] Swift-Hook, D.T. et al. Characteristics of a rocking wave power devices. Nature 254: 504. 1975.

[4] Sims, R.H. Not too late: IPCC identifies renewable energy as a key measure to limit climate change. Renewable Energy World 10 (4): 31-39. 2007.

[5] Trevor, T. Fridge recycling: bringing agents in from the cold. Waste Management World 5: 43-47. 2007.

[6] International Energy Agency (IEA). Indicators for industrial Energy Efficiency and CO2 Emissions: A Technology Perspective. 2007.

[7] Brain, G., and Mark, S. Garbage in, energy out: landfill gas opportunities for CHP projects. Cogeneration and On-Site Power 8 (5): 37-45. 2007.

[8] Rawlings, R.H.D. Technical Note TN 18/99 – Ground Source Heat Pumps: A Technology Review. Bracknell. The Building Services Research and Information Association. 1999.

[9] Oxburgh, E.R. Geothermal energy. Aspects of Energy Conversion. p. 385-403. 1975. [10] John, W. The glasshouse garden. The Royal Horticultural Society Collection. UK.

1993. [11] United Nations. World Urbanisation Prospect: The 1999 Revision. New York. The

United Nations Population Division. 2001. [12] WCED. Our common future. New York. Oxford University Press. 1987. [13] Herath, G. The Green Revolution in Asia: productivity, employment and the role of

policies. Oxford Agrarian Studies. 14: 52-71. 1985. [14] Jonathon, E. Greenhouse gardening. The Crowood Press Ltd. UK. 1991. [15] Achard, P., and Gicqquel, R. European passive solar handbook. Brussels: Commission

of the European Communities. 1986.


Chapter 4

EXPERIMENTAL AND MODELING EVIDENCES OF THE SOLAR WIND ENERGY INFLUENCE

ON THE EARTH ATMOSPHERE

L.N. Makarova1, and A.V. Shirochkov Arctic and Antarctic Research Institute, St.Petersburg, Russian Federation

Abstract

So far the solar wind energy contribution to energetic balance of the Earth atmosphere was ignored in any atmospheric and climatic research. However the solar wind is a permanent source of a significant amount of the electromagnetic energy emitted by the Sun which is constantly supplied to the near-Earth space. Traditionally this energy was attributed entirely to sustain a definite level of geomagnetic activity expressed as intensity of the geomagnetic substorms and storms. The authors of this paper found in 1997 after analysis of the data of the Russian rocket sounding in the Arctic that enhancement of the solar wind dynamic pressure do influence thermal regime of the polar middle atmosphere. Similar analysis of the atmospheric balloon sounding data obtained at different stations in both the Arctic and the Antarctica shows that the stratospheric temperature closely correlated with the solar wind electromagnetic energy. After establishing these statistically confident relations it was necessary to find a plausibly reasonable physical mechanism which could explain reality of the found coupling. A concept of the global electric circuit as a physical mechanism for explanation of a direct coupling between the solar wind and the middle atmosphere was suggested. We proposed a new, modified version of the global electric circuit with two Electro-Motive Force (EMF) generators: internal EMF generator driven by the thunderstorm activity of the Earth (a common feature of previous circuit configurations) and an external EMF generator driven by the solar wind energy. The passive elements of this circuit are the ionospheric E-layer (external element of previous version of the circuit), stratospheric conducting layer of heavy ions (h=20-25 km) and conducting layer of the Earth surface. In this configuration a previous scheme of the global electric circuit is a part of the proposed version of it. Numerical evaluation of the electromagnetic energy of the solar wind is a very

1 Correspondence to: Arctic and Antarctic Research Institute, St.-Petersburg, 199397 Russia, phone 7-812-352-06-

01, fax 7-812-352-26-88 e-mail: [email protected]

L.N. Makarova, and A.V. Shirochkov

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difficult task. It can be done only approximately. Structure of the Earth magnetosphere is changing constantly upon influence of the solar wind as well as a position of a boundary of the magnetosphere (magnetopause). The problem could be solved if we present boundary of the Earth magnetosphere and the ground surface as a giant capacitor with external and internal plates correspondingly. The external plate of this capacitor (magnetopause) could be moved toward the Earth under the solar wind pressure. The energy of the solar wind roughly can be calculated by estimation of energy which is required to move the magnetopause for a definite distance. The magnetopause is located at ~ 12 Re (were Re is the Earth radius) under a quite condition of the solar wind. During strong disturbances of the solar wind the magnetopause could approach the Earth at distance of approximately ~ 6 Re. Such estimation shows that energy required for movement of magnetopause at a distance of 6 Re is equal to ~ 5 10 15J. Preliminary numerical estimations showed that under typical conditions such amount of the Joule heating dissipated in stratosphere is comparable with a rate of heating of ozone layer by the solar UV radiation. Furthermore, such amount of energy is sufficient for enhancement of cyclonic activity in the Earth atmosphere. As the next step of exploration a numerical calculation scheme was elaborated, which took into account the abovementioned processes. This numerical scheme was successfully used in one of the global dynamical photo-chemical models of the atmospheric circulations. The results of these model simulations confirmed all previously made preliminary estimations concerning influence of the solar wind energy on the atmospheric processes. There are the definite plans to improve the effectiveness of the proposed physical mechanism describing interaction of the solar wind with the Earth atmosphere. Evaluation of the effects of different degree of the Earth electric conductivity must be taken into account in the next explorations on the subject.

Introduction

So far the solar wind energy contribution to energetic balance of the Earth atmosphere was actually ignored in any atmospheric and climatic research. However the solar wind is a permanent source of a significant amount of electromagnetic energy emitted by the Sun which is constantly supplied to the near-Earth space. Traditionally this energy was attributed entirely to sustain a definite level of geomagnetic activity expressed as intensity of the geomagnetic substorms and storms. The most of previous studies of the solar-terrestrial physics were based on search of statistical connections between a level of solar activity expressed as the sunspot number and various indices of geomagnetic activity. Such attempts were met with a definite skepticism although sometimes obtained statistical relations happened to be rather positive. Basically any index of geomagnetic activity in accordance with well-known Biot - Savart physical law is related to intensity of ionospheric currents flowing in the E-region of the Earth’s ionosphere (altitudes 100-120 km). However, no reliable physical mechanism which could explain declared statistical relations between solar activity and the Earth climatic processes has been proposed so far. A new era in studies of the solar-terrestrial relations began with start of regular satellite observations of the near-Earth space. The Space originated energy is universally adopted as a factor capable to control the Earth’s climate dynamics. A level of the Sun UV radiation expressed as the total solar irradiance (TSI) or the “solar constant” is taken as the most reliable indicator of the amount of the solar energy transferred to Earth. A great advantage of this parameter as compared to traditional index of the solar activity level –Sun spot number (SSN) - is that it is based on direct instrumental observations of the solar irradiance intensity in a wide frequency interval above the Earth’s atmosphere. Hence, the possibilities appeared to study the solar-terrestrial relations in both long-term and short-term intervals by using reliable parameter of TSI

Experimental and Modeling Evidences of the Solar Wind Energy Influence

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expressed in the direct energy units. On the other hand the Sun variability includes other electromagnetic emissions of different intensity and duration, which certainly contribute to the total energy of the solar wind - a well-established permanent component of the solar activity whose influence on the climate dynamics has been underrated so far. The solar wind permanently affecting near-Earth space could provide substantial amount of energy to sustain active atmospheric processes [6]. Quantitatively this energy could be evaluated crudely as the dynamic pressure of the solar wind. More accurately influence of the solar wind on the Earth’s magnetosphere-ionosphere-atmosphere system could be expressed by means of a newly introduced parameter-subsolar distance between the Earth and external boundary of the terrestrial magnetosphere –magnetopause [12]. The latter authors presented evidence of the close connections between various climatic characteristics and the solar wind disturbances expressed as the solar wind dynamic pressure enhancements [10]. They showed that temperature and baric regimes of the high-latitude middle atmosphere as measured by rocket sounding at the Heiss Island (Franz-Josef Archipelago in the Arctic) have changed under various magnitudes of the solar wind dynamic pressure. It was probably the very first experimental evidence of direct influence of the solar wind disturbances on the middle atmosphere behavior. These authors claimed that these couplings could be explained within the framework of the revised model of the global electric circuit [4] with external electro-mobile force (EMF) generator, which is located at the dayside magnetopause and is controlled by the solar wind energy. More lately some indirect evidences of the solar wind influence on the atmospheric processes in the southern polar region were given in [18]. However no indication of any possible physical mechanism capable to explain these coupling was introduced in this paper. It is clear that all these suggestions and conclusions need more exploration. The purpose of this paper is to demonstrate that the idea of a direct influence of the solar wind energy on the atmospheric processes is a plausible and reasonable suggestion. Several experimental and modeling evidences in favor of this statement will be presented together with indication of further steps in developing this idea.

Observations

It was shown previously that the solar wind energy evaluated as the subsolar distance between the Earth and magnetopause (expressed in the Earth’s radius units) is connected closely with the thermal regime of stratosphere at the polar and middle latitudes [12]. Although these results were based on statistical studies, the authors proposed a reasonable physical mechanism capable to explain such connections. Nevertheless further experimental data are needed to prove reality of the data presented on Figure 1.

Figure 1 shows the results of the atmosphere balloon sounding made in Murmansk (68o.25N; 33o.48 E; invariant latitude 64o.35 N) during October 10, 1988 – December 25, 1988.

The data of temperature measurements at baric surfaces 300 hPa (h=9 km), 30 hPa (h=23 km) and 10 hPa (h=28 km) made at local noon in winter are compared with the corresponding magnetopause position given in the Earth’s radius units and calculated from a model presented in [16].


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Figure 1. Variations of middle atmosphere temperature at Murmansk station in dependence on position of magnetopause relative to the Earth expressed in the Earth radius units Re.

It is clear that stratosphere becomes warmer with the magnetopause approaching the Earth at all heights shown here. However the best correlation (r=0,87) between two data sets is observed at height of 23 km. Statistical significance of these relations was checked by means of the Student t-distribution test. A confidence interval for 95 % confidence level is shown on figure 1 by thin vertical bars. Above and below this altitude there is a notable decrease in degree of this correlation. It seems that this systematic change of the degree of correlation between the solar wind energy and stratospheric temperature has a solid physical foundation. The main feature of the version of the global electric circuit developed by [10, 12] is existence of the conducting layer in the middle atmosphere at the height of about 23 km.

There are reliable experimental evidences (rocket sounding data) of the existence of such conducting layer formed by the heavy ion of cluster type [5, 15, 19]. Interaction of the solar wind energy with atmosphere in this scheme is as follows: under enhanced pressure of the


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solar wind during close approach of magnetopause to the Earth, excessive electric fields are generated. These fields induce electric current in the above-mentioned conducting layer of the middle atmosphere as a part of the global electric circuit. The Joule heating produced by this current contributes to the warming of the stratosphere during disturbances in the solar wind. These effects are concentrated in the core of the layer with reasonable diminishing of them at both higher and lower altitudes. The authors made numerical evaluations of these effects which will be presented in the following parts of the Chapter. However it is worth mentioning that these calculations supported explanations described above.

Since the solar wind energy is proved to be geoeffective force, it is worth trying to determine its relation to other kinds of the solar activity whose influence on the Earth weather and climate is commonly accepted.

Parameterization of the Heating in the Middle Stratosphere Due to the Solar Wind Induced Electric Currents

Most studies of the solar effects on the Earth’s atmosphere and climate paid attention to the radiative energy variations connected with 27-days and 11-year solar cycles [2]. The effects of the energetic particle precipitation induced by the solar wind disturbances on the middle atmosphere composition and dynamics have been considered also as a part of the solar output [6]. These processes can affect the ozone and other radiatively active atmospheric species and can be detected mostly in the upper and middle stratosphere. Analysis of the experimental data as well as theoretical considerations revealed that the solar wind energy could be transferred into the Earth’s atmosphere also by the electric fields [6, 12].

A high correlation between the solar wind activity and different atmospheric parameters suggests a strong coupling of these parts of the near-Earth space [10, 11, 12]. A new view on the global electric circuit proposed by Makarova et al. [11, 12] could help to explain this close coupling. According to this approach the main sources of energy controlling the global electric circuit are two Electro-Motive Force generators driven by the thunderstorm activity of the Earth and by the solar wind energy correspondingly. Variations of parameters of the atmosphere are connected with changes of these two sources of electric energy with time. The passive elements of the circuit are the conducting regions in the ionosphere, a layer of heavy ion-clusters in the middle stratosphere and conducting parts of the ground surface.

Demonstration of reality of a physical mechanism determining influence of the global electric circuit on the atmospheric parameters is connected with solving the following problems:

1) Existence of a conducting ion layer in the stratosphere. 2) Quantitative estimation of the effects caused by the electric currents in the middle

stratosphere. 3) Quantitative calculation of changes in thermal regime of the stratosphere caused by

electric currents with the realistic input parameters. 4) Influence of conductivity of the ground surface as one of the main parameters of the

global electric circuit. Every part of these questions will be considered below.


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1. Peak of Heavy Ion Density in the Earth’s Stratosphere and Its Influence on the Middle Atmosphere Processes

The first notes of reality of existence of the stratospheric heavy ion layer (so called cosmic layer C) appeared in scientific literature long time ago. This problem was explored theoretically as well as by means of special rocket mass spectrometer measurements in the middle atmosphere. For example, in paper [19] it was showed averaged altitude profile of electron concentration in the whole atmosphere with indication of the mean ions at each height. A definite maximum of the charged particles (heavy ions) at the heights around 30 km equal to ~ 5 x 103 cm-3 is clearly seen at these data. Brasseur and Chatel [5] demonstrated similar data but additional important information on the mean ion mass numbers is shown here. They showed that the heavy ion – clusters with ion mass numbers equal to 100 – 500 are the dominant charged particles at stratospheric heights (20 – 30 km).

Unfortunately this important information was obtained from the episodic rocket measurements made at the moderate latitudes of the Northern hemisphere. Rosen and Hoffmann [15] presented more long–term data concerning existence of stratospheric layer of charged particles.

These authors analyzed data of the balloon measurements of the ion content of the atmosphere by means of the Gerden collector method performed in two places: Saskatoon in Canada (geographic latitude 52° N) and Larami in Wyoming, USA (geographic latitude 41° N).

Maximum of ion concentration equal to Ni = ~5.5 x 103 cm-3 was steadily recorded at the height of~15 km. It is worthy to note that their data demonstrated almost unchanged shape of the profiles obtained during rather long period of measurements (December 1986–March 1987). Additional important feature of their measurements was disclosed in a case of simultaneous balloon measurements of height distribution of the positive and negative ions as well as ozone density at Larami on February 9, 1987 (their Figure 5). It was evident that concentration of the ions of both polarities are similar and maximum of their density is located at ~ 15 km. Maximum of the main ozone layer is located by several kilometers above the ion maximum. It seems that a close neighborhood of these two important atmospheric parameters is not a casual phenomenon. So, it is possible to claim that the stratospheric ion distribution with maximum equal to Ni =~5.5 x 103 cm-3 located at the heights 15 – 20 km is a permanent feature of the middle atmosphere.

There are two aspects of the problem of interaction of cosmic rays with stratosphere: a) production of permanent maximum in stratospheric ion distribution, and b) peculiarities of the specific physical and chemical processes in stratosphere under intense impact of the cosmic rays.

The former problem could be solved theoretically if one knows values of density of charged particles produced by intruding fluxes of cosmic rays. We used for this purpose magnitudes of the cosmic ray fluxes given by Bazilevskaya et al. [3] as well as values of the rates of ionization produced by these fluxes given in the same paper. The density of the charged particles in stratosphere was calculated by using equation of ion – recombination equilibrium:

αeff = q/ Ni2 (1)


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where: αeff – effective recombination coefficient; q – rate of ionization, Ni – density of the charged particles. The values of αeff were taken from Rosen and Hofmann [15]. We calculated height

profiles of the charged particles in the stratosphere by using this equation.(They are not shown here ). The profiles of Ni at the high geomagnetic latitudes (λ > 65°) demonstrate two maximums: the first one, equal to ~7 x103 cm-3 and located at h = 30 km and the second one, equal to 6 103 cm-3 and located at h ~ 15 km. Concentration of the charged particles in the stratosphere decreases with decrease of geomagnetic latitude due to geomagnetic field influence. It is worthy to note that calculated value of Ni for moderate latitude is almost identical to experimental data obtained by Rosen and Hofmann [15] for Saskatoon and Larami. So, we proved theoretically existence of maximum in stratospheric ion distribution by using independent reliable experimental data of the cosmic ray fluxes measured by atmospheric balloons at different geomagnetic latitudes.

It is important to note that interaction of the neutral and charged particles in stratosphere occur under condition of very high density (1017– 1018 cm-3) of the neutral atmospheric components. Therefore the main attention must be given to processes of collision between neutral and charged particles. Elementary kinetic theory [21] determines a value of mean free path of particles λa with radius ra and distance between the centers of the particles 2ra by the following equation:

λa = 1/π (2ra)2 Na (2)

where: Na – concentration of neutral molecules. If electron with very small radius moves amidst neutral molecules of gas we can assume

that collisions occur when distance between electron and neutral molecule is equal to ra. In this situation electron changes direction of its movement and loses its energy. Therefore mean free path of electron under the circumstances could be expressed as

λe =1/π (ra)2 Na (3) Small radius of the electron allows one to ignore collisions of electrons with each other.

We will obtain equation expressing magnitude of collision “electron – neutral” νea νea = Ve/λe =π (ra)2 Na (2kT/m)1/2 (4)

if we take into account dependence of electron velocity Ve on temperature equal to Ve = (2kT/m)1/2 (5) This equation (4) shows that value of collision “electron – neutral” depends on square of

radius of neutral component. It becomes to be very important for stratosphere with its giant molecules clusters of hydroxyls which size could be as great as 100 Å, while usual atmospheric molecules size is ~ 1 – 3 Å (10-8). It is reasonable to assume that stratospheric ions could also influence on the electron trajectory by means of collision “ion – electron”.


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Radius of ion impact is greater than of neutral particles ra due to insignificant diminishing of Coulomb forces with distance. It is reasonable to assume that electron will collide with ion at some distance reff when its kinetic energy will be equal to potential energy, i.e.

3/2kT ~ e2/ε0 reff (6)

where T - temperature of atmosphere; k – Boltzmann constant; e - charge of electron; ε0 – dielectric constant. Cross – section of collision “electron – ion” determined by magnitude of reff depends on

electron velocity. Taking into account these facts one can calculate numerically value of collision frequency “electron – ion” by means of equation:

νei = π (2e2/3ε0 kT)2 Ni (3kT/m)1/2 (7) The total value of collision frequency of electron with both neutral particles and ion could

be expressed as νe = νea + νei = π (ra)2 Na (2kT/m)1/2 + π (2e2/3ε0 kT)2 Ni (3kT/m)1/2 (8) If we take ra = 10-8 cm, Na =1018 cm-3, Ni = 5 x 103 cm-3, T = 220°K and substitute them

into correspondent expression for collisions we will obtain νea = 1.8 x 10-8 Nа (T/300) ~ 3 x 109 s-1

νei ~ 1 x 10-2 Ni (300/T)3/2 ~ 102 s-1 So the time between collisions of electrons with neutral particles is ~ 10-9 s while the

corresponding period between collisions of electrons with ions is ~ 10-2 s. It means that stratospheric electrons with additional energy obtained from electric field transform this energy to neutral particles for period of time, which is much shorter than photochemical interaction of charged particles with neutral components (this period is equal to ~ 10-3 s). This fact is a strong confirmation of reality of physical mechanism of transforming of the solar wind energy into middle atmosphere by means of Joule heating of atmosphere by the electric currents proposed by Makarova et al. [14].

2. Quantitative Estimation of the Effects by the Electric Currents in the Middle Stratosphere

A new mechanism of the thermal heating in the middle stratosphere by the electric currents which connected with parameters of the global electric circuit will be demonstrated here. We are using the approach of Alfven and Falthammar [1] to evaluate the electric currents effects in a weakly ionized plasma.


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Let us suggest that the density of the charged particles with charge ek and mass mk in atmosphere is equal to nk. An electric field of strength E will move these particles with an averaged drift velocity uk.

uk = bk E (9)

where bk is a constant, which can be called mobility in a case of weak fields. If the values of mobility of all atmospheric gases are known it is possible to calculate intensity of electric current I and of conductivity of atmosphere σ since I = σE give equations for the current (I) and conductivity (σ) in the following form [1]:

I = ∑ nk ek uk= ∑ nkekbk E (10) σ = ∑ nkekbk (11) An electrical resistance of the atmosphere R can be calculated as: R = 1/σ= 1/∑ nkekbk (12) We evaluate the effects of electric currents in the atmosphere with a simplified method

based on concept of “particle free path length”. The result of our calculations will depend on the parameters involved whose values are difficult to evaluate exactly. Among these the frequency of ion-neutral collisions and the concentration of the charged particles are poorly known. “Particle free path length” approach assumes that the charged molecules undergo instant collisions while between the collisions they move with acceleration under the influence of electric field.

Alfven and Falthammar [1] defined the mean velocity uk of a particle moving in the direction of electric field by the “particle free path length” method as:

uk = ( ekλk/2mk Vk) E (m/s), (13)

where λk= Vk /νk is a particle free path length; Vk is a mean thermal velocity of ions ; νk - is ion-neutral collision frequency.

Then the mobility of a particle follows from (1) as bk = uk /E = γ ekλk/mk Vk = γ ek/mk νk (m/s), (14)

where γ is a dimensionless coefficient. Values of γ vary in the range between 0.5 and 1.0. An accurate calculation of the

mobility taking into account statistical distribution of the velocities and the free path lengths gives the expression similar to equation (6) but with γ = 1 [1]. Inserting these values of mobility into the expressions for current intensity and resistance we obtain

I = ∑( nkek

2 E)/ mk νk (A/m) (15)


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R = 1/∑( nkek2 )/ mk νk = mk/∑( nkek

2 tk) (Ω m) (16) The charged component of the middle atmosphere consists of the electrons as well as

positive and negative ions. As a rule, these particles are in the state of electric equilibrium when the concentrations of positive and negative particles are equal. In the equations (15) and (16) the summation should be made for negative (mainly electrons) and positive particles separately. The mass of the electron (me =1.6 10-31 kg) is much less than mass of the ion (mi=M mp=M 1.6 10-27kg, where M is a mean mass number of ions). Their ratio me/mi is equal to 1.57 10-6 for M=400 at stratospheric heights [5]. In this case the part of the equation for electron component of the current is a dominant in expression for current (15) while ionic component is a main part in expression for resistance (16).

The amount of Joule heating produced by current I is dQ/dt = I2 R (J /m3 s). (17) Inserting (7) and (8) into (9) yields dQ/dt= n e2 E2 mi/ν me

2 (J /m3 s) (18)

where n=ni = ne – total concentration of the charged particles for electrodynamic equilibrium conditions.

The external parameters, which determine amount of the Joule heating, dissipated by the electric currents in the atmosphere (equation 10) are the following: electric field strength E, charged particle concentration n, collision frequency ν, and ion mass weight mi.

3. Quantitative Calculation of Changes in Thermal Regime of the Stratosphere Caused by Electric Currents with Realistic Input Parameters

Accurate values of these parameters are difficult to evaluate. In this section we will try to collect as much information as possible from different sources.

Speaking about strength of the electric field in the stratosphere E there are very few reliable measurements of this parameter. Bering [4] performed one of them by using the special long-lived balloons in summer seasons of 1988-1989 over South Pole Station in Antarctica. The range of the measured electric field values was 0.1 - 0.35 V/m. We have sorted these data in accordance with the solar wind disturbances taken as the subsolar distance between the Earth and dayside magnetopause position expressed in the Earth radius units Re [12] and got the following empirical relation between these two parameters

E = (527.01 – 31.5 Re) 10-3 (V/m). (19) This relation was derived for ~ 40 experimental values of stratospheric electric field.

Calculated correlation coefficient between the magnetopause positions and stratospheric electric field values turned out to be rather high – 0.78.


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This equation (19) is used for the calculation of electric field parameters. This choice is explained by the lack of other reliable measurements of stratospheric electric fields and must be considered as the first approximation of the global electric field distribution in the stratosphere. The magnetopause position is determined from an empirical model developed by Shue et al. [16]. The input parameters of this model are the solar wind density nsw , velocity Vsw as well as the magnitude and orientation of the interplanetary magnetic field (IMF) vertical component Bz. These parameters are given in the NASA periodic publications such as the Solar-Geophysical Data. The magnitude of the solar wind impact on the Earth’s atmosphere is maximal at the dayside of our planet during 06-18 hours of local time [11]. Physical processes responsible for interaction between the solar wind and the near-Earth space on the Earth night side (18-06 local time) have not been investigated properly yet. Therefore, the magnitude of the electric field strength induced by the solar wind on this part of the Earth could not be determined from the equation (11) and at the moment only very rough estimations could be made. These estimations show that the magnitude of stratospheric electric field on the Earth’s nightside is of about 40 percent of the corresponding daytime value.

As for concentration of the charged particles in the middle atmosphere (18-40 km) it is formed by many sources. The main source is the galactic cosmic rays (GCR), which permanently ionize this part of the atmosphere at all latitudes from the pole to the equator. Concentration of the free ions in the atmosphere is determined as proposed in [20]:

ni = [q/αeff]1/2 , (20)

where ni is the ion density in m-3; q is the rate of ionization in ion/m3s; αeff is the effective recombination coefficient in m3s-1. In general the latter parameter depends on altitude and the solar irradiance, but according to [20] we put it equal to 1.10-9 m3 s-1. Ionization rate (q) produced by the GCR fluxes could be calculated by the equation from [8]:

q= (A+B sin4ϕ) nа , (21)

where ϕ is the geomagnetic latitude; A and B are dimensionless coefficients depending on the solar activity level; na is the concentration of neutral molecules in the atmosphere. A is a constant coefficient equal to 1.74 10-18, B is a coefficient equal to 1.93 1017 for the years of maximum solar activity and equal to 2.84 10-17 for the years of minimum solar activity. The solar cosmic rays, the solar X-rays and aerosols are able of producing an anomalous ionization at these altitudes, only sporadically though. The rate of ionization by the GCR depends on geomagnetic latitude (it increases from the equator toward the pole) and on the solar activity (it is highest/lowest during the solar activity minimum/maximum).

The vertical distribution of the charged particles in the atmosphere obtained from the experimental data has been presented in [19]. The appearance of the secondary ionization maximum at 24 km altitude presumably consisting of the heavy ion-clusters is clearly seen. Its density is about 3.0 109 m-3. Another experimental data confirming the presence of similar layer in the stratosphere can be found in [5]. Thus, there are solid reasons to suggest the existence of a charged particles layer at stratospheric altitudes for any level of solar and geomagnetic activity. It is a very important point for the present investigation.


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Frequency of the ion-neutral collisions (νk) is an important parameter of the middle atmosphere determining electrodynamics of this region. In general form it could be calculated by the following equation [20]:

νk = 4.4 10-15 (T/300) nа (s-1) (22)

where T is the atmospheric temperature in K; nа is the density of the neutral molecules in the atmosphere in m-3 . There are few experimental measurements of this parameter at altitudes 18-40 km [20] which gave the value of νk equal to 1.5 109 s-1 at the 30 km altitude.

One of the main points of our investigation is the established fact of existence of a layer of heavy ions at altitudes ~25-35 km [5, 19]. This layer consists of the cluster ions with the mean mass weight of around 400. This value is taken as universal parameter in further studies.

4. Numerical Estimation of the Heating Rate in the Middle Atmosphere Produced by the Electric Currents

Using the parameterization of all components in the final equation (10) it is possible to make a numerical estimation of thermal effects produced by the electric currents in the atmosphere. For this calculation we have applied moderately disturbed conditions in the solar wind. For this particular case we can take the following values of the controlling parameters:

mp (proton mass) = 1.6 10-27 kg; me (electron mass ) = 9.1 10-31 kg; e ( charge of electron) = 1.6 10-19 C E = 3 10-1 V/m T = 220.0 K ni = 4 108 m-3 M = 400 νk = 1.51 109 s-1 By substituting these values into the equation (10) we can obtain the amount of Joule

heating equal to 1.8 .10-4 J/m3s. For the unit of volume (if we take cp = 240 kal/kg K and ρ = 4. 10-2 kg/m-3) we got dT/dt = 3. 10-2 K/ hour.

It is known that similar impact of the solar UV radiation on the ozone layer produces dT/dt = 0.5 10-2 K/day. If the maximal value of the charged particles density in the stratosphere (ni = 3.0 109 m-3) is used in this calculation we get dQ/dt = 3.0 10-4 (J/m3s). It means that the temperature tendency due to proposed mechanism would be equal to dT/dt =1.2 K/day. The latter value is comparable with correspondent atmospheric heating due to solar UV radiation [7]. Results of the similar calculations for various situations showed the same order of Joule heating due to the solar wind dynamics as those described above.

Figure 2 illustrates zonal mean distribution of the Joule heating rate. The calculations were performed for January and for moderate level of solar and interplanetary activity by


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using the method described above. The geographical distribution of the Joule heating rate at 10 hPa surface due to the solar wind dynamics is shown in Figure 2.

The heating rate increases monotonically from the equator to the poles in accordance with the ionization rate (see equation 21). The heating rate reaches its maximum over high latitudes of the summer hemisphere (Antarctica) since density of the neutral atmosphere is higher under such circumstances than in the winter. The both ionization rate and frequency of ion-neutral collisions crucially depend on this parameter (see equations 21 and 22). As one can see the magnitude of the Joule heating given in Figures 2 are about 3 times lower than the corresponding maximum values indicated earlier. This difference is explained by a moderate level of solar activity adopted for the calculations with correspondingly smaller ionization rate and density of the neutral atmosphere. The most important result of these calculations is that even these values of the Joule heating caused by the solar wind dynamics are comparable with correspondent atmospheric heating rates due to solar UV radiation at these heights [7].

Figure 2. Zonal mean heating rate (K/day) averaging over all longitudes for every value of latitude due to solar wind induced electrical currents in the middle stratosphere. The heating rates have been calculated using the parameterization and input data for January 1996.

The direct consequences of such warming could be the changes in dynamics of the stratospheric polar vortex, global ozone concentration and also climate/weather pattern. All these processes could only be accurately evaluated using a global scale 3D chemistry-climate model and the parameterization for the additional heating presented and explained here. A Chemistry Climate model [23] is used to evaluate of the possible influence of Joule heating induced by the solar wind and interplanetary magnetic field elements on the ozone concentration and dynamics of the Earth stratosphere. The Joule heating rates in the stratosphere are parameterized on the base of the time series of the solar wind and IMF parameters taken from NASA satellite dataset (1973-1999) for 1996. The results of the 10-


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year-long model run with the additional Joule source of heat are compared with the output of the 10-year-long control model run without it. Both simulations are performed in equilibrium mode with prescribed boundary conditions and for the minimum of the 11-year solar spot cycle. Figure 3 shows the monthly zonal mean temperature ratio changes from the control to disturbed run in March.

The temperature decreases more than 3 K at high northern latitudes in the stratosphere (Figure2). On the contrary the tropical lower stratosphere becomes significantly warmer (~2 K). Model calculation demonstrated [23] that the stratospheric circulation and ozone amount are rather sensitive to the Joule heating induced by the electromagnetic energy of the solar wind input in the stratosphere.

Figure 3. Simulated changes of the monthly zonal mean (a) temperature, in K in %, due to Joule heat forcing for March. The shading indicates the level of the statistical significance (light – at or more 80%; heavy – at or more 95.

5. Influence Conductivity of the Ground Earth as One Main Parameter of the Global Electric Circuit

The stratospheric warming as a result of the increasing energy of the solar wind and magnetopause approaching the Earth was explained by Makarova and Shirochkov [12] in the framework of a modified version of the global electric circuit with an external electromotive force (EMF) generator.

In this case some part of the solar wind energy is transferred into the system “magnetosphere – ionosphere – atmosphere” as the energy of induced electric fields.

The Earth’s stratosphere where a layer of increased heavy ion concentration is found [15] could be one of the conducting layers of the global electric circuit under certain circumstances. Furthermore, electric currents flowing through this stratospheric ion layer will


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produce Joule heating of the stratosphere. The reality of this hypothesis was proved by numerical calculations, which showed that this process could produce the observed warming of the stratosphere by several degrees [14]. The next step was the inclusion of this algorithm into one of the few existing global models of the atmosphere. Numerical experiments with this modified version of the model demonstrated efficiency of the proposed mechanism variability of stratospheric temperature and the ozone density [23].

Using a modified version of the global electric circuit mentioned earlier an increase of the solar wind dynamic pressure will produce more intense electric currents in the circuit and, consequently, a warming of the stratosphere. The observed phenomenon of cooling of the stratosphere could be explained by a re – distribution of the currents in the circuit due to change of electric conductivity of separate elements of the circuit. The electric conductivity of the stratosphere can generally be taken as σ = 10-10 S/m. The conductivity of the ground surface is much greater - σ = 2 - 10-2 S/m. The latter values are typical for seawater and cultivated soil. It is well known that the ground surface in the Arctic is typically either snow above ice or permafrost. These kinds of the ground surface are not good electric conductors since typical values of the conductivity of permafrost soil is σ = 10-7 S/m while for the dry ice it is σ = 10-8-S/m. A layer of increased ion concentration could exist in the stratosphere at altitudes 20 – 30 km. The ion density in this layer could be as high as n = 5 109 m-3 [15] which means that stratospheric conductivity here could be σ = 10-7 S/m. By comparison, ice conductivity is equal to σ = 10-8 S/m under air temperature of -10°C while it becomes equal to σ = 5 10-10 S/m under air temperature minus 40°C [22]. Therefore the situations could be expected when conductivity of the ground surface is close to the values of σ observed in the stratosphere.

The data of atmospheric balloon sounding at four arctic and subarctic stations were chosen for study of the variations of atmospheric temperature as functions of the solar wind energy and results are presented in Table 1.

Table 1. Correlation coefficients between stratospheric temperature at 50 hPa isobaric surfaces and the solar wind dynamic pressure for 1964 –2002 years

Station Geographic latitude

Geographic longitude December September June

Barter 70. 13o N 216. 36o E -0.71 -0.7 0.65 Fairbanks 64. 81o N 212. 13o E -0.8 0.54 0.49 Ziryanka 65. 73o N 150. 89o E -0.72 -0.54 0.51 Murmansk 68. 96o N 33. 04o E - - - Lulea 65.54o N 22.13o E 0.75 0.71 0.54

Data of Table 1 shows examples of the dependence of stratospheric temperature on the

solar wind dynamic pressure at several stations. Both parameters are taken for each December, September and June in the period from 1964 to 2002. Data of Table 1 demonstrate that the increased input of solar wind energy could cause a warming (positive correlation for Lulea) as well as a cooling of the stratosphere (negative correlations for Barter, Ziryanka, Fairbanks). Rather unusual data were obtained for Murmansk: the temperature of the stratosphere at this station could be either directly proportional to an increase of the solar


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wind or inversely proportional to it. Due to this, the correlation coefficient between these two parameters appears to be very low at this station. One can see that the correlation between stratospheric temperature and solar wind dynamic pressure for Barter is negative for all seasons, while it is always positive for Lulea. The same parameter for Fairbanks and Ziryanka changes its sign with the seasons (it is negative in winter and positive in summer). However, the data of Murmansk demonstrate its two-fold character of the relation between these parameters for all stations of year. Therefore the resulting correlation coefficient between solar wind dynamic pressure is very low for Murmansk in every season of the year.

It seems that the results obtained could be explained in the framework of the global electrical circuit concept under the assumption that changes of the electric conductivity of the stratosphere and the ground surface must redistribute the electric currents in the elements of the global electric circuit. In this case the seasonal variations of the obtained relations (see Table 1) could be attributed to natural seasonal changes of the conductivity of the ground surface, e.g., how wet it is, or how covered with ice.

The conductivity of the Arctic stratosphere could be higher than of the ground surface under the same circumstances. In this case the electric current in the global electric circuit will flow through the stratosphere under undisturbed conditions in the solar wind since the corresponding conductivity of the ground surface (ice) will be lower than in the stratosphere. As a result of such a redistribution of the currents the stratosphere will be warmed. This phenomenon is illustrated well by the data of Table 1 where it is shown that under quiet conditions in the solar wind (low dynamic pressure) the stratospheric temperature is higher at the high – latitude stations: Barter and Fairbanks than at the sub – auroral station Lulea.

One must take into account that the conductivity of the ground surface covered by ice could increase with increasing air humidity and temperature. In this case a re–distribution of the currents inside the global electric circuit takes place. Under increased solar wind dynamic pressure the currents flowing through the stratosphere will be less than the currents flowing through the ground surface. Consequently cooling of the stratosphere with an increase of the solar wind dynamic pressure can be explained. Confirmation of this effect can be seen in the data of Table 1 where a negative correlation between these two parameters is shown. The change of the sign of the correlation between the solar wind dynamic pressure and stratospheric temperature is connected closely with the seasonal variations of the ground surface conductivity.

Zakharov [22] demonstrated the maps of the ice distribution in the Arctic for different seasons. The areas covered by permanent ice, as well as by drifting ice were shown on these maps. These maps showed, that ground surface at Barter station (northern coast of Alaska) is covered by permanent ice for the whole year. Quite naturally we have the negative correlation between the solar wind dynamic pressure and stratospheric temperature (see Table 1).

At the stations Fairbanks and Zirynka located at lower latitudes the ground surface thaws in summer, therefore the negative correlation sign for the winter months is transformed to positive values in summer. The sub-auroral station Lulea is located beyond the permafrost zone; thus the ground surface conductivity here does not change significantly with season. The stratospheric temperature at this station will depend primarily on the level of the solar wind disturbance. The greater the solar wind dynamic pressure the warmer will be the stratosphere at this station. The different situation in ground surface conductivity is observed at Murmansk in all seasons where either approaching sea ice or open seawater are presented. Therefore we obtained the complicated dependence between the stratosphere temperature and


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the solar wind dynamic pressure at this station. So, variations of temperature of the middle atmosphere are connected with both EUV radiation and solar wind energy. Observed results can be explained in framework of global electrical circuit driving by thunderstorm activity and energy of the solar wind. Temperature of stratosphere is increasing during disturbances of solar wind if conductivity of the Earth’s surface is high. And vice versa-temperature of stratosphere has negative correlation with energy of the solar wind above places covered by ice. Middle atmosphere is warmer above places covered by ice than the surface with good conductivity during quite solar wind. Situation is opposite during disturbances of solar wind

The Solar Wind Energy as a Part of the Total Solar Activity

Other data similar to those shown on Figure 1 demonstrate that the short-term variations of the stratospheric temperature are under influence of the solar wind energy changes [10, 12]. Furthermore it was found that the same relation could be traced in the long-term (several cycles of the solar activity) variations of stratospheric temperature in the polar atmosphere [13]. The latter authors showed that enhanced solar wind dynamic pressure caused warming of the stratosphere above both the Northern and Southern geographic poles while quite opposite effect was observed above Antarctic station Vostok located at distance about 1500 km from the South Pole. All these relations are found for winter months i.e. for the “polar night” conditions when the solar UV radiation impact on the polar atmosphere is minimal.

Since the solar wind energy is proved to be geoeffective force, it is worth trying to determine its relation to other kinds of the solar activity whose influence on the Earth weather and climate is commonly accepted.

Figure 4. Time of various parameters of the solar activity (annually averaged values f W) (a) and the solar wind dynamic pressure (annually averaged values of nV2, nPa) (b)


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Figure 4 shows time series of the annually averaged values of the Sun spot numbers and the annually averaged values of the solar wind dynamic pressure for period of 1970-2008. One can see that the both data sets vary synchronously during period of 1970-2000 when their extremes coincide in time. However, this similarity disrupted suddenly in the last 23d cycle of the solar activity. If the sunspot number W continue to vary in accordance with usual 11-year period the solar wind dynamic pressure demonstrate monotonous diminishing. In order to explain this unusual solar anomaly we considered temporal variations of other important solar parameters shown at Figure 5.

Figure 5. The long term variations a) the monthly averaged values of the total solar irradiance (TSI, Wm –2); b) the monthly averaged values of the magnetic field of the solar wind (B, nTl) and c) the monthly averaged values of the position magnetopause.

The quasi-stationary variations of the parameters of the solar wind during 23 cycle of solar activity were studied. It was found that the main peculiarity of this cycle is diminishing magnetic field of the solar wind as compared with the previous two cycles. Maximum of magnetic field of the solar wind as well as many high velocity fluxes with low density of plasma is observed in 2003 -2004 after phase of sunspot maximum in June of 2002. The high


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velocity solar fluxes with low density plasma are connected with increasing of corona mass injections during early declining phase of the solar activity. The main peculiarity of the 23 cycle of the Sun activity is diminishing magnetic field of the solar wind and TSI on the end of cycle, and quasi-stationary changes position of the magnetopause position as indicator of electromagnetic energy of the solar wind. The quasi-stationary variations of the parameters of the solar wind during 23 cycle of solar activity are shown on Figure 5. The quasi-stationary values of magnetic field of the solar wind during minimum solar activity in 2005 -2007 years became to be equal to 4 nTl while it was approximately 6 nTl in the previous 21 and 22 cycles. Non - stationary and dense fluxes of the solar wind with values of velocity approximately 450 km/s are characteristic for minimum solar activity in the 23 cycle. It is reasonable to suggest existence of connection between these fluxes with development of heliospheric current sheaths and coronal streamers when large magnetic fields of the Sun are not strong.

The quasi-stationary values of magnetic field of the solar wind shows some more long cycle of variation which is approximately 50 years with maximum in 21 and 22 cycles and minimum in 20 and 23 cycles. Structure of magnetic fields of the Sun determines different kinds of the solar activity including intensity of total solar irradiance (TSI) and energy of the solar wind transferred into the near- Earth space. One of the main products of energy of the solar wind is the electric field system, which is observed in the ionosphere, middle atmosphere and on the ground surface. Therefore it could influence climate of the Earth. Knowledge of the real periodicity of the solar activity is very important for human activity.

Conclusion

1. Temporal variations of the temperature of the middle atmosphere are connected with the solar wind energy

2. The results observed can be explained in the framework of the global electrical circuit driven by energy of the solar wind.

3. The temperature of the stratosphere increases during disturbances of the solar wind if the conductivity of the Earth’s surface is high. Vice versa-the temperature of the stratosphere above places covered by ice has a negative correlation with energy of the solar wind

4. The stratospheric layer with increased concentration of ions created by galactic or solar charged particles is an important element of the global electric circuit in the polar regions.

5. Long –term variations of the different kind of the solar activity can influence on electromagnetic energy and fluxes of galactic or solar charged particles which enter the near - Earth Space and change the Earth climate and weather.

Acknowledgement

This work was performed partly due to assistance of the Russian Basic Research Foundation (RBRF) Grant 06-05-64311.


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References

[1] Alfven, H., Falthammar, C.G. Cosmical electrodynamics; Clarendon Press, Oxford, UK, 1963, 5-280.

[2] Baker, D.N. J. Atmos. Solar-Terr. Physics. 2000, vol. 62, 1669 – 1681. [3] Bazilevskaja, G.A., Krainev, M.B., Makhmutov, V.S. J. Atmos.Solar-Terr.Physisc,

vol.62, 2000, 1577-1588. [4] Bering, III, E.A., Few, A. A., Benbrook, J. R. Physics Today. 1998, vol. 51(10), 24-30. [5] Brasseur, G., Chatel, A. Ann. Geophys. 1983, vol. 1, 173-185. [6] Callis, L.B., Nataranjan, M., Lambeth, J. B., Baker, D.N. J. Geophys. Res. 1998, vol.

103, 28421- 28438. [7] Ginzburg, E.I. In: Construction principles of the upper atmosphere dynamics models;

Editor Ginzburg, E.I., Hydrometeoizdat, Moscow, USSR, 1989, 3-121 (in Russian). [8] Heaps, M.G., Planet. Space Sci. 1978, vol. 26, 513-517. [9] King, J.H., Couzens, D.A.. Interplanetary Medium Data Book-Supplement 3A, NASA,

Washington, D.C., USA, 1986. [10] Makarova, L.N., Shirochkov, A.V., Grigor’eva, J.A., Volobuev, D.M., Geomagnet. and

Aeronomy, 1997, vol. 37, 158- 164 (in Russian). [11] Makarova, L.N., Shirochkov, A.V., Koptjaeva, K.V., Geomagnet. and Aeronomy,

1998, vol. 38, 159-162 (in Russian). [12] Makarova, L.N., Shirochkov, A.V. 2000, Phys. Chem..Earth, 2000, vol. C 25, 495-498. [13] Makarova, L.N., Shirochkov, A.V. Phys. Chem. Earth, 2002, vol. C 27, 449-453. [14] Makarova, L.N., Shirochkov, A.V., Nagurny, A.P., Rozanov, E.V., Schmutz, W. . J.

Atmos. Solar-Terr. Physics, 2004, vol. 66, 1173-1177. [15] Rosen, J.M., Hofmann, D.J. J. Geophys. Res., 1988, vol. 93A, 8415-8422. [16] Shue, J.H., Chao, J.K., Fu H.C. et al., J. Geophys. Res. 1997, vol. 102A, 9497-9506. [17] Solanki, S.K., Fligge, M. Geophys.Res.Lett. 1998, vol. 25, 341-344. [18] Troshichev, O.A., Egorova, L.V., Vovk, V.Ya. Adv. Space. Res., 2004, vol. 34, 1824-

1829. [19] Volland, H. In: Modern Ionospheric Science; Editors Kohl, H., Ruster, R., Schlegel, K.,

Max-Planck-Institut fur Aeronomie, 37191 Katlenburg-Lindau, FRG, 1996, 102-135. [20] Webber, W. J. Geophys. Res. 1962, vol. 67, 5091-5106. [21] Whitten, R.C., Poppoff, I.G. Physics of the lower ionosphere; Prentice-Hall, Inc.,

Englewood Cliffs, N. J., USA, 1965, 3-292. [22] Zakharov, V.F. Sea ice in climatic system. Hydrometeoizdat, Saint-Petersburg, Russia,

1996, 3-213 (in Russian). [23] Zubov, V.A., Rozanov, E.V., Shirochkov, A.V., Makarova, L.N., Egorova, T.A.,

Kiselev, A.E., Ozolin, Y.A., Karol, I.L., Schmutz, W. . J. Atmos. Solar-Terr. Physics, 2005, vol. 67, 155-162.


Chapter 5

ELECTROSTATIC WIND PROPULSION1

Alexander Bolonkin2 C & R, Brooklyn, NY, USA

Abstract

A method for space flights in outer space is suggested by the author. Research is present to shows that an open high charged (100 MV/m) ball of small diameter (4–10 m) made from thin film collects solar wind (protons) from a large area (hundreds of square kilometers). The proposed propulsion system creates many Newtons of thrust, and accelerates a 100 kg space probe up to 60–100 km/s for 100–800 days. The 100 kg space apparatus offers flights into Mars orbit of about 70 days, to Jupiter about 150 days, to Saturn about 250 days, to Uranus about 450 days, to Neptune about 650 days, and to Pluto about 850 days.

The author developed a theory of electrostatic wind propulsion. He has computed the amount of thrust (drag), to mass of the charged ball, and the energy needed for initial charging of the ball and discusses the ball discharging in the space environment. He also reviews apparent errors found in other articles on these topics. Computations are made for space probes with a useful mass of 100 kg.

Key words: Electrostatic wind propulsion, Solar wind.

Introduction

Current method of space flight

At present, we use only one main method of launch for extra-planetary flight – that is liquid or solid fuel rockets. This method is very complex, expensive, and dangerous.

1 The work was presented as AIAA-2005-3857 at the 41st Propulsion Conference, 10–13 July 2005, Tucson, Arizona, USA. 2 Correspondence to: C&R, A.Bolonkin, 1310 Avenue R, #F-6, Brooklyn, NY 11229, USA, T/F 718-339-4563,

[email protected], or [email protected], http://Bolonkin.narod.ru

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The current method of flight has reached the peak of its development. In the last 30 years it has not allowed cheap delivery of loads to space, or made tourist trips to the cosmos affordable, much less individual flights to the upper atmosphere. Space flights are very expensive and not conceivable for average people. The main method used for electric energy separation is photomontage cells. Such solar cells are expensive and have a low energy storage capacity.

The aviation, space, and energy industries need revolutionary ideas which will significantly improve the capability of future air and space vehicles. The author has offered a series of new ideas1–47 particularly in manuscripts presented to the World Space Congress (WSC)-1992, 199444-47, and to WSC-2002, 10–19 October 2002, Houston, Texas, USA4– 5, 7–

13 and in his articles, patent applications1–47, 53–57 . In this chapter a method and installations for future space flights are proposed. The

method uses an open high charged ball made from thin film which collects solar wind from a large area. The offered propulsion system creates many Newtons of thrust, and accelerates a 100 kg space apparatus to high speeds. This allows it, in an acceptable time of 100–800 days, to reach speeds of up to tens of km/s (50–100 km/s). A flight to Mars would take only 70 days, to Jupiter about 150 days, to Saturn about 250 days, to Uranus about 450 days, to Neptune about 650 days, and to the farthest planet, Pluto, about 850 days.

History of innovation

During 1982–1983 in series of patent applications29–41 the author offered some methods and installations for space propulsions and electric generators using solar wind. In 1987 these ideas were published in Report ESTI42. In 1990 the author published brief information about this topic43 (see pp. 67–80) and in 1992–1994 he reported on further researches at the World Space Congresses-1992, 1994, 200244–47. In 2003 N. Omidi and H. Karimabadi published an article on a similar topic48. Differences between the ideas and results in this chapter and their work48 an are raised in the Discussion section.

Information about Solar Wind

The Sun emits plasma which is a continuous outward flow (solar Wind) of ionized solar gas through out our solar system. The solar wind contains about 90% protons and electrons and some quantities of ionized α-particles and gases. It attains speeds in the range of 300–750 km/s and has a flow density of 5×107 – 5×108 protons/electrons/cm2s. The observed speed rises systematically from low values a 300–400 km/s to high values of 650–700 km/s in 1 or 2 days and then returns to low values during the next 3 to 5 days (Figure 1b). Each of these high-speed streams tends to appeal at approximately 27-day intervals or to recur with the rotation period of the Sun. On days of high Sun activity the solar wind speed reaches 1000 (and more) km/s and its flow density 109 – 1010 protons/electrons/cm2s, 8–70 particles in cm3. The Sun has high activity periods some days each year.

The pressure of the solar wind is very small. For full braking it is in the interval 2.5×10–

10 ÷ 6.3×10–9 N/m2. This value is double when the particles have full reflection. The

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interstellar medium also has high energy particles. Their density is about 1 particle/cm3. The interaction of the solar wind with the Earth’s magnetosphere is shown in Figure1a.

Figure 1a. Interaction of solar wind with Earth’s magnetosphere.

Figure 1b. Speed and density variations of solar wind in the Earth’s orbit. The speed is in km/s, the density is in protons/cm3.

Description of the proposed Propulsion System

Offered Space Propulsion System

The suggested propulsion system is very simple. It includes a hollow ball made up of a thin, strong, film – covered conductive layer or a ball of thin net. The ball is charged by high voltage static electricity which creates a powerful electrostatic field around it. Charged

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particles of solar wind of like charges repel and particles with the unlike charges attract. A small proportion of them run through the ball, a larger proportion flow round the ball in hyperbolic trajectory into the opposite direction, and another proportion are deviates from their initial direction in hyperbolic curves. As a result the charged ball has drag when the ball speed is different from solar speed (Figures 2, 3). The drag also occurs when the particles and the ball have the same electrical charge. In this case the particles are repelled from the charged ball (Figure 3) and brake it. This solar wind drag provides thrust in our proposed propulsion system. The pressure of solar wind is very small, but the offered system (a charged ball of radius 6–10 m) collects particles (protons or electrons) from a large area (an area of tens of kilometers radius for protons and hundreds of kilometers for electrons), creates a thrust of some Newtons and a 100-kg space ship reaches speeds of tens of km/s in 50–300 days (see theory and computation below and Referances29, 42–47).

Figure 2. a - Interaction between solar wind and the electrostatic field of a charged ball. Notations are: 1 – solar wind (protons/electrons), 12 – charged particles (protons/electrons); 13 – electrically charged ball (balloon); 14 – line of turn of angle γ of a particle that is attracted (attracted force of unlike charges); 15 – line of turn of angle of a particle that is repelled (repulsive force of like charges); R – radius of interaction or neutral radius, r1 – radius of integration, Vs – wind speed, V – ship speed. b – change of particle direction caused by electric ball field. c – collection area (top view).

Steerability of the System and Control of Thrust

The magnitude of thrust is determined by the controlled ball charge value, and the deviation of this thrust from the direction of the Sun is controlled using one of the two methods shown in Figure 4. In the first method the inclination of a plane formed by balls in a triangle is changed by adjusting the cable length, 8, and the thrust T is deviated from the direction of the Sun (Figure 4a). In the second method the propulsion system has a cylindrical capacitor, 20 (Figure 4b,c), which accelerates the particles on one side and brakes or turns back the particles on the opposite side (for the opposite side the capacitor works as an electrostatic mirror, Figure 4c). As a result the thrust is deviates from the direction of the Sun. A collection


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of three balls enables the thrust to be deviated by up to 10 degrees (Figure 4a), and an additional net capacitor enables deviation of up to 20–30 degrees (Figure 4b).

Figure 3a. (Left) Hyperbolic trajectory of protons around static negative charge (or electrons around positive charge) (unlike charges). Notations are: 1 – solar wind (charged particles); 2 – hollow negatively charged ball of thin film; 3 – hyperbolic trajectory of charged particles; 4 – positively charged particles (protons). (Right). Trajectory of particles having the same charge as the ball. Notations are: 5 – negatively charged particles.

Figure 3b. A very large sphere, even of a thin film, can hold a massive charge. Here is an Echo balloon satellite of the early ‘60s, 30 meters (100 feet) across; note the men for scale. With suitable insulation and charge protection a very light sphere can hold enormous energies within. Credit: NASA. http://dayton.hq.nasa.gov/IMAGES/SMALL/GPN-2002-000203.jpg.

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Figure 4. Two methods of controlling of the thrust direction: a – control using three balls. Notations are: 7 – spaceship (probe); 8 – links (cables) connected to the space ship and the electrostatic balls. 9 – cable connection of balls; 10 –T – thrust of the propulsion system; b – control of thrust direction by capacitor (electrostatic mirror). c – top view of capacitor. The other notations are presented in Figure 3a.

Discharge of Electrostatic Ball

The solar wind has high speed at a large distance from the ball. This means the particles have a trajectory close to a hyperbolic curve in the ball’s area of influence and most of them will fly again into infinity. Only a proportion of them will travel through the ball. These particles decrease its speed and can discharge the ball. However, their speed and kinetic energy are very large because they are accelerated by the high voltage of the ball’s electric field (some tens or hundreds of MV). The necessary ball film is very thin (only of microns). The particles pierce through the ball. If their loss of speed is less then the solar wind speed, their trajectory will be close to a hyperbolic curve and they will fly into space. If their loss of a speed is more than the solar wind speed, their trajectory will be close to an ellipse, so they will return to the ball and after many revolutions they can discharge it if their perigee is less then the ball’s radius. This discharge may be compensated using special methods.

There are some possible methods for decreasing this discharge (Figure 5a,b,c): a) A ball made of net; b) a charged cylindrical capacitor located in front of the ball to deflect the particles from the ball; c) a capacitor located behind ball to increase the speed of the particles to hyperbolic speed (this is a particle accelerator) and to reflect the returning particles.


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Figure 5. Two methods of decreasing the ball discharge: a – a charged cylindrical capacitor located in the front of the ball deflects particles from the ball; b – a capacitor located behind the ball adds speed to the particles and reflect the returned particles. c – top view of capacitor. Notations are: 30 – cylindrical capacitor, 31 – back capacitor (particles accelerator and electrostatic mirror).

Problem of Blockading of the Ball Charge

Blockading of the charge on the ball by unlike particles is the main problem with this method. The charge on the ball attracts unlike particles and repels like particles. The opposite charge particles accumulate near the ball and block its charge. As a result only the area near the ball deflects and reflects the particles. That area many times less than the area of interaction of the ball are the particles when there is no blockading. The forces are thus greatly reduces. Omidi and Karimabadi48 apparently had not seen this and all their results seem to be wrong. There are other apparent errors in their text which affect all their other results (see Discussion section).

The author of this work proposed two models for estimation of the efficient charge area (diameter of neutral working charge). In the first model the radius of the efficient area is computed as the area where particles of like charge to the ball are absent and the density of opposite-charge (unlike) particles is the same as the solar wind. This model gives the lower limit of the efficient area. In the second model the radius of the efficient area is computed as the area where the density of unlike particles is less than the solar wind density because the unlike particles inside the efficient area have generally higher velocity than a those outside this area. The neutral area (neutral sphere) in model 2 is large than in model 1. Model 2 is better, but this problem needs more detailed research.

The proposed system could be used as a thermonuclear propulsion system and a thermonuclear electric generator. The suggested idea may be useful in the design of thermonuclear propulsion systems and electric generators. The solar wind particles approach

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the ball with very high energy (hundreds of MV). Their density near the ball axis and behind the ball may also be high. An energy of 5–15 MV is enough for a nuclear reaction. This may be a proton–proton reaction or protons with any other matter (central electrode). In last case the cylindrical capacitor (Figure 6a) is located behind the ball. This capacitor changes the particle speed (energy) to the required value. The capacitor has a central electrode made of matter which gives a nuclear reaction (product). The products of the reaction are reflected by a parabolic electrostatic mirror in one direction. That forms the thermonuclear propulsion system. The products of nuclear reaction may be photons and the mirror may be a light reflector, in which case we have a photon propulsion system. The electrostatic mirror is made from a thin net; the light reflector is made from a thin film with a reflective layer. They do not influence the particle flow to the central electrodes because the particles have very high speed and energy. The energy of the charged particles can be converted to electrical energy by braking of the electrostatic field as the author has proposed 31–47. These tasks need more detailed research.

Figure 6a. Nuclear propulsion system using solar wind (or interstellar particles). Notations are: 50 – space apparatus; 51 – cable connecting the space apparatus and the ball; 52 – collector particles and thermonuclear reactor; 53 – reflector of reaction products or light photons. Other notations are the same as previous Figs.

Application as Interplanetary Propulsion System

The previously proposed (no-nuclear) propulsion system does not allow speeds to be reached more than the maximum speed of the solar wind – 1000 km/s. This is not enough for an interstellar trip. For an interstellar voyage the speed must be about 100,000 km/s. The thermonuclear wind propulsion system does increase propulsion capability. The space speed can be greater than the wind speed and the space ship can therefore move against the solar wind.

The interstellar medium also contains high energy particles (cosmos rays) a density of about one particle per cubic centimeter. These particles can be collected from a large area by the electrostatic ball and used by the thermonuclear propulsion system. The author calls on all nuclear scientists to research these possibilities. The thermonuclear propulsion system and


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power thermonuclear electric generator may be easier to design for space than for the Earth because we have a natural high vacuum and a multitude of natural particles in space, and the suggested method and installation solve a major problem of thermonuclear reaction – obtaining high energy particles and collecting them in a small volume with high density. Possible form of interplanetary flight system is shown in Figure6b.

Figure 6b. Possible form of interplanetary flight system,

Theory of the Solar Wind Installation. Main Estimations and Computations.

1. General Theory

Interplanetary space has a magnetic field. The motion of the charged particles in the magnetic and ball electric field is described by the Lorenz force law:

mdV/dt = q(E+V×B), (1)

where m – mass of particles [kg], V – speed of particles [m/s] (vector), t – time [s], q – charge [C], E – electric intensity of charged ball field [V/m, or N/C] (vector), B – interplanetary magnetic field [T] (vector).

For a charged ball the electric intensity is E = kQ/r2, where the coefficient k ≈ 9×109 [Nm2/C2], Q is ball charge [C], r is distance from the ball center [m].

The first element on the right os equation (1) is electrostatic (Coulomb’s) force; the second element is Lorenz force.

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The interplanetary magnetic field, B, at 1 AU (AU – Astronomical Unit, 150×106 km, radius of Earth orbit) is typically very small at 10 nT and makes an angle of 45o with the Sun–Earth line (i.e., the radial direction). For a typical wind speed, Vs, the second element is small (∼4 mV/m). In a full vacuum (without space plasma) the electric intensity from 1 C of the ball at a distance of 1000 km is ∼10–2 V/m. Moreover, the Lorenz force does not increase the radial speed. it only deflects the particle’s trajectory from the radial line. Because of that we can ignore the Lorenz force.

The charged ball repels the like charged particles. In particular, a negatively charged ball repels the space plasma’s electrons. .

It is possible to find the minimum distance which solar wind electrons can approach a negatively charged ball. The full energy of a charged particle (or body) is the sum of the kinetic and potential electric energy. Any change of energy equals zero:

02

,11,,,02

2

2

2

=−−=⎟⎠⎞

⎜⎝⎛ −∞

====+ ∫∞ r

kqQmVr

kqQr

kqQErqQkFFdrEEmV

p

r

pp, (2)

where m is the mass of a particle [kg] (mass of a proton is mp = 1.67.10–27 kg, mass of an electron is me = 9.11.10–31 kg); V is the speed of particle [m/s] (for solar wind Vs = 300–1000 km/s); Ep is the potential energy of a charged particle in the electric field [J]; F is the electric force, N; q is the electrical charge of a particle [C] (q = 1.6×10–19 C for electrons and protons); k = 9×109 is coefficient, r is the distance from a particle to the center of the ball [m]; Q is ball charge [C].

From equation (2) the minimum distance for a solar wind electron is (m = me , V = Vs):

mEqaK

kEaQ

mkqQKwhere

VmEqa

VK

VmkqQr

ses

22

2

2

22min ,,,222====== , (3)

where K is a coefficient; me is electron mass; Vs is the solar wind speed [m/s]; a is the radius of ball [m]; E is electrical intensity at the ball surface [V/m]. The maximum electrical intensity of negative charge is about 108 – 2×108 V/m in a vacuum.

For a = 6 m, E = 108 V/m, Vs = 4×105 m/s we have rmin ≈ 8×106 km. Other values are presented in Figure 7a,b.

2. Estimation of Minimum Neutral Sphere around a Charged Ball

a) Model 1. Constant Particle Density The charge density of the unlike space plasma particles inside a neutral sphere is equal to the density of solar wind. The minimum radius of the neutral sphere is

NqdkdEa

dQRdRQ nn

632

33 10,43

43,

34

====ππ

π , (4)

where d is density of solar wind [C/m3]; Rn is the minimum radius of the neutral sphere [m]; N is the number of particles in cm3. The solar wind charge density may be taken by linear interpolation from Table 1 for a distance from the Sun equals to 1 AU = 150 million km.


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Figure 7a. Minimum distance of a single electron from a negatively charged ball with electric intensity of E = 100 million volts/m.

Figure 7b. Minimum distance of a single proton from positively charged ball with electric intensity of E = 100 millions volts.

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Table 1. Distance from Sun is 1 AU.

s m/s 0 4×105 106

N in cm30 0 10 70

Computation of the minimum radius of the neutral sphere is presented in Figure 8.

Figure 8. Radius of the neutral sphere in Model 1, when particle density in the sphere equals space plasma density.

b) Model 2. Variable Particle Density Density of the unlike particles inside the neutral sphere will be less than the density of solar wind particles because the particles are strongly accelerated by the ball charge to speed approximately the speed of light. The new density and new corrected radius can be computed in the following way:

1) The speed of protons along a ball radius is

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

0

20

2 112rr

KVrVr , (5)


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where V0 = Vs – proton speed at an initial radius of R >> Rn, and Rn is the radius of the neutral sphere.

2) Particle charge density, dp, along a ball radius is

0

260 ,/10,)( S

SssNqdrV

Vdd por

pop === , (6)

where S is distance from the Sun in AU; S0 = 1 AU; s is relative distance from the Sun; dpo is density at 1 AU.

3) Charge of the neutral sphere along a sphere radius is

( )drrV

rVdQQR

a rpor ∫−=

2

04π . (7)

4) The radius of the neutral sphere can be found from the condition Qr = 0. For our

estimation we will find it using the stronger condition Qr = 0.5Q, and call it the efficiency radius Re of charge q.

Results of computation are presented in Figure 9.

Figure 9. Radius of the neutral sphere in Model 2 via distance from the Sun, when particle density is variable with radius in the neutral sphere and depends on the variable speed of accelerated particles.

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As you can see the efficiency radius in Model 2 is significantly more than in Model 1.

3. Estimation of Electrostatic Sail Drag

All protons in the neutral sphere change the direction of their trajectories from 0o to 180o. The drag (thrust), D, of the electrostatic sail can be estimated by the equation

VVVsRVNmCD speppD −== ,/10 2226 π , (8)

where Vp is relative speed of the probe [m/s]; CD is the drag coefficient. If not all particles change their direction, CD = 0; if all particles turn to 90o, CD = 1; if all particles turn to 180o, CD = 2. We take CD = 1.5 for our computation. V is the probe speed [m/s]. When V << Vs, the relative speed is Vp ≈ Vs.

Results of computation of the sail drag for Vp ≈ Vs using equation (8) are presented in Figure 10 and 11.

Figure 10. Drag of the electrostatic sail versus ball radius at the Earth’s orbit (at 1 AU) for the solar wind speed 400 km/s and electrical intensity E = 100 million volts/meter.

4. Estimation of the Ball Stress, Cover Thickness and Ball Mass.

The ball has tensile stress from the like electric charge. We need to find the ball stress and the required thickness of the ball cover. If the ball is in a vacuum and the ball charge, Q, is constant, its ball internal force is


211

( )k

aEfkEaQ

akQf

akQWk

kaC

CQW

aWf

2,,

2

,2

,1094

1,,2

,

22

2

2

29

0

2

−==−=

=×====∂∂

=πε

(9)

where f is the tensile force inside the ball [N]; W is the charge energy [J]; C is the capacity of the ball as a sphere capacitor [F]; E is electrical intensity [V/m].

Figure 11. Drag of the electrostatic sail versus distance from the Sun (in AU) for ball radius a = 2–10 m, solar wind speed 400 km/s and electrical intensity E = 100 million volts/meter.

The internal ball pressure is

,8

,4,2

2

kEpaS

Sfp

ππ === (10)

where p is the internal pressure [N/m2], S is the ball surface area [m2].

The thickness of the ball cover, δ, is

σπδ

σδδσππ

kaEapapa

16,

2,2

22 === , (11)

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where δ is cover thickness [m]; σ is safe cover stress [N/m2]. The ball mass is

σγπδγ

kEaMaSSM ss 4

,4,23

2 === , (12)

where Ms is the ball (sail) mass [kg]; γ is the ball cover density [kg/m3]; σ is safe stress of the ball cover [N/m2].

Computation of the ball thickness and ball mass are presented in Figs. 12 and 13.

Figure 12. Thickness of ball cover versus ball diameter for different safe cover stress value, electrical intensity E = 100 million volts/m.

5. Estimation of Probe Acceleration, Speed, and Flight Time

We estimate these values only for a probe moving along the Sun’s radius. The equations are ( ) ds

Vdtds

VMMRDdV

MMRDA

s

e

s

ec

1,)(

)(, =+

=+

= , (13)

where Ac – probe acceleration [m/s]; D – probe drag [N]; M – probe mass [kg]; Ms – sail (ball) mass (Figure 13) [kg]; V – radial probe speed [m/s]; t – flight time [s]; s – distance from Sun [m].


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Figure 13. Mass of ball cover versus ball diameter for different safe ratio’s of stress/cover density and

electric intensity E = 100 million volts/m.

The result of computation for a = 6 m, E = 108 V/m, M = 100 kg, σ = 180 kg/mm2 , γ = 1800 kg/m3 , s = 1–40 AU are presented in Figs. 14, 15, 16, and 17.

The ball (sail) weight increases as a cubic value and the total acceleration reaches a maximum. Figure 14 shows optimal ball radius for current materials.

Figure 14. Probe acceleration versus ball radius for useful probe mass M = 100 kg, and the sail weight computed for safe cover stress σ = 180 kg/mm2, cover density γ = 1800 kg/m3, electric intensity E = 100 million volts/meter, at a distance from the Sun of 1 AU (Earth orbit).

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Figure 15. Probe acceleration versus distance from the Sun and ball radius for useful probe mass M = 100 kg, and sail weight computed for safe cover stress σ =180 kg/mm2, cover density γ = 1800 kg/m3, electric intensity E = 100 million volts/meter, at a distance from the Sun of 1–40 AU.

Figure 16. Probe velocity versus distance from Sun and the ball radius for useful probe mass M = 100 kg, and sail weight computed for safe cover stress σ = S = 180 kg/mm2, cover density γ = 1800 kg/m3, electrical intensity E = 100 million volts/meter, at a distance from Sun 1–40 AU, Vp ≈ Vs .


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Figure 17. Probe trip time versus distance from the Sun and the ball radius for useful probe mass M = 100 kg, and sail weight computed for safe cover stress σ = S = 180 kg/mm2, cover density γ = 1800 kg/m3, electrical intensity E = 100 million volts/meter, at a distance from the Sun of 1– 40 AU, Vp ≈ Vs .

The proposed probe can reach Mars orbit in about 70 days (and reaches a speed of 50 km/s), Jupiter in about 150 days, Saturn in about 250 days, Uranus in about 450 days, Neptune in about 650 days, and the farthest planet Pluto (5800 million km) in about 850 days.

The final (interstellar) speed is about 100 km/s. The parameters of the probe (spaceship) are not optimal, but may be improved.

6. Estimation of Absorption of Particles by Ball Cover

The particle (proton) track in the matter can be computed in following way (p. 953, table 44.150),

l = Rt/γ , (14)

where l is track distance of the particles [cm]; Rt = Rt (U) is magnitude (from table) [g/cm2]; γ is matter density [g/cm3]. The magnitude of Rt depends on the kinetic energy (voltage) of the particles. For protons the values of Rt are presented in Table 2.

Table 2. Magnitude of Rt as a function of accelerated voltage U = aE, volts.

U, MV 100 200 300 400 500 600 700 1000 2000 3000 5000 Rt g/cm2 10 33.3 65.8 105 149 197 248 370 910 1463 2543

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The proton energy is U = aE. For magnitudes a = 6 m, E = 108 V/m, proton energy U = 600×106 V and ball cover density γ = 1.8 g/cm3 the proton track is l = 197/1.8 = 109 cm. The required ball cover thickness is only 230 microns (see Figure12). All protons will run across the ball cover. However, if the losses of speed in the ball cover are less Vs = 400 km/s, the protons will leave a neutral sphere. In other cases, they can rotate in a neutral sphere, cross the cover thousands of times, lose their energy and discharge the ball’s charge.

The safe ball cover thickness may be estimated using the following method. The solar wind proton energy is

2

2sp

d

VmE = . (15)

For Vs = 400×103 m/s the proton energy is Ed = 4×10–17 J = 4×10–17 ×0.625×1019 eV =

840 eV. If the loss of proton energy is proportional to the cover thickness, the maximum safe

cover thickness (which will not discharge the ball) will be

aEUU

lVEdorl

UE sd === ,)(, max

max δδ . (16)

For a = 6 m, E = 108 V/m the required ball cover thickness is δmax = 1.53 micron. For a =

4, 10 m δmax = 1.22, 1.73 microns respectively. This magnitude is less than the ball thickness required for the charge stress (see Figure

12) for current cover matter. Methods of decreasing the cover discharge are offered in the description section.

For electrons the thickness of half absorption may be calculated using equation (p. 95850)

][,],/[)(095.0 5.022/3 cmRdcmgaE

AZR r

r γ== . (17)

Here Z is the nuclear charge of the ball matter; A is the mass number of the ball matter.

7. Estimation of Initial Expenditure of Electrical Energy Needed to Charge the Ball

The ball must be charged with electrical energy of high voltage (millions of volts). Let us estimate the minimum energy when the charged device has 100% efficiency. This energy equals the work of moving of the ball charge to infinity, which may be computed using equation

,2

,,,2

2322

kEaW

kaC

kEaQ

CQW ==== (18)


217

where W is ball charge energy [J]; C is ball capacitance [F]; Q is ball charge [C]. The result of this computation is presented in Figure 20. As can be seen this energy not great as it is about 1–20 kWh for a ball radiu of a = 5 m and the electrical intensity is 25–100 MV/m. This energy may be restored through ball discharge by emitting the charge into space using a sharp edge.

Figure 18. Initial expenditure of electrical energy needed to charge the space apparatus, a = 1– 8 m, electrical intensity is 25–100 MV/m and coefficient of efficiency 1.

8. Short Notes about Thermonuclear Propulsion from Solar Wind

When particles are moved toward the ball, they gain a huge amount of energy equal to the voltage (aE) of the charged ball in infinite space U= aE (100 – 1000 MeV), approaching the speed of light. The particle reactions have the greatest efficiency when the particles move in opposite directions. Their energy is then more than the energy of most common thermonuclear reactions (5 – 20 MeV). The electric field of the brake capacitor can decrease this energy to the required value. The particles may be used for a proton–proton reaction (as inside the Sun), or proton–electrode, or electron–electrode thermonuclear reaction, where the central electrode is made from a suitable matter. The solar wind also contains alpha–particles and ions of other elements (up to 10%). These are accelerated to high energy and can take part in the thermonuclear reaction.

The thermonuclear reaction also needs a certain concentration of the free particles. These are concentrated in the area of the central electrode. This concentration, Qx, can be computed. The angle of deviation of the initial (in infinity) solar wind particles is small (about 1–2 degrees) and the diameter of the central area (maximum concentration near the electrode) is small (possibly less than 1 mm), meaning the thermonuclear cross-section is large. The Lawson criterion is executed because the collision time is infinity. We have continuous particle flow and do not use internal apparatus energy. I call on nuclear experts to research the

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possibility of thermonuclear reactions in the proposed engine (and generator). This thermonuclear engine is impossible on Earth where the solar wind is blocked by the atmosphere and the Earth’s magnetic field, but it is possible in extra-planetary space, in a high vacuum. It may be a way of achieving not only interplanetary trips, but also interstellar apparatus where a space-craft is accelerated to a relativistic velocity.

9. Estimation of Charging the Ball

The main innovation in the proposed idea is the open electric charge of one sign and high intensity. To obtain this open charge, it is necessary to send an opposite charge into infinite space. This is possible if we accelerate the opposed particles (protons, electrons, ions) with energy of more than aE = 100–103 MV (a is ball diameter [m], E is electrical intensity [MV/m]). It can be carried and using simple electrostatic accelerators or linear accelerators (electric guns). Their design for use in space is easier than for Earth because outer space has a high vacuum and a high allowable electrical intensity. For example, the allowable electrical intensity is only 3 MV/m on the ground belong the Earth’s atmosphere and >100 MV/m in a space vacuum. A Van de Graff accelerator on the ground needs a special high pressure camera and special vacuum camera, but in space they are not needed. Below are data of some ground accelerators of protons (p) and electrons (e).

Electrostatic accelerators (Tandem Van de Graff, Tandem pelletron, Vivitro) accelerate particles (p, d, α, e) up to 20–35 MV, linear accelerators (p) up to 50–800 MeV, electron linear accelerators (e) up to 100 GeV and alter-gradient synchrotron (p, e) up to 900 GeV (p) (v. 13, p. 13051).

These data show there is no significant problem in designing a high efficiency space charging gun which will move charges to infinity and create the open charged ball. The energy for this charging is not high (see Figure 18).

These and other possible problems are discussed in the next section. One of possible form of offered space propulsion used the solar wind is shown in Figure

19.

Figure 19. Possible form of offered propulsion used the solar wind.


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Discussion

1. Possibile Limitations of offered solar wind system

The above computations suggest a range of possibilities for acceleration using solar wind. The pressure of solar wind is very small but charged particles may be collected by the open charged ball from a big region. They will the give enough thrust for mobile space apparatus. They can accelerate the direct able apparatus to speeds of about 100 km/s and offer flights to far planets of the Solar system in a short time. If the thermonuclear engine (and the electric generator) is possible, thermonuclear wind propulsion will permit us to realize interstellar trips. This is a revolutionary breakthrough in interstellar space.

What restrictions may appear in detailed researches to limit these possibilities? The author sees the following problems:

a) Discharging of the ball. The author offers some methods (Figure 5) for reducing of

this discharging. Detailed computation is needed. b) Design of an acceptable charging gun. This is a technical problem which can be

solved by current technology. c) Source of energy. d) Research and development into the offered space thermonuclear propulsion system

and power generator.

2. Comparison with Other Works about Solar Wind Propulsion System

The author suggested a series of solar wind propulsion systems and generators in 1982–1983 and later29–47. These works included also the nuclear propulsion system and electric generators, and particle and solar wind electrostatic mirrors. In American scientific literature the author found only work published in 200348. The proposed methods, installation and results have the following differences:

a) The offered propulsion installation design is very different from work48. Authors of

work48 use a magnetic field; I use only an electric field. They use a conventional spherical capacitor with two skins (layers) and polarity (unlike) charges (see Figure648). These authors wrote (p. 6): “So, from the point of EPS power consumption, it is highly desirable to keep the charge separation distance as small as possible while achieving acceleration”.

In my opinion this design cannot work efficiently, because the main part of the electric

field is inside the capacitor. The authors48 understood that when they wrote (p. 6); ”one charge layer is exposed to the solar wind electric field the other is exposed to a considerably reduced electric field.”

My proposed propulsion design has a single-skin ball, one type of charge (the opposite charge is expelled in infinity), and an open electric field effective over long distance. The intensity of this field is decreased as 1/r2. If the charges in the other system48 are dipolar their

Alexander Bolonkin

220

intensity will be small and decrease as 1/r3. This means, the author’s electric field should be stronger by thousands of times over long distance.

b) The work48 contains only common speculation. It doesn’t contain theory, initial data,

detailed numerical results. The authors give only some pictures of solar wind disturbances. In Figure3, p. 4 the apparatus speed is twice the wind speed (??). No explanation is given for this strange result.

Omidi and Karimabad48 use the very high specific charges of up to 300–500 C [0.1–1

(and more) C/kg for full spacecraft mass]. This requires a very large spherical capacitor and very high electrical intensity which is impossible in physics. They wrote: ‘this technology would initially be applied to the propulsion of micro spacecraft where charge levels of a low C would be sufficient. “

My results are very different from these48. The authors do not show their calculation’s, but say their apparatus with its propulsion can reach a speed of 64 km/s at a distance 33 AU of 5 years. This means the acceleration is 0.0004 m/s and the thrust is very small.

There are also many articles about magnetic sails using solar wind drag into a magnetic field of a gigantic superconductive ring (diameter 60–150 km). Unfortunately, no theory currently exists to allow computation of magsail drag. It is beyond the capability of current technology. The reader can find information about the space magsail in Reference52.

Conclusion

The proposed new propulsion mechanism differs from previous concepts in very important respects; including the coupling to the protons of the solar wind using an open single-charge ball. The opposite charge is expelled into infinite space. This innovation increases the area of influence by up to hundreds of kilometers for protons and allows the acquisition of significant vehicle thrust. This thrust is enough to accelerate a heavy space craft to very high speed and permits very short flight times to far planets.

The offered revolutionary propulsion system has a simple design, which can give useful acceleration to various types of spacecraft. The offered propulsion system creates many Newtons of thrust, and can accelerate a 100 kg space probe up to 60–100 km/sec in 100–800 days.

In the offered wind propulsion system the particles run away from the ball, brake and return in infinity for initial speed. These premises must be examined using more complex theories to account for the full intersection between the suggested installation and solar wind (including thermonuclear reactions). This would be a revolutionary breakthrough in interplanetary space exploration.

The author has developed the initial theory and the initial computations to show the possibility of the offered concept. He calls on scientists, engineers, space organizations, and companies to research and develop the offered perspective concepts.


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References

(The reader can find part of these articles at the author’s website: http:// Bolonkin.narod.ru/p65.htm, http://arxiv.org, search term: “Bolonkin”, in the book "Non-Rocket Space Launch and Flight", Elsevier, London, 2006, 488 pgs., and book “New Concepts, Ideas, Innovations in Aerospace, Technology and Human Science”, NOVA, 2008, 502 pgs.; “Macro-Projects: Environment and Technology”, NOVA, 2009, 536 pgs.)

[1] A.A. Bolonkin, “Theory of Flight Vehicles with Control Radial Force”. Collection

Researches of Flight Dynamics, Public house “Mashinostroenie”, Moscow, 1965, pp. 79–118 (in Russian).

[2] A.A. Bolonkin, “Air Cable Transport and Bridges”, TN 7567, International Air & Space Symposium – The Next 100 Years, 14–17 July 2003, Dayton, Ohio, USA.

[3] A.A. Bolonkin, “Kinetic Space Towers and Launchers”, JBIS (Journal of British Interplanetary Society), Vol. 57, No 1/2, pp. 33–39, 2004.

[4] A.A. Bolonkin, “Non-Rocket Space Rope Launcher for People”, IAC-02-V.P.06, 53rd International Astronautical Congress. The World Space Congress – 2002, 10–19 Oct 2002, Houston, Texas, USA.

[5] A.A. Bolonkin, “Non-Rocket Missile Rope Launcher”, IAC-02-IAA.S.P.14, 53rd International Astronautical Congress. The World Space Congress – 2002, 10–19 Oct 2002, Houston, Texas, USA.

[6] A.A. Bolonkin, “Optimal trajectory of air vehicles”. AEAT (Aircraft Engineering and Aerospace Technology), Vol. 76, No. 2, pp. 193–214, 2004 .

[7] A.A. Bolonkin, “Inexpensive Cable Space Launcher of High Capability”, IAC-02-V.P.07, 53rd International Astronautical Congress. The World Space Congress – 2002, 10–19 Oct. 2002, Houston, Texas, USA.

[8] A.A. Bolonkin, “Hypersonic Launch System of Capability up 500 tons per day and Delivery Cost $1 per Lb”. IAC-02-S.P.15, 53rd International Astronautical Congress. The World Space Congress – 2002, 10–19 Oct 2002, Houston, Texas, USA.

[9] A.A. Bolonkin, “Employment Asteroids for Movement of Space Ship and Probes”. IAC-02-S.6.04, 53rd International Astronautical Congress. The World Space Congress – 2002, 10–19 Oct. 2002, Houston, Texas, USA.

[10] A.A. Bolonkin, A.A., “Optimal Inflatable Space Towers of High Height”. COSPAR-02 C1.1-0035-02, 34th Scientific Assembly of the Committee on Space Research (COSPAR). The World Space Congress – 2002, 10–19 Oct 2002, Houston, Texas, USA.

[11] A.A. Bolonkin, “Non-Rocket Earth-Moon Transport System”, COSPAR-02 B0.3-F3.3-0032-02, 02-A-02226, 34th Scientific Assembly of the Committee on Space Research (COSPAR). The World Space Congress – 2002, 10–19 Oct 2002, Houston, Texas, USA.

[12] A.A. Bolonkin, “Non-Rocket Earth-Mars Transport System”, COSPAR-02 B0.4-C3.4-0036-02, 34th Scientific Assembly of the Committee on Space Research (COSPAR). The World Space Congress – 2002, 10–19 Oct 2002, Houston, Texas, USA.

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[13] A.A. Bolonkin, “Transport System for delivery Tourists at Altitude 140 km”. IAC-02-IAA.1.3.03, 53rd International Astronautical Congress. The World Space Congress – 2002, 10–19 Oct. 2002, Houston, Texas, USA.

[14] A.A. Bolonkin, “Optimal Inflatable Space Towers with 3-100 km Height”, JBIS, Vol. 56, pp. 87–97, 2003.

[15] A.A. Bolonkin, “Asteroids as Propulsion Systems of Space Ships”, JBIS, Vol. 58, pp. 97–107, 2003.

[16] A.A. Bolonkin, A.A. ”Hypersonic Gas-Rocket Launch System.”, AIAA-2002-3927, 38th AIAA/ASME/ SAE/ASEE Joint Propulsion Conference and Exhibit, 7–10 July, 2002. Indianapolis, IN, USA.

[17] A.A. Bolonkin, “Non-Rocket Transportation System for Space Travel”, JBIS, Vol. 56, No 7/8, pp. 231–249, 2003.

[18] A.A. Bolonkin, A.A., “Hypersonic Space Launcher of High Capability”, Actual problems of aviation and aerospace systems, Kazan, No. 1(15), vol. 8, 2003, pp. 45–58.

[19] A.A. Bolonkin, “Centrifugal Keeper for Space Stations and Satellites”, JBIS, Vol. 56, pp. 314–327, 2003.

[20] A.A. Bolonkin, “Non-rocket Earth-Moon Transport System”, Advances in Space Research, Vol. 31/11, pp. 2485–2490, 2003, Elsevier.

[21] A.A. Bolonkin, “Earth Accelerator for Space Ships and Missiles”. JBIS, Vol. 56, pp. 394–404, 2003.

[22] A.A. Bolonkin, “Air Cable Transport”, Journal of Aircraft, Vol. 40, No 4, July–August 2003.

[23] A.A. Bolonkin, “High Speed Catapult Aviation”, AIAA-2005-6221, AIAA Atmospheric Flight Mechanic Conference, 15–18 August, 2005, USA.

[24] A.A. Bolonkin, “High Efficiency Transfer of Mechanical Energy”, AIAA-2004-5660, International Energy Conversion Engineering Conference, Rhode Island, 16-19 Aug. 2004.

[25] A.A. Bolonkin, “Light Multi-Reflex Engine”, Journal JBIS, Vol. 57, No 9/10, pp. 353–359, 2004.

[26] A.A. Bolonkin, Multi-Reflex Propulsion System, JBIS, Vol. 57, No. 11/12, pp. 370–390, 2004.

[27] A.A. Bolonkin, “Sling Rotary Space Launchers”, 41 Propulsion Conference, 10–13 July, 2005, Tueson, Arizona, USA, AIAA-2005-4035.

[28] A.A. Bolonkin, “Kinetic Anti-Gravitator”, 41 Propulsion Conference, 10–13 July, 2005, Tueson, Arizona, USA. AIAA-2005-4504.

[29] A.A, Bolonkin, “Space Propulsion using Solar Wing and Installation for It”. Russian patent application #3635955/23 126453, 19 August, 1983 (in Russian). Russian PTO.

[30] A.A. Bolonkin, “Installation for Open Electrostatic Field”. Russian patent application #3467270/21 116676, 9 July, 1982 (in Russian). Russian PTO.

[31] A.A. Bolonkin, “Getting of Electric Energy from Space and Installation for It”. Russian patent application #3638699/25 126303, 19 August, 1983 (in Russian). Russian PTO.

[32] A.A. Bolonkin, “Protection from Charged Particles in Space and Installation for It”. Russian patent application #3644168 136270 of 23 September 1983, (in Russian). Russian PTO


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[33] A.A. Bolonkin, “Method of Transformation of Plasma Energy in Electric Current and Installation for It”. Russian patent application #3647344 136681 of 27 July 1983 (in Russian), Russian PTO.

[34] A.A. Bolonkin, “Method of Propulsion using Radioisotope Energy and Installation for It”. Russian patent application #3601164/25 086973 of 6 June, 1983 (in Russian), Russian PTO.

[35] A.A. Bolonkin, “Transformation of Energy of Rarefaction Plasma in Electric Current and Installation for it”. Russian patent application #3663911/25 159775 of 23 November 1983 (in Russian). Russian PTO.

[36] A.A. Bolonkin, “Method of a Keeping of a Neutral Plasma and Installation for it”. Russian patent application #3600272/25 086993 of 6 june 1983 (in Russian). Russian PTO.

[37] A.A. Bolonkin, Radioisotope Propulsion. Russian patent application #3467762/25 116952 of 9 July 1982 (in Russian). Russian PTO.

[38] A.A. Bolonkin, “Radioisotope Electric Generator”. Russian patent application #3469511/25 116927 of 9 July 1982 (in Russian). Russian PTO.

[39] A.A. Bolonkin, “Radioisotope Electric Generator”. Russian patent application #3620051/25 108943 of 13 July 1983 (in Russian). Russian PTO.

[40] A.A. Bolonkin, “Method of Energy Transformation of Radioisotope Matter in Electricity and Installation for it”. Russian patent application #3647343/25 136692 of 27 July 1983 (in Russian). Russian PTO.

[41] A.A. Bolonkin, “Method of stretching of thin film”. Russian patent application #3646689/10 138085 of 28 September 1983 (in Russian). Russian PTO.

[42] A.A.Bolonkin, “New Way of Thrust and Generation of Electrical Energy in Space”. Report ESTI, 1987, 109 p. (Soviet Classified Project).

[43] A.A.Bolonkin, “Aviation, Motor and Space Designs”. Emerging Technology in the Soviet Union, 1990, Delphic Ass., Inc., pp. 32–80, (English).

[44] A.A.Bolonkin, “A Space Motor Using Solar Wind Energy”. The World Space Congress, Washington, DC, USA, 28 Aug. – 5 Sept., 1992, IAF-0615.

[45] A.A.Bolonkin, “The Simplest Space Electric Generator and Motor with Control Energy and Thrust”, 45th International Astronautical Congress, Jerusalem. Israel. Oct. 9–4, 1994, IAF-94-R.1.368 .

[46] A.A.Bolonkin, “Space Electric Generator, run by Solar Wing”. The World Space Congress, Washington, DC, USA, 28 Aug.–5 Sept., 1992, IAF-92-0604.

[47] A.A.Bolonkin, “Simple Space Nuclear Reactor Motors and Electric Generators Running on Radioactive Substances”, The World Space Congress, Washington, DC, USA, 28 Aug. –5 Sept., 1992, IAF-92-0573.

[48] N.Omidi and H.Karimabadi, “Electrostatic Plasma Sail”, AIAA 2003-5227, 2003. 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit 20–23 July 2003, Hurtisville, Alabama. See also this work in NIAC site http://niac.usra.edu , Omidi final report where director NIAC Mr. Cassanova awarded this work $75000.

[49] V.I. Feodosev, Base of Rocket Flight Techniques, Moscow, “Science”, 1981 (in Russian).

[50] I.K. Kikoin, (ed), Directory, Tables of physic values, Moscow, Atomizdat, 1976 (in Russian).

[51] McGraw-Hill Encyclopedia of Science & Technology.

Alexander Bolonkin

224

[52] L.Funaki, et. al, “Trust Production Mechanism of Magnetoplasma Sail”, AIAA 2003-4292.

[53] A.A. Bolonkin, “Electrostatic Solar Wind Propulsion System”, AIAA-2005-3653. 41 Propulsion Conference, 10-12 July, 2005, Tucson, Arizona, USA.

[54] A.A. Bolonkin, “Electrostatic Utilization of Asteroids for Space Flight”, AIAA-2005-4032. 41 Propulsion Conference, 10–12 July, 2005, Tucson, Arizona, USA.

[55] A.A. Bolonkin, “Radioisotope Space Sail and Electric Generator”, AIAA-2005-4225. 41 Propulsion Conference, 10–12 July, 2005, Tucson, Arizona, USA.

[56] A.A. Bolonkin, “Guided Solar Sail and Electric Generator”, AIAA-2005-3857. 41 Propulsion Conference, 10–12 July, 2005, Tucson, Arizona, USA.

[57] A.A. Bolonkin, “Problems of Electrostatic Levitation and Artificial Gravity”, AIAA-2005-4465. 41 Propulsion Conference, 10–12 July, 2005, Tucson, Arizona, USA.

[58] Bolonkin A.A., “Non-Rocket Space Launch and Flight”, Elsevier, 2006, 488 pgs. [59] Bolonkin A.A., “New Concepts, Ideas, and Innovation in Aerospace, Technology and

Human Science”, NOVA, 2008, 502 pgs. [60] Bolonkin A.A., “Macro-Projects: Environment and Technology ”, NOVA, 2009, 536

pgs.

Figure 20. Interaction solar wind with the Earth.


225

Figure 21. The Solar Wind at Mars. Energy of particles. (Credit: NASA/JPL). 25K

Figure 22. Possible form of Solar wind space ship. 40K.

Alexander Bolonkin

226

Figure 23. Alien Solar Wind Ship. 17K.

In: Handbook on Solar Wind: Effects, Dynamics...Editor: Hans E. Johannson

ISBN 978-1-60692-572-0c© 2009 Nova Science Publishers, Inc.

Chapter 6

SOLAR WIND AND M OTION OF I NTERPLANETARY

DUST GRAINS

J. Klacka, L. Komar, P. Pastor and J. PetrzalaDepartment of Astronomy, Physics of the Earth and Meteorology

Faculty of Mathematics, Physics and Informatics, Comenius UniversityMlynska dolina, 842 48 Bratislava, Slovak Republic

Abstract

Effect of solar wind particulates on motion of dust grain moving in Solar Systemis derived in space-time. Acceleration of the grain under the effect of solar wind(including the non-radial component of its velocity vector) and grain’s mass changeare obtained. The results for the effect of solar wind are used in space-time derivationof the effect of electromagnetic radiation.

The contribution considers simultaneous action of the solar electromagnetic ra-diation and solar wind, together with gravity of the Sun and planets, on motion ofinterplanetary dust grains with radii of several microns and tens of micrometres. Ap-plications for the standardly used radial solar wind and real solar wind velocity vectorare compared. The important results can be summarized as follows:1. Spherical dust grain can be captured in mean-motion orbital resonances with planetNeptune when the secular evolution of the grain’s semi-major axis is an increasingfunction of time. Nothing like this exists for the Poynting-Robertson effect and radialsolar wind. The effect of the real solar wind velocity vector mimics the behavior of thecomplicated case of the behavior of nonspherical dust grain under the action of solarelectromagnetic radiation.2. Simultaneous action of the Poynting-Robertson and real solar wind effects causesspiralling of the dust grain outward from the Sun, in the zone of outer planets. Theflux of interstellar gas is also important in this zone. This additional nongravitationaleffect stabilizes dust grain’s orbit in the zone of the Edgeworth-Kuiper belt.

1. Introduction

Various systems of dust particles exist in the Solar System: zodiacal cloud (e. g., Dohnanyi1978, Leinert and Grun 1990, Grun 2007, Sykes 2007) mean motion orbital resonanceswith planets (e.g., Jackson and Zook 1989, Dermottet al. 1994, Reachet al. 1995), dust

228 J. Klacka, L. Komar, P. Pastor et al.

particles around planets, dust particles in the Edgeworth-Kuiper belt, dust particles gener-ated by comets and asteroids (Sekaninaet al. 2001, Sykes 2007). Evolution of the systemsis given by various forces acting on the particles. Gravitational force of the Sun is im-portant. As for mean motion orbital resonances with a planet, also gravitational force ofthe planet is important. Moreover, also nongravitational forces are important for orbitalevolution of interplanetary dust particles. Submicron dust particles are driven mainly byLorentz force (motion of charged particles in the interplanetary magnetic field, Dermottetal. 2001). Collisions among particles are important for particles of radii larger than hun-dred of micrometres, approximately (Dermottet al. 2001, Grunet al. 1985). This chapterdeals with evolution of interplanetary dust particles of radii several microns up to tens ofmicrometres. For these particles, the effects of solar electromagnetic and corpuscular radi-ation are relevant. The effect of the solar corpuscular radiation corresponds to the effect ofthe solar wind. Dealing with evolution of dust particles beyond the planet Neptune, i.e. inthe zone of the Edgeworth-Kuiper belt, also the effect of interstellar gas, streaming to theSolar System, plays an important role.

Sections 2 and 3 derive relativistically covariant equations of motion of an arbitrarilyshaped particle under the action of solar wind (including non-radial component of the solarwind velocity) and solar electromagnetic radiation. Sec. 4 deals with secular evolution ofparticle’s orbital elements under the action of solar radiation, in an analytical way. Thefollowing section Sec. 5 concentrates on detail treatment of the mean motion orbital res-onances with a planet and the effect of solar wind and solar electromagnetic radiation onbehavior of dust grains near the zones of the resonances. Sec. 6 presents results on times ofspiralling for dust grains in the Edgeworth-Kuiper belt and compare the results for conven-tional radial solar wind velocity with those obtained for real solar wind velocity. The lastSec. 7 concerns the stay of dust particles in the Edgeworth-Kuiper belt for the more generalcase, when also the stream of interstellar gas moving through the Solar System is taken intoaccount as a further nongravitational effect influencing orbital evolution of dust particles.

2. Equation of Motion - Solar Wind Effect

The action of the solar wind on motion of interplanetary dust particle was discussed, e. g.,by Whipple (1955). He has mentioned also the results of laboratory experiments: intensebombardment of a material by energetic particulates destructs the material and this effect isknown as a ”sputtering”. Current opinion is that we have two different effects of the solarwind: i) motion of dust particle is influenced by the incident solar wind, and, ii) corpuscularsputtering causes decrease of mass of the particle (e. g., Whipple 1955, Dohnanyi 1978,Kapisinsky 1984, Leinert and Grun 1990). However, there has been an attempt to betterunderstand physics of the action of the solar wind on the motion of dust particle. As afirst attempt, we can mention Robertson and Noonan (1968, pp. 122-123). The authorsformulate relativistically covariant equation of motion of the particle under the action ofthe solar wind. However, their result does not admit any destruction of the particle. Amore realistic view was presented in Klacka and Saniga (1993), where also space-timeformulation of the problem is suggested. As a result, equation of motion and corpuscularsputtering represent one effect of the action of solar wind on interplanetary dust particle, inreality. This section presents the space-time problem and derives equation of motion in a

Solar Wind and Motion of Interplanetary Dust Grains 229

relativistically covariant form. The last subsection presents results with an accuracy to theorder(~v/u)2, where~v is orbital velocity of the particle with respect to the Sun andu is thesolar wind speed.

2.1. Incident Radiation

Let us introduce two inertial reference frames. The first is the proper reference frame of aparticle moving with velocity~v around the Sun. The particle is at rest in it’s proper frame ofreference. Quantities measured in this frame will be primed. The second frame is associatedwith Sun. This frame is ”stationary reference frame”.

We will suppose that all particles of the solar wind are of the same massm1 and ofthe same velocity~u (or ~u′ in the proper reference frame of the particle). Thus, each of theparticulates has the following four-momentum

p′µ1 =

(E ′

1/c ; ~p′1

)= m1γ

(u′)(c ; ~u′

)(1)

in the proper reference frame of the interplanetary dust particle, or

pµ1 = (E1/c ; ~p1) = m1γ (u) (c ; ~u) (2)

in the stationary reference frame;c is the speed of light.Let a beam of such solar wind particulates hits the dust grain. An energy and momentum

incident on the particle per unit time in its proper frame are

E′in = A′n′u′E ′

1 ,

~p′in = A′n′u′~p′1 , (3)

wheren′ is the concentration of the solar wind particulates andA′ is the geometrical cross-section of the interplanetary dust particle. Using Eq. (1), we can rewrite Eqs. (3) into theform of the incident four-momentum per unit time

p′µin = A′n′u′

(E′

1

c; ~p′1

)=

1c

A′n′u′E ′1

(1 ;

~u′

c

). (4)

Introducing the flux density of the incident energyS′ = n′u′E ′1 (energy flow per unit area

perpendicular to the beam of solar wind particulates per unit time), Eq. (4) can be rewrittento the form

p′µin =

1c

S ′A′

(1 ;

~u′

c

). (5)

Having a four-vectorB′µ = (B′0 ; ~B′) in the proper reference frame, the componentsof the four-vector in the stationary reference frame are given by generalized special Lorentztransformation:

B0 = γ (v)

(B′0 +

~v · ~B′

c

),

~B = ~B′ +

[γ (v) − 1]

~v · ~B′

v2+

γ (v)c

B′0

~v , (6)


or inverse

B′0 = γ (v)

(B0 − ~v · ~B

c

),

~B′ = ~B +

[γ (v)− 1]

~v · ~B

v2− γ (v)

cB0

~v , (7)

Now, using Eqs. (5) and (6) we get

p0in =

1c

S ′A′ γ (v)

(1 +

~v · ~u′

c2

),

~pin =1c2

S′A′

~u′ +

[(γ (v)− 1)

~v · ~u′

v2+ γ (v)

]~v

. (8)

We have to express the primed quantities (exceptA′) on the right-hand sides of Eqs. (8),i.e. S ′ = n′u′E ′

1 and~u′, through unprimed quantities measured in the stationary referenceframe of the Sun. The energyE′

1 we obtain from Lorentz transformation ofpµ1 to the proper

reference frame of the interplanetary dust particle. It holds

E ′1 = γ (v) (E1 − ~v · ~p1) = E1γ (v)

(1 − ~v · ~u

c2

)= E1ω , (9)

where we defined the quantity

ω ≡ γ (v)(

1 − ~v · ~uc2

). (10)

Other quantities we get from transformation of the four-vector of the current densityjµ

= (nc ; n~u) to the corresponding four-vectorj ′µ = (n′c ; n′~u′). The transformation yields

n′ = nω ,

~u′ =1ω

~α , (11)

where the vector

~α ≡ ~u +[(γ (v) − 1)

~v · ~uv2

− γ (v)]~v , (12)

has magnitude

α =

u2 + γ2 (v) v2 − 2γ2 (v)~v · ~u + γ2 (v)

(~v · ~u

c

)21/2

. (13)

Thus,u′ = α/ω and the flux density of energy is

S ′ =α ω

unuE1 =

α ω

uS . (14)


Finally, using Eqs. (8), (10), (11), (12), (14) one obtains

p0in =

1c

A′Sα ω

u

1ω

,

~pin =1c

A′Sα ω

u

1ω

~u

c. (15)

The incident four-momentum of solar wind per unit time is

pµin =

1c

A′Sα ω

uξµ ,

ξµ ≡(

1ω

;1ω

~u

c

). (16)

2.2. The Reaction of Dust Particle on the Incident Solar Wind

The incident solar wind particulate may be reflected from the surface of the interplanetarydust particle (IDP) or may cause its erosion/destruction and decrease the mass of the IDP.We will suppose that thex-part of the incident energy per unit time of the IDP is lost in theproper reference frame of the IDP. The relation

E ′out = x E′

in (17)

holds for the outgoing energy. The outgoing momentum per unit time is given by somereaction force~F ′

R acting on the dust particle

~p′out = − ~F ′R = −

3∑

j=1

F ′R,j

~e′j , (18)

where~e′j , j = 1, 2, 3 is an orthonormal vector basis in proper reference frame of the par-ticle. These unit vectors are connected with corresponding unit vectors~ej in the stationaryreference frame by Lorentz transformation (aberration of light: Eq. 7 is used for a photonof four-momentumpµ = (hν/c ; hν~ej/c), whereh is Planck constant andν is frequencyof the photon):

~e′j =1wj

~ej +

[(γ (v)− 1)

~v · ~ej

v2− γ (v)

c

]~v

,

wj ≡ γ (v)(

1 − ~v · ~ej

c

), j = 1, 2, 3 ; (19)

~e1 corresponds to the radial direction (i.e. the Sun - particle direction).Then, the outgoing four-momentum per unit time is

p′µout =

1

cA′S′x ; −

3∑

j=1

F ′R,j

~e′j

, (20)


Generalized special Lorentz transformation ofp′µout, using Eqs. (14) and (19), gives for theoutgoing four-momentum per unit time in the stationary reference frame

pµout =

1c

A′Sα ω

ux

Uµ

c−

3∑

j=1

F ′R,j

(bµj − Uµ

c

), (21)

whereUµ = (γ(v) c ; γ(v) ~v) (22)

is four-velocity of the IDP, and, the other four-vectors are

bµj =

(1wj

;~ej

wj

), j = 1, 2, 3 . (23)

2.3. Equation of Motion

Now we can write equation of motion of the IDP under the action of the solar wind, in arelativistically covariant form:

dpµ

dτ= pµ

in − pµout . (24)

Eq. (24) yields, using Eqs. (16) and (21),

dpµ

dτ=

1c

A′Sα ω

u

(ξµ − x

Uµ

c

)+

3∑

j=1

F ′R,j

(bµj − Uµ

c

), (25)

wherepµ = mUµ is four-momentum of the IDP of massm andτ is the proper time of theparticle.

Usingdpµ

dτ=

d

dτ(mUµ) =

dm

dτUµ + m

dUµ

dτ, (26)

Eq. (25) yields not only acceleration of the particle, but also change of the particle’s (rest)mass, due to the interaction of the IDP with the solar wind. The change of the mass isgiven, on the basis of Eqs. (10), (16), (22), (25) and (26), by the expression (UµUµ = c2,Uµ dUµ/dτ = 0)

dm

dτ=

1c2

A′Sα ω

u(1 − x) . (27)

One can easily verify that Eq. (27) corresponds to the famous Einstein’s equationdm/dτ= (E ′

in − E ′out) /c2, if also Eqs. (3) and (17) are used.

Eqs. (25)-(27) yield for the four-acceleration of the IDP

dUµ

dτ=

A′S

mc

α ω

u

(ξµ − Uµ

c

)+

1m

3∑

j=1

F ′R,j

(bµj − Uµ

c

). (28)

In the further treatment we will consider the case~F ′R = 0, i.e. ~p′out = 0 in the proper

frame of reference of the particle. As a consequence, the equation of motion will be of theform

dpµ

dτ=

1c

A′Sα ω

u

(ξµ − x

Uµ

c

), (29)


and the four-acceleration will be

dUµ

dτ=

A′S

mc

α ω

u

(ξµ − Uµ

c

). (30)

2.3.1. Equation of Motion to the Second Order inv/u

In the approximation to the first order inv/c, we can replace the spacelike part of the four-acceleration of the IDP by accelerationd~v/dt, wheret is time measured in the stationaryreference frame (associated with the Sun). Further, using Eqs. (2), (10), (13), (14), (16)and (22), we can express the right-hand side of Eq. (30) in the approximation to the secondorder inv/u. We get

d~v

dt=

A′nm1u2

m

[(1 − ~v · ~u

u

)~u − ~v

u

]+

12

v2

u2~u +

~v · ~uu

~v

u

, (31)

where~u ≡ ~u/u is the unit vector in direction of the solar wind.Let us introduce the cylindrical coordinate system associated with the orbital plane of

the IDP and determined by unit vectors~eR (radial vector),~eT (transversal vector) and~eN

= ~eR × ~eT (normal vector). We can write (Klacka 1994)

~u = γR~eR + γT ~uT , (32)

whereγR = cos ε , γT = sin ε (33)

and

~uT =1N

(~eT cos i − ~eN cosΘ sin i) ,

N =√

(cos i)2 + (cosΘ)2 (sin i)2 . (34)

The quantityε is an angle between the radial direction and the real direction of the solarwind. The inclination of the orbital plane of the IDP with respect to the solar equatorialplane isi. Finally,Θ is a position angle of the IDP (an angle measured from the ascendingnode of the orbit of the IDP to its actual position).

Inserting Eqs. (32) and (34) to Eq. (31), and using the decomposition of the velocityvector into its radial and transversal components,~v = vR~eR + vT~eT , one obtains

d~v

dt=

A′nm1u2

mXR~eR + XT~eT − XN~eN

+ γRvR

u

~v

u+ γT

cos i

N

vT

u

~v

u

,

XR = γR −(1 + γ2

R

) vR

u− γRγT

cos i

N

vT

u+ γR

12

v2

u2,

XT =(

1 − γRvR

u− γT

cos i

N

vT

u+

12

v2

u2

)γT

cos i

N− vT

u,

XN =(

1 − γRvR

u− γT

cos i

N

vT

u+

12

v2

u2

)γT

cosΘ sin i

N. (35)


The angleε is small, its value lies between 2 -3 (Brunoet al. 2003). Thus, we can neglectterms proportional toγ2

T andγT (v/u)2. Similarly, we putγR ≈ 1. Then

d~v

dt=

A′nm1u2

m

(1 − 2

vR

u− γT

cos i

N

vT

u+

12

v2

u2

)~eR

+[(

1 − vR

u

)γT

cos i

N− vT

u

]~eT

−(1 − vR

u

)γT

cos Θ sin i

N~eN +

vR

u

~v

u

. (36)

3. Equation of Motion - Electromagnetic Radiation Effect

Up to now, we dealt with the action of solar wind on the motion of an IDP. The role of solarelectromagnetic radiation cannot be neglected in the motion of the IDP in the Solar System.We will derive relativistically covariant equation of motion for an arbitrarily shaped dustparticle under the action of parallel beam of photons.

3.1. Proper Reference Frame of the Particle

The flux density of photons scattered into an elementary solid angledΩ′ = sin θ′ dθ′ dφ′ isproportional top′(θ′, φ′) dΩ′, wherep′(θ′, φ′) is the “phase function”. The phase functiondepends on orientation of the particle with respect to the direction of the incident radiationand on the particle characteristics; anglesθ′, φ′ correspond to the direction (and orientation)of travel of the scattered radiation,θ′ is the polar angle which vanishes for propagation alongthe unit vector~e′1 of the incident radiation. The phase function fulfills the normalisationcondition ∫

4πp′(θ′, φ′) dΩ′ = 1 . (37)

The momentum of the incident beam of photons which is lost in the process of in-teraction with the particle is proportional to the cross sectionC′

ext (extinction). The partproportional toC′

abs (absorption) is emitted in the form of thermal radiation and the partproportional toC′

ext − C′abs = C′

sca is scattered. The differential scattering cross sectiondC′

sca/dΩ′ ≡ C′sca p′(θ′, φ′) depends on the polarization state of the incident light as well

as on the incidence and scattering directions (e. g., Mishchenkoet al. 2002).The momentum (per unit time) of the scattered photons into an elementary solid angle

dΩ′ is

d~p′sca =1c

S′em C′

sca p′(θ′, φ′) ~K′ dΩ′ , (38)

where the unit vector in the direction of scattering is

~K ′ = cos θ′ ~e′1 + sin θ′ cosφ′ ~e′2 + sin θ′ sin φ′ ~e′3 . (39)

S ′em is the flux density of the electromagnetic radiation energy (energy flow through unit

area perpendicular to the ray per unit time). The system of unit vectors used on the right-hand side of the last equation forms an orthogonal basis. The total momentum (per unit


time) of the scattered photons is

~p′sca =1c

S′em C′

sca

∫

4πp′(θ′, φ′) ~K′ dΩ′ . (40)

The momentum (per unit time) obtained by the particle due to the interaction withradiation – radiation force acting on the particle – is

d~p′

dτ=

1c

S′em

C′

ext ~e′1 − C′sca

∫

4πp′(θ′, φ′) ~K′ dΩ′

+ ~F ′

e(T′) , (41)

where ~F ′e(T ′) is the emission component of the radiation force acting on the particle of

absolute temperatureT ′ (Mishchenko 2001; Mishchenkoet al. 2002, pp. 63-66).Equation (41) can be rewritten to the form

d~p′

dτ=

1c

S′em

[C′

ext − < cos θ′ > C′sca

]~e′1 +

[− < sin θ′ cos φ′ > C′

sca

]~e′2 +

[− < sin θ′ sin φ′ > C′

sca

]~e′3

+3∑

j=1

F ′e,j ~e′j , (42)

where< x′ > ≡∫4π x′ p′(θ′, φ′) dΩ′ andF ′

e,j ≡ ~F ′e(T

′) ·~e′j. As for the energy, we assumethat it is conserved: the energy (per unit time) of the incoming radiationE′

in, equals to theenergy (per unit time) of the outgoing radiation (after interaction with the particle)E′

out.Summarising important equations, we can write them in a short form

d~p′

dτ=

3∑

j=1

(S′

em

cC′

pr,j + F ′e,j

)~e′j ;

dE′

dτ= 0 , (43)

whereC ′pr,1 ≡ C′

ext − < cos θ′ > C′sca, C ′

pr,2 ≡ − < sin θ′ cosφ′ > C′sca, C ′

pr,3 ≡ − <sin θ′ sinφ′ > C′

sca are cross sections for radiation pressure. We have added an assumptionof equilibrium state when the particle’s mass does not change.

3.1.1. Summary of the Important Equations

Using the text concerning energy below Eq. (42) and the last Eq. (43), we may describe thetotal process of interaction in the form of the following equations (energies and momentaper unit time):

E ′out = E ′

in = S ′em C′

ext ,

~p′out =(

1 −C′

pr,1

C′ext

)~p′in −

(C′

pr,2

C′ext

~e′2 +C ′

pr,3

C′ext

~e′3

)E′

in

c−

3∑

j=1

F ′e,j

~e′j ,

~p′in =E ′

in

c~e′1 . (44)


The index”in” represents the incoming (incident) radiation, beam of photons, the index”out” represents the outgoing radiation.

The changes of energy and momentum of the particle due to the interaction with elec-tromagnetic radiation are

dE ′

dτ= E′

in − E ′out = 0 ,

d~p′

dτ= ~p′in − ~p′out . (45)

3.2. Stationary Frame of Reference

3.2.1. Incoming Radiation

We can use the results obtained in Sec. 2.1. It is sufficient to make the following threetransformations:~u −→ c ~e1, S −→ Sem, A′ −→ C′

ext. Eqs. (10), (13) and (16) yield

pµin =

w21 Sem C′

ext

cbµ1 , (46)

where also Eqs. (19) and (23) have to be used.

3.2.2. Outgoing Radiation

Applying Eqs. (6) to the quantity(E ′out/c ; ~p′out) (four-momentum per unit time – proper

time is a scalar quantity), we can write

Eout = γ (v)(E ′

o + ~v · ~p′out

),

~pout = ~p′out +

[γ (v) − 1]

~v · ~p′out

~v2+ γ (v)

E′out

c2

~v . (47)

Using also~p′in = E ′in

~e′1/c and Eqs. (19), (44), (47),

Eout =C ′

pr,1

C′ext

w21 Sem C′

ext γ (v) +(

1 −C′

pr,1

C′ext

)w1 Sem C′

ext

+ w21 Sem C′

ext

(C ′

pr,2

C′ext

+C ′

pr,3

C′ext

)γ (v)

− w21 Sem C′

ext

(C ′

pr,2

C′ext

1w2

+C′

pr,3

C′ext

1w3

)

−3∑

j=1

F ′e,j

[c

wj− γ (v) c

],

~pout =(

1 −C ′

pr,1

C′ext

)w1 Sem C′

ext

c~e1 +

C′pr,1

C′ext

w21 Sem C′

ext

c2γ (v) ~v

−3∑

j=2

C′pr,j

C′ext

w21 Sem C′

ext

c2

[c

~ej

wj− γ (v)~v

]


− 1c

3∑

j=1

F ′e,j

[c

~ej

wj− γ (v)~v

]. (48)

Eqs. (48) can be rewritten in the following covariant form (see also Eqs. 22 and 23):

pµout =

w21 Sem C′

ext

c

bµ

1 −3∑

j=1

C′pr,j

C′ext

(bµj − Uµ

c

)

−3∑

j=1

F ′e,j

(bµj − Uµ

c

). (49)

3.2.3. Equation of Motion

In analogy with Eqs. (45), we have for the changes of energy and momentum of the particledue to the interaction with electromagnetic radiation:

dpµ

dτ=

3∑

j=1

(w2

1 Sem C′pr,j

c2+

1c

F ′e,j

)(c b

µj − Uµ

), (50)

wherepµ is four-vector of the particle of massm four-vector of the world-velocity of theparticle is given by Eq. (22) and four-vectorsbµ

j , j = 1, 2, 3 are given by Eqs. (23). It canbe easily verified that Eq. (50) yieldsdm/dτ = 0, i.e., mass of the particle is conserved,under the action of electromagnetic radiation.

If we take into account continuous distribution of density flux of energy, averaging over(solar) frequency spectrum has to be done. The result can be written in the form

dpµ

dτ=

3∑

j=1

(w2

1 Sem C′pr,j

c2+

1c

F ′e,j

)(c bµ

j − Uµ)

. (51)

To first order in~v/c, Eq. (51) yields

d~v

dt=

Sem

m c

3∑

j=1

C ′pr,j [(1 − 2 ~v · ~e1/c + ~v · ~ej/c) ~ej − ~v/c]

+1m

3∑

j=1

F ′e,j

[(1 +

~v · ~ej

c

)~ej − ~v

c

],

~ej = (1 − ~v · ~e′j/c) ~e′j + ~v/c , j = 1, 2, 3 . (52)

It is worth mentioning to stress that the values of radiation pressure cross sectionsC ′pr,j ,

j = 1, 2, 3, depend on particle’s orientation with respect to the incident radiation – theirvalues are time dependent.

It can be verified that Eq. (51) (or Eq. 52 within the accuracy to the first order in~v/c)yields as special cases the situations discussed in Einstein (1905) and Robertson (1937).However, the case treated by Poynting (1903) and Robertson (1937) is not consistent with


Eq. (49). The reason is that perfectly absorbing spherical dust particle fulfillsC′pr,1/C′

ext

= 1/2 and not 1, as it is stated by Poynting (1903), Robertson (1937), Wyatt and Whipple(1950) and others (see Klacka 2008a, 2008b for more details); spherical symmetric distri-bution of mass yieldsC ′

pr,2 = C ′pr,3 = ~F ′

e = 0. The case of spherically symmetric massdistribution is known as the Poynting-Robertson effect, and, according to Eq. (52), we canwrite

d~v

dt=

Sem A′ Q′pr,1

m c

(1 − ~v · ~e1

c

)~e1 − ~v

c

, (53)

where a dimensionless efficiency factor of radiation pressureQ′pr,1 is defined by relation

Q′pr,1 = C ′

pr,1/A′. The values ofQ′

pr,1 can be calculated according to Mie (1908; see alsovan de Hulst 1981, Bohren and Huffman 1983).

General equation of motion, represented by Eq. (51) or Eq. (52) differs from thePoynting-Robertson effect represented by Eq. (53). Eqs. (51)-(52) hold for arbitrarilyshaped particles. Experimental evidence that nonspherical dust grains move in a differentway than spherical particles was given by Krauss and Wurm (2004).

4. Secular Evolution of Particle’s Orbital Elements under theAction of Solar Radiation

Let us consider spherical IDP orbiting the Sun under the action of solar radiation, i.e. solarwind and solar electromagnetic radiation. The effect of the solar electromagnetic radia-tion on the motion of spherical particle corresponds to the Poynting-Robertson effect (P-Reffect).

For description of motion of the dust particles it is useful to introduce parameterβ

defined as ratio of radial component of radiation force and gravitation force between theSun and the particle

β =LA′Q′

pr

4πcmµ. (54)

L is luminosity of the Sun,Q′pr = Q′

pr,1 andµ≡ GM , whereG is the gravitational constant,M is mass of the Sun. For homogeneous spherical particle we can write

β = 5.763× 10−4 Q′pr

R[m] ρ[kg/m3], (55)

whereR is radius of the particle andρ is mass density of the particle. In this section wewill suppose thatβ = const: neither optical properties nor mass of the IDP change.

Now, using Eq. (54), relationSem = L/(4πr2); r is a heliocentric distance of IDP; andthe decomposition of velocity vector~v = vR~eR + vT~eT , we can rewrite Eq. (53) into theform (

d~v

dt

)

P−R

= βµ

r2

[(1 − 2

vR

c

)~eR − vT

c~eT

], (56)

This is the acceleration of the IDP under the Poynting-Robertson effect.


Let us replace the fraction behind the curly braces in Eq. (36) by new quantities

A′nm1u2

m≡ β

η

Q′pr

u

c

µ

r2, (57)

whereη is a constant,η .= 1/3 (see, e. g., Dohnanyi 1978, Gustafson 1994; the valueu =400 km/s is used in modelling of orbital evolution under the action of solar wind). Further,we puti = 0 in Eq. (36). Then, the acceleration of the IDP caused by solar wind has theform

(d~v

dt

)

SW

= βη

Q′pr

µ

r2

(u

c− 2

vR

c

)~eR − vT

c~eT

− γT

[vT

c~eR −

(u

c− vR

c

)~eT

]

+12

v2

uc~eR +

vR

c

~v

u

. (58)

Gravitational acceleration from the Sun is−(µ/r2)~eR. Neglecting the solar wind pres-sure termβ(η/Q′

pr)(µ/r2)(u/c) in Eq. (58), we can write the final equation of motion ofIDP in the form

d~v

dt= − (1 − β) µ

r2~eR − β

(1 +

η

Q′pr

)µ

r2

(2

vR

c~eR +

vT

c~eT

)

+ βη

Q′pr

µ

r2

− γT

vT

c~eR + γT

(u

c− vR

c

)~eT

+12

v2

uc~eR +

vR

c

~v

u

. (59)

We have introduced new central acceleration−(1− β)µ~eR/r2, i.e. the gravitational accel-eration from the Sun reduced by the solar electromagnetic radiation pressure. Other termson the right-hand side of Eq, (59) constitute the nongravitational disturbing acceleration.We will calculate the secular evolution of semimajor axisa, eccentricitye and argumentof perihelionω of the particle’s orbit under this nongravitational perturbation. The timeevolution of the osculating elements is given by equations

da

dt= 2

a

1 − e2

√p

(1 − β)µ[aR e sin f + aT (1 + e cos f)] ,

de

dt=

√p

(1 − β) µ

[aR sin f + aT

(cos f +

e + cos f

1 + e cos f

)],

dω

dt= −

√p

(1 − β)µ

1e

[aR cos f − aT sin f

2 + e cos f

1 + e cos f

], (60)

wherep = a(1− e2) andf is true anomaly of the IDP. Moreover,aR andaT are radial andtransversal components of the disturbing acceleration. Using Eq. (59) and expressions

vR =

√(1 − β) µ

pe sin f , vT =

√(1 − β) µ

p(1 + e cos f) , (61)


known from celestial mechanics, we obtain

aR = − β

(1 +

η

Q′pr

)µ

r2

2c

√(1 − β)µ

pe sin f

+ βη

Q′pr

µ

r2

1c

− γT

√(1 − β)µ

p(1 + e cos f)

+12u

(1 − β)µ

p

(1 + e2 + 2e cos f

)+

1u

(1− β)µ

pe2 sin2 f

,

aT = − β

(1 +

η

Q′pr

)µ

r2

1c

√(1 − β)µ

p(1 + e cos f)

+ βη

Q′pr

µ

r2

1c

γT u − γT

√(1− β)µ

pe sin f

+1u

(1− β)µ

pe sin f (1 + e cos f)

. (62)

Secular evolution of the orbital elementg we get by the time averaging ofdg/dt over oneorbital periodT , i.e.

⟨dg

dt

⟩≡ 1

T

∫ T

0

dg

dtdt =

1a2√

1 − e2

12π

∫ 2π

0r2 dg

dt(f) df . (63)

We have used the second and the third Kepler’s laws:r2df/dt =√

µ(1 − β)p − dω/dt −(dΩ/dt) cos i

.=√

µ(1 − β)p anda3/T 2 = µ(1− β)/(4π2); p = a(1− e2), ω is argumentof perihelion andΩ is longitude of the ascending node. Application of the last equation onEqs. (60) and using Eqs. (63) yields

⟨da

dt

⟩= − β

µ

c

2 + 3e2

a (1 − e2)3/2

×

1 +

η

Q′pr

[1 − γT

2u

2 + 3e2

√p

(1 − β)µ

],

⟨de

dt

⟩= −β

µ

c

5e/2a2√

1 − e2

×

1 +η

Q′pr

[1 − γT

51 −

√1− e2

e22u

√p

(1 − β)µ

],

⟨dω

dt

⟩= −β

µ

c

1a2√

1 − e2

η

Q′pr

×

[γT

1−√

1 − e2

e2− 1

2u

√p

(1 − β)µ

]. (64)

Let us look on secular evolution of semimajor axisa of the particle’s orbit. If the P-R effectand radial velocity component of the solar wind are considered (i.e.γT = 0), then Eqs. (64)


show thata is a decreasing function of time. If one takes into account also the non-radialvelocity component of the solar wind, the situation may be different. For some specialconditions, the expression in curly braces in equation for〈da/dt〉 can be negative andais an increasing function of time. Thus, the effect of real solar wind may cause particle’sspiralling outward from the Sun.

Initial conditions must be added to the set of differential equations for orbital elements.If the particle is ejected from a parent body of known orbital elements, then the particle’sinitial orbital elements have to be calculated from Eqs. (58)-(59) in Klacka (2004).

If one would take into account also change of optical properties of the spherical dustparticle, then also perihelion motion exists for the pure P-R effect. We do not deal with thiscase (see Klackaet al. 2007).

4.1. Time of Spiralling

From Eqs. (64) we can determine also the secular evolution of the semi-latus rectump ofthe particle’s orbit. Whencep = a(1 − e2) we can write

⟨dp

dt

⟩=(1− e2

)⟨da

dt

⟩− 2ae

⟨de

dt

⟩, (65)

what using Eqs. (64) yields

⟨dp

dt

⟩= −2β

(1 +

η

Q′pr

)µ

c

(1 − e2

)3/2

p

+ 2βη

Q′pr

µ

cγT u

√p

(1 − β) µ

1 − e2

p. (66)

Let us rewrite equation for〈de/dt〉 into the form

⟨de

dt

⟩= − 5

2β

(1 +

η

Q′pr

)µ

c

e(1− e2

)3/2

p2

+ βη

Q′pr

µ

cγT u

√p

(1 − β)µ

×

(1−

√1 − e2

) (1 − e2

)3/2

p2 e. (67)

4.1.1. Radial Solar Wind and P-R Effects

Now, let us consider only the P-R effect and the radial solar wind effect. We putγT = 0 inEqs. (66)-(67). In this case, we obtain the following equation

dp

de=

45

p

e(68)

from Eqs. (66) and (67). Eq. (68) yields the relation

p = p0

(e

e0

)4/5

, (69)


wherep0 ande0 are initial values of semi-latus rectum and eccentricity of the particle’sorbit. Eq. (69) can be considered as a generalization of the result obtained by Wyatt andWhipple (1950): we have taken into account not only the P-R effect, but also the radialsolar wind effect. Eq. (69) allows us to write equation for secular evolution of eccentricityin the form ⟨

de

dt

⟩= − 5

2β

(1 +

η

Q′pr

)µ

c

e8/50

p20

(1 − e2

)3/2

e3/5. (70)

It is evident from Eqs. (64) that due to the P-R effect and radial solar wind the particleis spiralling inward to the Sun. Semimajor axisa and eccentricitye of the particle’s orbitconverge to 0 (see Eqs. 66, 67 and 69). Eq. (70) can offer the time of spiralling of theparticle with initial orbital elementsa0 ande0 into the orbit with osculating elementsa, e.This time is given by relation

τ (e0, e) = − 25

[β

(1 +

η

Q′pr

)µ

c

]−1

a20

(1 − e2

0

)2

e8/50

I (e0, e) ,

I (e0, e) =∫ e

e0

x3/5

(1 − x2)3/2dx . (71)

The time of spiralling of the particle into the Sun is then

τ (e0, 0) = − 25

[β

(1 +

η

Q′pr

)µ

c

]−1

a20

(1 − e2

0

)2

e8/50

I (e0, 0) . (72)

Let us consider two particles characterized by the valuesβ1 andβ2. Moreover, let theparticles have the same value ofQ′

pr. If we are interested in times of stay of the particleswithin an interval of semimajor axes (alower, aupper), then Eq. (71) yields:τ1/τ2 = β2/β1,if the initial values of semimajor axes and eccentricities are equal for both particles. On thebasis of Eqs. (66)-(67), this result can be approximately generalized also to the case of realsolar wind effect, under the assumptionβ1, β2 1.

4.2. Decrease of Particle’s Radius

According to Eq. (27), the mass of the particle may decrease. Whence we take into accountthe homogeneous spherical particle, we can replace Eq. (27) by the equivalent equationexpressing a decrease of particle’s radiusR

dR

dt= − K

r2, (73)

whereK is a constant depending on the material properties. We will suppose that thedecrease of the particle’s radius is small enough to enable analytic calculations in secularevolution. Averaging of Eq. (73) over orbital period (see Eq. 63) then yields

⟨dR

dt

⟩= − K

a2√

1 − e2. (74)


When we consider only the P-R effect and radial solar wind effect (γT = 0), we are able tocalculate the radius of IDP as a function of its orbital eccentricity. From Eqs. (64) and (74)we obtain

dR

de=

25

K

[β

(1 +

η

Q′pr

)µ

c

]−11e

. (75)

Let us consider the particle of radiusR0 on the orbit characterized by eccentricitye0. Aftersome time, the particle will inspiral to the orbit with an eccentricitye. We can obtain anidea about qualitative relation betweenR ande using a simple model. The model may bebased on the assumption thatQ′

pr is a constant. By integration of Eq. (75) we obtain thatparticle’s radius will be

R = R0

(e

e0

)ζ

,

ζ =25

K

β

(1 +

η

Q′pr

)R[m]

µ

c

−1

. (76)

4.3. Summary

As for the secular evolution, under the assumption that particle’s radius decreases slowly,we have to solve Eqs. (55), (64) and (74), simultaneously. This set of differential equationssignificantly simplifies if only radial component of the solar wind velocity is considered: itis sufficient to solve only one differential equation Eq. (70) and one immediately obtainsresults for semi-latus rectum (semimajor axisa = p / (1 − e2)) and radius of the particlefrom Eqs. (69) and (76).

5. Mean Motion Resonances

Commensurability resonances have been well-known since 1857, when Kirkwood foundgaps in the distributionof asteroidal semimajor axes (histogram: number of known asteroidsversus their semimajor axes) in the asteroid belt. A body is in resonance with a planet whenthe ratio of their mean motions (mean motionn = 2π/T, whereT is orbital period) isthe ratio of two small natural numbers: the semimajor axis of the body oscillates around aconstant value. The physics of these mean motion resonances with Solar System planetshas been successfully studied since 1980 (Wisdom 1980). The orbital evolution of dustgrains near resonances with planets has been intensively studied during the last twenty years(Jackson and Zook 1989). Besides gravitational forces of the Sun and planet(s), the effect ofsolar electromagnetic radiation in the form of the Poynting-Robertson effect is also usuallytaken into account: e. g., Jackson and Zook (1989),Sidlichovsky and Nesvorny (1994),Beauge and Ferraz-Mello (1994), Marzari and Vanzani (1994), Liou and Zook (1995), Liouet al. (1995), Liou and Zook (1997), Liouet al. (1999), Kehoeet al. (2002), Holmeset al.(2003). Observations confirming the existence of a dust ring around the Sun in resonancewith the Earth are discussed in Brownlee (1994), Dermottet al. (1994), Reachet al. (1995).Qualitatively new results are obtained when we allow that real particles are nonsphericaland instead of the Poynting-Robertson (P-R) effect (based on the assumption that material


within dust grains is distributed in a spherically symmetric way), we use Eqs. (40)-(41)of Klacka (2004) (plus gravitational acceleration of the third body, a planet) in modelingmean motion resonances. The generalization of the P-R effect considers interaction ofthe incident electromagnetic radiation with nonspherical dust grains and, thus, non-radialradiation pressure terms also are present in the general covariant equation of motion (Eq. 41in Klacka 2004). For an application of the equation of motion to mean motion resonances,we refer to Klackaet al. (2005a, 2005b) and Klacka and Kocifaj (2006a, 2006b).

Our aim is to take into account the newest observational results on the solar wind. Weare interested in the effect of the non-radial velocity component of the solar wind (in thereference frame of the Sun) on the motion of dust grains in the regions of mean motionorbital resonances. Up to now, the non-radial component of the solar wind velocity wasconventionally neglected (e. g., Grunet al. 1994, Liou and Zook 1997). It was assumedthat the azimuthal velocity component decreases as 1/r with the heliocentric distancer(e. g., Hundhausen 1972 – p. 87, Stix 2002 – pp. 424-425): according to these results,the non-radial velocity component of the solar wind should be 1 km/s at 1 AU, which is avery small value in comparison with the radial velocity component equal to 400 km/s fora low velocity solar wind (the value of 400 km/s is standardly used in the modeling of theorbital evolution of interplanetary dust, e. g., Dohnanyi 1978, Grunet al. 1994, Liou andZook 1997). However, the new observations of the solar wind show that the non-radialvelocity component of the solar wind is not a decreasing function of heliocentric distance,at least for the distances covered by observations from Helios 2 during its first solar missionin 1976 (Brunoet al. 2003). The angle between the solar wind velocity vector and theradial heliocentric vector is close to 3 for a low velocity solar wind. We will use theobservational value in modeling the orbital evolution of dust grains near the mean motionorbital resonances with planet Neptune. We will discuss spherical dust grains, since theyenable a partial analytical treatment. The solar wind and the Poynting-Robertson effectwill be considered, together with the planar restricted three-body problem. Results of thissection include also results presented by Pastoret al. (2008) and Klackaet al. (2008).

5.1. Equation of Motion

Let us consider a spherical dust grain under the action of gravitational forces generated bythe Sun and a planet moving around the Sun. Moreover, the grain is evolving under theaction of solar electromagnetic radiation and solar wind. Equation of motion of the particleis considered in the form

d ~v

d t= − µ (1 − β)

r2~eR

− β

(1 +

η

Q′pr

)µ

r2

(~v · ~eR

c~eR +

~v

c

)

+ βη

Q′pr

µ

r2

(− γT

~v · ~eT

c+

12

v2

cu

)~eR

+ γT

(u

c− ~v · ~eR

c

)~eT +

(~v · ~eR

c

)~v

u


− µmP

M

~r − ~rP

|~r − ~rP |3+

~rP

|~rP |3

, (77)

where~v = vR~eR + vT~eT is velocity vector of the particle,v = |~v|, r = |~r|, ~eR = ~r/r, ~eT

is transversal unit vector,~r and~rP are position vectors of the particle and the planet (massmP ) with respect to the Sun (massM), µ = GM, u is speed of solar windu ≈ 400km/s,γT = sin ε, ε is angle between radial direction and direction of solar wind (accordingto Brunoet al. 2003, the angleε lies between 2.3 and 2.9 degrees and the value ofε doesnot significantly depend on heliocentric distance),η depends on properties of the solar windandη ≈ 1/3. Eq. (77) is obtained on the basis of Eq. (59) and the gravitational effect of theplanet is also taken into account.

5.2. Mean Motion Resonances

A particle is in a mean motion orbital resonance with a planet if the ratio of mean motionsof the planetnP and the dust particlen is approximately equal to the ratio of small naturalnumbers. For exterior resonancenP /n = (p + q)/p and for interior resonancenP /n =p/(p+ q), whereq is order of the resonance. In terms of orbital periods:T/TP = (p+q)/p

for the exterior andT/TP = p/(p+q) for the interior resonance. Particle’s stay in resonanceis characterized by relation ⟨

da

dt

⟩= 0 , (78)

wherea is semimajor axis of the particle. This relation holds due to the libration of thesemimajor axis around a constant value, since for any functiona of the propertya(TL) =a(0) fulfills ⟨

da

dt

⟩=

1TL

∫ TL

0

da

dtdt =

a(TL)− a(0)TL

= 0 , (79)

whereTL is the period of the resonant libration of the semimajor axis.As a central acceleration for calculation of orbital elements we will use the first Keple-

rian term in Eq. (77), namely−µ(1 − β)~eR/r2. The particle’s semimajor axis in the meanmotion resonance can be determined from the third Kepler’s law. We have

a3P n2

P = G (M + mP ) ,

a3 n2 = G M (1 − β) , (80)

whereaP anda are the semimajor axes of the planet and the particle. The parameterβ

characterized optical properties of the particle. Eq. (80) yields for semimajor axis of theparticle

a = (1 − β)1/3(nP

n

)2/3(

1 +mP

M

)−1/3

aP . (81)

On the basis of definitions of the mean motion resonance and Eq. (80), we can write

a = (1 − β)1/3

(p + q

p

)2/3 (1 +

mP

M

)−1/3

aP , (82)

for the semimajor axis of the particle in theq−th order exterior resonance with the planetof massmP . A similar relation can be obtained for the interior resonance.


5.3. Secular Evolution of Eccentricity in Mean Motion Resonances with aPlanet in a Circular Orbit

Secular evolution of a semimajor axis is characterized by its constant value when the parti-cle is in a resonance with a planet (see Eq. 78). Let us assume that the planet is moving ina circular orbit around the Sun. This is a special gravitational problem of three bodies. Thegravitational problem is calledthe circular restricted three-body problem in celestial me-chanics. At the end of the 19-th century French astronomer F. F. Tisserand found a quantitythat does not change during the motion of the third body, whose mass is negligible in com-parison to the masses of the planet and the Sun (see, e. g. Brouwer and Clemence 1961).For our case, when also Keplerian term−µ(1 − β)~eR/r2 is considered, we can write theTisserand parameter in the form

CT =1 − β

a+ 2

√(1 − β) a (1 − e2)

a3P

cos I , (83)

wheree is the eccentricity of the particle characterized by parameterβ andI is the incli-nation of the particle’s orbital plane with respect to the plane of the planetary orbit. Wehave to stress that Tisserand’s quantityCT does not change only for the special case of thecircular restricted problem of three bodies. In reality, small nongravitational forces act onthe particle. Eq. (83) enables to find the secular change of the eccentricity of the particlecaptured into a resonance. For this purpose, we will considerI = 0 in Eq. (83). We canwrite

dCT

dt=

∂CT

∂a

(da

dt

)

total

+∂CT

∂e

(de

dt

)

total

, (84)

for the total time derivative of the Tisserand quantityCT defined by Eq. (83). However,according to Eq. (77), time derivatives of the semimajor axis and eccentricity of the particleare caused by gravitational perturbations of the planet (these terms will be denoted by thesubscriptG) and nongravitational perturbations caused by solar electromagnetic radiationand the solar wind (these terms will be denoted by the subscriptNG):

(da

dt

)

total

=(

da

dt

)

G

+(

da

dt

)

NG

,

(de

dt

)

total

=(

de

dt

)

G

+(

de

dt

)

NG

. (85)

On the basis of Eqs. (84)-(85) we can write

dCT

dt=

∂CT

∂a

(da

dt

)

G

+(

da

dt

)

NG

+∂CT

∂e

(de

dt

)

G

+(

de

dt

)

NG

. (86)

According to Tisserand, gravitational terms do not change the value ofCT :

∂CT

∂a

(da

dt

)

G

+∂CT

∂e

(de

dt

)

G

= 0 . (87)


Putting Eq. (87) into Eq. (86) yields:

dCT

dt=

∂CT

∂a

(da

dt

)

NG

+∂CT

∂e

(de

dt

)

NG

. (88)

If we are interested in secular changes of orbital elementsa ande, then the particle’s stay inthe resonance is characterized by Eq. (78). After averaging over the period of the resonantlibration of the semimajor axis, Eq. (84) reduces to

⟨dCT

dt

⟩=

∂CT

∂e

⟨de

dt

⟩. (89)

Parallelly, averaging of Eq. (88) gets

⟨dCT

dt

⟩=

∂CT

∂a

⟨da

dt

⟩

NG

+∂CT

∂e

⟨de

dt

⟩

NG

. (90)

Eqs. (89) and (90) yield

⟨de

dt

⟩=⟨

de

dt

⟩

NG

+∂CT /∂a

∂CT /∂e

⟨da

dt

⟩

NG

, (91)

for the total secular change of the eccentricity of the particle. Eqs. (64), (83) and (91)finally yield

⟨de

dt

⟩= β

µ

c

(1 +

η

Q′pr

) (1 − e2

)1/2

a2 e(X − Y ) ,

X = 1−(1 + 3e2/2

)(1 − β)1/2

(a/aP )3/2 (1− e2)3/2,

Y =γT

γC

1 − (1 − β)1/2

(a/aP )3/2 (1 − e2)

,

γC =1 + η/Q′

pr

η/Q′pr

1u

√µ(1 − β)

a, (92)

where the ratioa/aP can be expressed through the rationP /n from Eq. (81). The obtainedequation reduces to the equation of Liou and Zook (1997) under assumption thatη ≡ 0 (Y= 0 in this case). The special caseγT ≡ 0 reduces Eq. (92) to the equation consistent withEq. (83) in Klacka and Kocifaj (2006a) (see also Eq. 20 in Klacka and Kocifaj 2006b).

5.4. Orbital Evolution of a Dust Particle under the Action of the P-R Effectand Radial Solar Wind in Mean Motion Resonances

We will study an influence of the P-R effect and the radial solar wind on the orbital evolutionof dust particle in the mean motion resonance with a planet, in this subsection. We will


consider equation of motion in the form

d ~v

d t= − µ (1 − β)

r2~eR

− β

(1 +

η

Q′pr

)µ

r2

(~v · ~eR

c~eR +

~v

c

)

− µmP

M

~r − ~rP

|~r − ~rP |3+

~rP

|~rP |3

. (93)

This equation can be obtained from Eq. (77) by puttingγT = 0 and neglecting the termproportional tov2/(uc). Using the first component of the right-hand side of Eq. (93)as a central acceleration, the secular time derivatives of semimajor axis, eccentricity andargument of perihelion, caused by nongravitational terms, are

⟨da

dt

⟩

NG

= − βµ

c

(1 +

η

Q′pr

)2 + 3e2

a (1 − e2)3/2,

⟨de

dt

⟩

NG

= −βµ

c

(1 +

η

Q′pr

)5e/2

a2√

1 − e2,

⟨dω

dt

⟩

NG

= 0 . (94)

Figure 1. Evolution of eccentricity of dust particle withβ = 0.01 andη/Q′pr = 1/3 in

resonances with a planet of mass approximately equal to mass of Neptune, semimajor axisaP = 30.058 AU and eccentricityeP = 0. The left part is for the exterior mean motion 4/3resonance. Various evolutions correspond to different initial values of eccentricity in theresonance. Initial eccentricities are: 0.55, 0.45, 0.35, 0.25, 0.15 and 0.05. The right part ofthe figure is for the interior mean motion 2/3 resonance. Initial eccentricities are: 0.8, 0.6,0.4 and 0.2. The evolutions are numerically calculated from Eq. (73) and are consistentwith Eq. (95).


5.4.1. Evolution of Eccentricity in Mean Motion Resonances with a Planet in Circu-lar Orbit

Inserting secular time derivatives of the semimajor axis and eccentricity from Eq. (94) intoEq. (91), using also Eq. (93) withI = 0, we obtain for the secular time derivative ofeccentricity in the mean motion resonance

⟨de

dt

⟩= β

µ

c

(1 − e2

)1/2

a2 e

(1 +

η

Q′pr

)1 −

(1 + 3e2/2

) √1 − β

(a/aP )3/2 (1 − e2)3/2

. (95)

This result is identical to equation obtained by insertingγT = 0 into Eq. (92). Eq. (95)determines the secular evolution of eccentricity of the spherical particle under the actionof the P-R effect and the radial solar wind, if the particle is captured into the mean motionresonance with the planet moving in a circular orbit. This equation enables us to determinethe detailed evolution. If we take some special mean motion resonance, we already knowthe valuenP /n and we can calculatea/aP from Eq. (81). If the initial secular eccentricityis greater than a limiting valueelim, then the eccentricity of the particle is a decreasingfunction of time during the stay of the particle in the exterior mean motion resonance. Theeccentricity of the particle can only asymptotically approach the limiting valueelim givenby the condition that the value in the combined brackets in Eq. (95) is zero:

p + q

p=

1 + 3e2lim/2

(1− e2lim)3/2

. (96)

If the initial eccentricity is smaller thanelim, then〈de/dt〉 is always positive and the eccen-tricity of the particle is an increasing function of time, during the stay of the particle in theexterior mean motion resonance. The eccentricity of the particle can only asymptoticallyapproach the limiting valueelim. Characteristic property of the valueelim is that it doesnot depend onβ. The left part of Fig. 1 depicts evolutions of an osculating eccentricityof the particle withβ = 0.01 andη/Q′

pr = 1/3 in exterior 4/3 resonance with a planetof mass approximately equal to mass of Neptune (mNeptune ≈ 17.24mEarth, mEarth =5.9742× 1024 kg), semimajor axisaP = 30.058 AU and orbital eccentricityeP = 0. Theevolutions are calculated from numerical solution of Eq. (93). Asymptotical approachingto the limiting valueelim = 0.3108 (given by Eq. 96) can be easily seen.

The secular evolution of eccentricity is always a decreasing function of time for interiorresonances defined by the relationn/nP = p/(p+q). Evolutions of osculating eccentricityof the particle withβ = 0.01 andη/Q′

pr = 1/3 in the interior 2/3 resonance with a planet ofmass equal to the mass of Neptune, semimajor axisaP = 30.058 AU and orbital eccentricityeP = 0 is shown in the right part of Fig. 1. Evolutions of eccentricities for the givenresonance and particle are parallel – the evolutions are shifted along time axis, since Eq.(95) yields the same value of〈de/dt〉 for the same eccentricitye. If β = 0 (e. g., anasteroid), then〈de/dt〉 = 0, according to Eq. (95).

5.4.2. Evolution of the Argument of Perihelion in Mean Motion Resonance with aPlanet in a Circular Orbit

Let us assume that a function of the type of Eq. (95) exists for secular evolution of the par-ticle’s argument of perihelion if the particle is captured in a mean motion orbital resonance


Figure 2. Two orbital evolutions of dust particle withβ = 0.01 andη/Q′pr = 1/3 captured

in the exterior 4/3 resonance with a planet of Neptune’s mass, semimajor axisaP = 30.058AU and eccentricityeP = 0. Particle’s initial values area ≈ 36.2909 AU,e = 0.45,ω =149.76 for the first evolution (solid line), and,a ≈ 36.2909 AU,e = 0.45,ω = 42.84

for the second evolution (dashed line). Evolutions of the arguments of perihelia intersect attime t ≈ 1.25× 105 years.

with a planet in circular orbit in the planar case. Let us denote this function asS. Theassumption is that the functionS depends on semimajor axis, eccentricity and argument ofperihelion of the particle in the form:

⟨dω

dt

⟩= S(a, e, ω) (97)

for a given central star, the planet, the particle and the resonance. Fig. 2 depicts two evolu-tions of the orbital elements of the particle withβ = 0.01 andη/Q′

pr = 1/3 in the exterior4/3 resonance with the planet of Neptune’s mass, semimajor axisaP = 30.058 AU andeccentricityeP = 0. The particle’s initial values of the orbital elements area ≈ 36.2909AU (given by Eq. 82),e = 0.45,ω = 149.76, for the first evolution, depicted by solidline, and,a ≈ 36.2909 AU,e = 0.45,ω = 42.84, for the second evolution, depicted bydashed line. At the timet = 0 the particle is at the perihelia of the orbits. The planet’sinitial position is at X-axis (axis, from which the argument of the perihelion is measured),in both integrations. Evolution of the secular eccentricity in Fig. 2 is consistent with the


Figure 3. Five evolutions of arguments of perihelion of dust particle withβ = 0.01 andη/Q′

pr = 1/3 in the exterior mean motion 4/3 resonance with a planet of mass approximatelyequal to mass of Neptune, semimajor axisaP = 30.058 AU and eccentricityeP = 0.

behavior expected from Eq. (95). We are interested in secular evolution of the argumentof perihelion. Evolutions of the arguments of perihelia intersect at the timet ≈ 1.25× 105

years. Secular values of the semimajor axes are practically identical, for the both orbits. Thesame holds for the eccentricities. However, the values of the〈dω/dt〉 differ. This meansthat the functionS(a, e, ω) does not exist for a givena, e andω, since different values of〈dω/dt〉 occur for the samea, e andω. In order to find secular time derivative of the argu-ment of perihelion in mean motion resonance, one must take into account other argumentsthan only secular values of semimajor axis, eccentricity and argument of perihelion. In thiswork we restrict ourselves on computing evolution of the argument of perihelion in meanmotion resonance from numerical solution of the equation of motion. By application of thismethod on Eq. (93) we obtained five evolutions of argument of perihelion depicted in Fig.3. Each of the evolutions is for dust particle withβ = 0.01 andη/Q′

pr = 1/3 captured in theexterior mean motion 4/3 resonance with a planet of Neptune’s mass, semimajor axisaP =30.058 AU and eccentricityeP = 0. The particle is initially in the resonancea ≈ 36.2909AU. Initial eccentricity and argument of perihelion of the particle orbit ise = 0.2 andω

= 0, respectively. Different evolutions were created using different initial positions of theparticle with respect to the planet (planetary initial position was always on the X-axis). Thefigure may suggest that the greater decrease of the initial shift of argument of perihelion, thelonger capture in the resonance exists. But this is not always true. Secular evolution of theeccentricity corresponding to all the five evolutions of the argument of perihelion depictedin Fig. 3 is consistent with the behavior expected from Eq. (95) for the initial value of the


eccentricity equal to 0.2 (see left part of Fig. 1).

Figure 4. Orbital evolution of dust particle withβ = 0.01 andη/Q′pr = 1/3 captured in the

exterior 4/3 resonance with a planet of mass approximately equal to the mass of Neptune,semimajor axisaP = 30.058 AU and eccentricityeP = 0.1. The particle’s initial values area ≈ 36.2909 AU,e = 0.2,ω = 0.

5.4.3. Evolution of Eccentricity and the Argument of Perihelion in a Mean MotionResonance with a Planet in an Elliptical Orbit

We cannot derive the secular time derivative of the particle eccentricity using the Tisserandparameter defined in Eq. (83), in the case of an elliptical orbit of a planet. The reasonis that Eq. (87) does not hold for the elliptical restricted three-body problem. As for theevolution of the argument of perihelion, the situation for the elliptical planetary orbit is evenmore complicated than it is in the case of circular planetary orbit (see previous section).But we can always find the evolution of the eccentricity and the argument of perihelionusing numerical solution of the equation of motion. Fig. 4 shows orbital evolution of theparticle withβ = 0.01 andη/Q′

pr = 1/3 captured in the exterior 4/3 resonance with a planetof mass approximately equal to mass of Neptune, semimajor axisaP = 30.058 AU andeccentricityeP = 0.1. The particle is initially located inside the resonance. The capturetime is 381× 106 years. The secular eccentricity of the particle does not asymptoticallyapproaches to any limiting value. This is the difference between the secular evolutionsof the eccentricity in the mean motion resonance with the planet in circular and elliptical


Figure 5. Black color lines represent orbital evolutions of dust particle withβ = 0.01 andη/Q′

pr = 1/3 captured in an exterior 4/3 resonance with a planet of mass approximatelyequal to the mass of Neptune. Also semimajor axisaP = 30.058 AU and eccentricityeP =0.0112 correspond to the values of Neptune. The particle’s initial values area ≈ 36.2909AU, e = 0.1,ω = 0. Gray color lines represent evolutions of the particle orbital elementsin the resonance with the planet in a circular orbit.

orbits (see Fig. 1). Fig. 5 shows two evolutions of orbital elements of the particle withβ

= 0.01 andη/Q′pr = 1/3 captured in the exterior 4/3 resonance with a planet of Neptune’s

mass and semimajor axisaP = 30.058 AU. Black color line represents orbital evolution inthe resonance with the planet in the elliptical orbit of eccentricityeP = 0.0112 (Neptune’seccentricity, approximately) and gray color line represents evolution in the resonance withthe planet in the circular orbit. Black line eccentricity evolution does not show a simpleoscillatory behavior around the evolution valid for circular planetary orbit. This kind ofbehavior occurs when small values of the shift of perihelion exist (argument of perihelionis practically constant). The oscillatory behavior is valid only during the first 1.5× 108

years and at the end of the capture when the secular evolution of the argument of perihelionrapidly increases (see Fig. 5). However, a tendency (for large times) toward the limitingvalue of eccentricity exists. For more detailed information about the connection betweenoscillation in the secular evolution of eccentricity and the secular evolution of the argumentof perihelion we can refer to Pastoret al. (2008).


5.5. Influence of Non-Radial Solar Wind, P-R Effect and Mean Motion Res-onances on Dynamics of Spherical Dust Particles

In this subsection we will discuss properties of the orbital evolution of spherical dust particleunder action of the non-radial solar and the P-R effect in a mean motion resonance with aplanet in a circular orbit. We will show that the evolution of eccentricity has qualitativelydifferent properties from the case when only radial solar wind is considered. Presence ofthe non-radial component of the solar wind velocity also changes dynamics of capture ofthe particles to mean motion resonances.

Figure 6. Evolution of eccentricity obtained from Eq. (92). Dust particle withβ = 0.01 andη/Q′

pr = 2/3 is captured in the exterior mean motion 2/1 orbital resonance with a planetof mass approximately equal to the mass of Neptune, semimajor axisaP = 30.058 AUand eccentricityeP = 0. Solar wind parameterε = 0. Evolution curves for various initialconditions of eccentricity are shown.

5.5.1. Evolution of Eccentricity in a Mean Motion Resonance with the Planet in aCircular Orbit

If we take into account also non-radial component of the solar wind (ε 6= 0), then theequation of motion takes the form of Eq. (77). Secular evolution of the eccentricity of aparticle in a mean motion resonance with the planet in a circular orbit is given by Eq. (92).We define the functionW (e) = X(e) − Y (e), whereX(e) andY (e) are defined in Eq.(92):

X(e) = 1 −(1 + 3e2/2

)(1− β)1/2

(a/aP )3/2 (1 − e2)3/2,

Y (e) =γT

γC

1 − (1− β)1/2

(a/aP )3/2 (1 − e2)

,

γC =1 + η/Q′

pr

η/Q′pr

1u

√µ(1 − β)

a, (98)


Figure 7. Evolution of eccentricity obtained from Eq. (92). Dust particle withβ = 0.01andη/Q′

pr = 2/3 is captured in an exterior mean motion 2/1 orbital resonance with a planetof mass approximately equal to mass of Neptune, semimajor axisaP = 30.058 AU andeccentricityeP = 0. Solar wind parameterε = 2.5. Evolution curves for various initialconditions are shown.

γT = sin ε ≥ 0. Now, let us calculate derivatives ofX(e) andY (e) with respect to theeccentricity

dX

de= − 3e(1 − β)1/2(4 + e2)

2(a/aP )3/2(1− e2)5/2< 0 , (99)

dY

de= −γT

γC

2e(1− β)1/2

(a/aP )3/2(1 − e2)2< 0 . (100)

The functionsX(e) andY (e) are decreasing functions of eccentricity. Now, it is easy toshow thatdX/de < dY/de for all e ∈ (0,1), if γT/γC < 3. The functionX(e) decreasesfaster than the functionY (e) for γT/γC < 3 when eccentricity increases. The derivative ofW (e) is

dW

de=

e(1− β)1/2

(a/aP )3/2(1− e2)2

−3

24 + e2

(1− e2)1/2+ 2

γT

γC

. (101)

Eq. (101) shows that the functionW (e) is a decreasing function for alle ∈ (0,1) and forγT/γC < 3. The valueW (e = 0) is

W (0) = 1 − (aP /a)3/2(1− β)1/2(1 − γT/γC) . (102)

We begin with exterior mean motion resonances. For exterior mean motion resonanceswe can use Eq. (82) and Eq. (102) reduces to

W (0) = 1 − p/(p + q)(1− γT/γC) ; (103)

we have assumed thatmP M in Eq. (82). IfγT/γC ≤ 1 < 3, then the functionW is adecreasing function of eccentricity. IfγT/γC < 1, thenW (0) > 0 andW (e) has one rootfor e ∈ [0,1), becauselime→1 W = −∞. This root ofW (e) we denote aseI. If we choose


initial eccentricity greater thaneI, then the eccentricity asymptotically decreases toeI. Ifwe choose initial eccentricity less thaneI, then the eccentricity asymptotically increases toeI. If γT = 0, then the value ofeI is determined by Eq. (96). In this case:eI = elim.Insertingelim into the functionW for the case 0< γT/γC < 1, we obtainW (elim) < 0.The statement follows from the equation

(1 + 3e2/2)(1− β)1/2

(a/aP )3/2(1− e2)3/2>

(1− β)1/2

(a/aP )3/2(1 − e2), (104)

which holds for alle ∈ [0,1). This means thateI must be smaller thanelim, since thefunctionW is a decreasing function of eccentricity. If we assume that eccentricity is greaterthaneI and less thanelim, thenX(e) > 0 andY (e) > 0. We have alsoW (e) = X(e)−Y (e)< 0, i.e.X(e) < Y (e). The value ofX increases faster than the value ofY when the valueof eccentricity decreases (see Eqs. 99 and 100). IfX andY approach to such values thatX ≈ Y , then the eccentricity approaches toeI. The value ofY is proportional toγT/γC .If γT/γC is greater, then the value ofX must increase more rapidly in order to reach theconditionX − Y ≈ 0. Thus,eI will be a decreasing function ofγT/γC. If γT/γC reachesthe valueγT/γC = 1, thenW (0) = 0. Thus,eI = 0. This means that the secular evolutionof eccentricity asymptotically decreases toeI = 0, whenγT/γC = 1, (since,lime→0〈de/dt〉= 0). ForγC . sin 5, we can define the angleεcrit for which eI = 0. We get

sin εcrit = γC =1 + η/Q′

pr

η/Q′pr

1u

√µ(1 − β)

a. (105)

If the value ofγT increases from 0 toγC , then the value ofeI decreases fromelim to 0. If 1< γT/γC < 3 for an exterior mean motion resonance, thenW (e) does not have root fore ∈[0,1), sinceW (0) < 0 andW is a decreasing function of eccentricity. Secular evolution ofeccentricity is always a decreasing function of time and the eccentricity non-asymptoticallydecreases to 0. IfγT/γC ≥ 3 for exterior mean motion resonance, thenW (0) < 0. ThefunctionW can be also an increasing function of eccentricity. But only for the eccentricityvalues determined by the inequality (see Eq. 101)

34

4 + e2

(1− e2)1/2<

γT

γC. (106)

Three possibilities exist:1. W (e) does not have a root fore ∈ [0,1),2. W (e) has only one rooteII for e ∈ [0,1),3. W (e) has two rootseIII andeIV for e ∈ [0,1).In the first case, the secular evolution of eccentricity is always a decreasing function of time.In the second case, we can write foreII

34

4 + e2II

(1 − e2II)1/2

=γT

γC, (107)

sinceeII is maximum of the functionW . If initial eccentricity is greater thaneII, then ec-centricity asymptotically decreases to the valueeII. If initial eccentricity is less thaneII,


then the value of eccentricity non-asymptotically decreases to 0. In the third case, we puteIII < eIV. If the initial eccentricity is greater thaneIV, then the eccentricity asymptoticallydecreases to the valueeIV. If the initial eccentricity lies betweeneIII andeIV, the eccen-tricity asymptotically increases to the valueeIV. Finally, if the initial eccentricity is smallerthan the valueeIII, then the eccentricity non-asymptotically decreases to 0.

As for the interior mean motion resonances, the situation is much simpler than for theexterior mean motion resonances. Eq. (102) yields for the interior resonances

W (0) = 1 − (p + q)/p(1− γT/γC) . (108)

If γT/γC < 1, thenW (0) < 0. Thus, the secular evolution of eccentricity is always adecreasing function of time. The eccentricity non-asymptotically decreases to 0. IfγT/γC

= 1, thenW (0) = 0. Thus,eV = 0 is the root ofW (e). Secular evolution of the eccentricityasymptotically decreases toeV = 0. For the valueγC . sin 5 we can define an angleεcrit

for which eV = 0. We can calculateεcrit for the interior resonances from the conditionsin εcrit = γC . If γT/γC > 1, thenW (0) > 0. In this case, at least one rooteV of W (e)exists. We will show thatW (e) has only one rooteV. If eccentricity fulfills inequality Eq.(106), thenW is an increasing function of eccentricity. If the following inequality

34

4 + e2

(1− e2)1/2>

γT

γC, (109)

is fulfilled, then the functionW is a decreasing function of eccentricity (see Eq. 101). SinceW (0) > 0 andlime→1 W = −∞, the functionW (e) has only one root. The inequalitiesX(e) < 0 andY (e) < 0 always hold for the case of interior resonances. If the initialeccentricity is smaller thaneV, then−X(e) < −Y (e). If inequality represented by Eq.(109) is fulfilled, then the function−X increases faster than the function−Y with anincreasing eccentricity (see Eqs. 99 and 100). This is necessary in order to reach theconditionX − Y ≈ 0. The value of−Y is proportional toγT/γC , and, thus,eV is anincreasing function ofγT/γC . If the initial eccentricity is greater than the valueeV, thenthe eccentricity asymptotically decreases to the valueeV. If the initial eccentricity is lessthan the valueeV, then the eccentricity asymptotically increases to the valueeV .

Secular evolutionof eccentricity forε < εcrit qualitativelydiffers from the caseε > εcrit

both for the exterior and interior mean motion resonances. (Theoretically, a newεcrit(new)> εcrit exists for exterior resonances, with qualitatively different behavior of secular eccen-tricity.) For the exterior resonances the secular evolutionof the eccentricity changes from anasymptotic behavior (approaching to the limiting value of the eccentricity) to the decreasingevolution. As for the interior resonances the secular evolution of eccentricity changes fromthe decreasing evolution to the asymptotic behavior (approaching to the limiting value ofeccentricity). If we use Eq. (82) and similar equation for the interior resonances (using theassumptionmP M), then we get

sin εcrit =1 + η/Q′

pr

η/Q′pr

√µ/aP

u(1 − β)1/3

(p

p + q

)1/3

, (110)

for the exterior resonances and

sin εcrit =1 + η/Q′

pr

η/Q′pr

√µ/aP

u(1 − β)1/3

(p + q

p

)1/3

, (111)


for the interior resonances.Table 1 presents values ofεcrit for β = 0.01, η = 1/3, Q′

pr = 1/2, 1 and 3/2, forseveral exterior and interior resonances with a planet of mass approximately equal to massof Neptune in a circular orbit of radiusaP = 30.058 AU.

Table 1. Values ofεcrit (in degrees) for various exterior and interior resonances witha planet of mass approximately equal to mass of Neptune in circular orbit of radius

aP = 30.058 AU. Particle properties are characterized byβ = 0.01,η = 1/3.

resonant εcrit εcrit εcrit

type Q′pr = 1/2 Q′

pr = 1 Q′pr = 3/2

2/1 1.539 2.463 3.3883/2 1.694 2.711 3.7294/3 1.762 2.820 3.8795/4 1.800 2.881 3.9636/5 1.825 2.921 4.0181/2 2.444 3.912 5.3832/3 2.220 3.554 4.8893/4 2.135 3.417 4.7004/5 2.089 3.344 4.6005/6 2.061 3.299 4.538

Figs. 6 and 7 depict secular evolution of the particle’s eccentricity in exterior meanmotion 2/1 resonance with a planet of mass approximately equal to mass of Neptune incircular orbit of radiusaP = 30.058 AU for the caseβ = 0.01 andη/Q′

pr = 2/3. Fig. 6holds forε = 0 and Fig. 7 holds forε = 2.5. If ε < εcrit = 1.539, then the evolutionof the eccentricity is similar to Fig. 6. If 4.621 > ε > 1.539, then the secular evolutionof eccentricity is similar to Fig. 7. The detailed numerical integrations of Eq. (77) areconsistent with Eq. (92) (forε = 0 see Fig. 1). Evolutions depicted in Fig. 6 and 7 arecalculated from numerical solution of Eq. (92).

5.5.2. Secular Evolution of Orbital Elements Near Resonances

Fig. 8 presents orbital evolution of a particle. The results are obtained by numerical inte-gration of Eq. (77) withβ = 0.01 forε = 2.5 andη/Q′

pr = 2/3. Secular evolution of thesemimajor axis is an increasing function of time before capture into the 20/9 resonance withNeptune. The same holds after ejection of the particle from the resonance. The cases char-acterized by〈da/dt〉 > 0 can be found from Eq. (64) for various combinations ofη/Q′

pr,β, a ande – this relation shows when〈da/dt〉 > 0 before the grain is captured into anexterior/interior resonance. Up to now, only nonspherical dust grains were captured whenthe secular change of semimajor axis was an increasing function of time near the zone ofthe resonance (Klackaet al. 2005a, 2005b, Klacka and Kocifaj 2006a, 2006b).

Let us deal with exterior mean motion orbital resonances. Secular evolution of an ec-centricity is a decreasing function of time (ε > εcrit = 1.486): the initial resonance valueeinitial = 0.3 is less than the limiting valueelim = 0.5154 for the caseε = γT = 0 (see


Figure 8. Orbital evolution of spherical dust particle withβ = 0.01 andη/Q′pr = 2/3

captured in the exterior mean motion orbital 20/9 resonance with a planet of mass approx-imately equal to mass of Neptune, semimajor axisaP = 30 AU and eccentricityeP = 0.Solar wind parameterε = 2.5.

Eq. 96) and〈de/dt〉 < 0. The numerical secular evolution of the eccentricity is consistentwith Eq. (92). In general, no limiting value of the eccentricity exists in the resonance. Thisresult holds not only for nonspherical grains, but also for spherical grains in the ellipticalrestricted three-body problem with the action of electromagnetic radiation of the central star(see Sec. 4.3 or Pastoret al. 2008). We have just shown that the discussed cases can occuralso for spherical dust grains, if a more realistic disturbing force – non-radial solar wind –is taken into account together with the circular restricted three-body problem. Also simpledisturbing force can generate non-asymptotic eccentricity behavior if elliptical restrictedthree-body problem is considered.

As for the shift of perihelion (secular evolution of the argument of perihelion),〈dω/dt〉> 0 and its behavior is not significantly influenced by the capture into a resonance. Nu-merical calculations yield〈dω/dt〉 > 0 and∂〈dω/dt〉res/∂ε < 0. This can be easily un-derstood in terms of the shift of perihelion given by Eq. (77) for the central acceleration−µ (1 − β)~eR/r2 when gravitational perturbation of the planet is neglected:

⟨dω

dt

⟩

NG

= − βη

Q′pr

µ

c

1a2√

1 − e2


Figure 9. Orbital evolution of spherical dust particle withβ = 0.01 andη/Q′pr = 2/3

captured in the interior mean motion orbital 15:17 resonance with a planet of mass approx-imately equal to mass of Neptune, semimajor axisaP = 30 AU and eccentricityeP = 0.Solar wind parameterε = 2.5.

×

γT

1 −√

1 − e2

e2−

√µ (1 − β)

p

12u

. (112)

Fig. 9 presents the orbital evolution of dust grain withβ = 0.01 forε = 2.5 andη/Q′pr

= 2/3. The secular evolution of the semimajor axis is an increasing function of time beforethe grain is captured into the interior mean motion orbital 15/17 resonance with Neptune.The valueεcrit for this resonance is 2.022, i.e. ε > εcrit and due to the results obtained inSec. 5.1, the eccentricity is an increasing function of time and asymptotically approachesthe limiting valueeV = 0.1242. This is consistent with numerical simulations. As for theshift of perihelion,〈dω/dt〉 > 0 before the capture into the resonance and〈dω/dt〉 is adiscontinuous function of time at the moment of capture – this is the difference betweenthe exterior and interior orbital resonances (compare with Fig. 8).〈dω/dt〉 > 0 before thecapture can be understood in terms of the shift of perihelion given by Eq. (77) for the centralacceleration−µ (1− β)~eR/r2 when planetary gravitational perturbation is neglected, seealso Eq. (112).


5.6. Summary

Orbital evolution of a spherical dust particle captured in a mean motion resonance with aplanet in circular or elliptical orbit was discussed in this subsection.

Let us assume that action of the P-R effect and radial solar wind are considered. Ec-centricity in the exterior mean motion resonance asymptotically approaches to a limitingvalue for the circular restricted three-body problem. If the non-radial component of solarwind velocity is considered and the angle between radial direction and velocity of the so-lar wind fulfills 0 < γT/γC < 1, then evolution of eccentricity is similar to the case ofradial solar wind. If 1≤ γT /γC < 3, then eccentricity can be only a decreasing functionof time for the exterior resonances. The behavior of particle’s eccentricity for the interiorresonances, in the circular restricted problem, is inverted to the behavior for the exteriorresonances. Eccentricity is always a decreasing function of time for the P-R effect and theradial solar wind, in the interior resonances. If the non-radial component of solar windvelocity is considered and 0< γT/γC < 1, then the evolution of eccentricity is similar tothe case of radial solar wind. If 1≤ γT/γC < 3, the eccentricity asymptotically approachesthe limiting value. If γT/γC ≥ 3, then eccentricity non-asymptotically decrease to 0 ormay asymptotically decrease or increase to a limiting value, for exterior resonances. IfγT/γC ≥ 3, then evolution of eccentricity has always an asymptotic behavior, for interiorresonances. The argument of perihelion of the particle in a mean motion resonance withcircular planetary orbit does not have such a ”simple” behavior as it holds for eccentricity.For a given resonance and a given initial values of semimajor axis, eccentricity and argu-ment of perihelion, it is possible to find various evolutions of the argument of perihelion.If we admit also non-zero eccentricity of the planet, the evolution of particle’s eccentricity(P-R effect and radial solar wind) may not show an asymptotic behavior in exterior meanmotion resonances. If the planetary eccentricity is small and the particle’s shift of perihelionis sufficiently fast, then oscillations arounde(t) given by Eq. (95) exist. This holds bothfor exterior and interior resonances. Moreover, the non-radial component of the solar windcan produce capture of spherical dust particles in the interior and exterior mean motionresonances also when the particle’s semimajor axis is an increasing function of time. Thisresult is qualitatively equivalent to the action of electromagnetic radiation on nonsphericalparticles Klackaet al. (2005a, 2005b). The conventional idea ”capture of spherical grainsinto a resonance is characterized by decrease of the semimajor axis and eccentricity outsidethe resonance” must be modified. It is sufficient to change nongravitational forces (e. g.,consideration non-radial solar wind velocity) acting on spherical dust particle and secularincrease of particle’s semimajor axis may exist before capture into the resonance.

6. Times of Spiralling for Dust Grains in theEdgeworth-Kuiper Belt

Let us consider dust particles with various initial orbital elements: semimajor axisain ∈(30 AU, 50 AU), eccentricitye < 0.5, uniformly distributed within the given intervals. Thevalues ofain correspond to the positions of the particles in the Edgeworth-Kuiper belt.We are interested in mean time of spiralling within the Edgeworth-Kuiper belt: what isthe average time for the particle’s stay in the intervala ∈ (30 AU, 50 AU)? The results


are shown in Tab. 2, where results for the following four cases are presented (gravity ofthe Sun is included in all of the cases): i) P-R effect+ radial solar wind, ii) P-R effect+ radial solar wind+ gravity of Neptune, iii) P-R effect+ real solar wind (also its non-radial velocity component is considered,γT = 0.05), iv) P-R effect+ real solar wind+gravity of Neptune. The planet Neptune was assumed to be moving in circular orbit andvarious initial positions of the particles with respect to the Neptune were considered in thetwo-dimensional problem.

It is easily seen (see Tab. 2) that mean times, for the case of ignoring Neptune, yield thefollowing results: mean times forβ = 0.01 are 10-times greater than the times forβ = 0.1for a given value ofQ′

pr. This is consistent with the analytical result presented by Eq. (71).The similar result holds when also non-radial solar wind is considered.

The case i) corresponds to the inspiralling toward the Sun and the case iii) holds for theoutspiralling from the Sun.

Mean times for the stay in the Edgeworth-Kuiper belt with Neptune are larger for thecases of radial solar wind and smaller for non-radial solar wind, than the cases when Nep-tune is not considered. The results for radial solar wind are easily understandable: theparticles can be captured into mean motion orbital resonances with Neptune and the timesof inspiralling toward the Sun have increased. The results of numerical calculations for non-radial solar wind seem to be unexpected. While non-radial solar wind generates spirallingoutward from the Sun, gravitation of the Neptune may significantly disturb this behaviourand particle can slowly spiral toward the Sun. This fact explains also the values presentedin Tab. 3. Tab. 3 confirms that gravity of the planet can increase the stay in the zone ofthe Edgeworth-Kuiper belt for the radial solar wind (the valuesτR+G/τR are greater than1), while the result for non-radial solar wind corresponds to the decrease of the particle’sstay in the Edgeworth-Kuiper belt (the valuesτNR+G/τNR are less than 1). As the valuesof Tab. 3 show, the results almost do not depend onQ′

pr for a given value ofβ.In reality, the solar wind effect causes decrease of particle’s mass. If one would take

into account also the decrease of the mass in accordance with Eq. (27), then one could takeits equivalent form yielding a decrease of the particle’s radiusdR/dt = − K/r2, whereK

(measured in cm yr−1 AU2) is a constant depending on the material properties and the otherquantities are given in the following units: [R] = cm, [t] = yr,[r] = AU (see also Eq. 73).Consideration of the decrease of the particle’s radius yields that the mean times presentedin Tab. 2 are prolonged in less than 2% even for the largest values ofK (4× 10−9 cm yr−1

AU2 for ice, see Dohnanyi 1978, Kapisinsky 1984, Leinert and Grun 1990); the decreaseof the radiusR is less than 5%.

Conventional approach is that radial solar wind is considered, when dealing with motionof dust particles in the Solar System. Tab. 2 shows, that more realistic case of non-radialsolar wind yields 10-times larger values of mean times than the radial solar wind offers,for simultaneous action of the P-R effect and solar wind effect atQ′

pr = 1 (the caseQ′pr

= 1/2 decreases the ratio to 2.3). However, the consideration of Neptune’s gravity yieldsmean times practically independent on the real velocity vector of the solar wind particulates:again,τNR+G / τR+G < 1 for Q′

pr = 1 andτNR+G / τR+G < 1 for Q′pr = 1/2, compare

also values in Tab. 3.Some of the results can be obtained almost in an analytical way. This can be done if the

P-R effect and radial solar wind effect are considered. It is sufficient to use Eqs. (71), (69)


Table 2. Mean times (years) of spiralling of dust particles within theEdgeworth-Kuiper belt: a ∈ (30 AU, 50 AU). Two values ofβ and Q′

pr are used. ThePoynting-Robertson effect, the effect of the solar wind (radial and non-radial) andgravity of the planet Neptune are considered. Mass of the particle does not change.

Forces β = 0.1 β = 0.01Q′

pr = 1 Q′pr = 1/2 Q′

pr = 1 Q′pr = 1/2

P-R + SW (R) 1.7E+06 1.3E+06 1.7E+07 1.3E+07P-R + SW (R)+G 6.4E+06 4.9E+06 3.1E+07 2.6E+07P-R + SW (NR) 1.7E+07 3.0E+06 1.7E+08 3.1E+07

P-R + SW (NR)+G 7.4E+06 1.1E+06 6.0E+07 8.9E+06

Table 3. Ratios of mean times of spiralling. The values are obtained from the datapresented in Tab. 2.

β = 0.1 β = 0.01Q′

pr = 1 Q′pr = 1/2 Q′

pr = 1 Q′pr = 1/2

τR+G/τR 3.8 3.6 1.9 2.0τNR+G/τNR 0.4 0.4 0.3 0.3

and (76).

7. Influence of the Neutral Interstellar Gas on the Motionof Dust Grains

The neutral interstellar gas penetrates into the heliosphere because of the relative motion ofthe Sun with respect to the interstellar medium. The gas affects motion of dust grains mainlyin the outer solar system. In the outer region of the heliosphere (> 20 AU) the neutral gasdensity becomes larger than the solar wind plasma density (Kausch and Fahr 1997). Inthis section, the numerical results of the equation of motion including the P-R effect, realsolar wind (its non-radial component is included) and the effect of neutral interstellar gas ispresented.

Equation of motion for a spherical dust grain under the influence of the neutral inter-stellar gas (IG) is (Scherer 2000):

(d~v

dt

)

IG

= − γHcD |~v − ~vH | (~v − ~vH) , (113)

where~vH is velocity of the neutral hydrogen atom,~v is velocity of the dust grain,cD is thedrag coefficient,γH is the collision parameter. For the collision parameter we can write

γH = nHmH

mA , (114)

wheremH is mass of the neutral hydrogen atom,nH is the concentration of interstellarhydrogen atoms,A = πR2 is the cross section of the spherical dust grain of radiusR and


massm. For the drag coefficient we can write

cD =ξ

M

[(1 +

12M2

)e−M2

√π

+ M

(1 +

1M2

− 14M4

)erf(M)

], (115)

with MachnumberM = |~v−~vH |/√

2kBTH/mH , (kB is Boltzmann constant andTH is thetemperature of interstellar medium),ξ is an adsorbtion or sticking factor (1≤ ξ ≤ 2), whichdescribes the relevant type of collision (i.e., specularξ = 1, diffuseξ = 1, or adsorbtionξ> 1), and,erf(M) is the error function.

The vector of the bulk velocity of the interstellar matter is∼ 25 km/s and it is oriented in90 degrees (in positive orientation) from the constellation Aries direction (Lallement 1996;Witte et al. 1996). The density of the neutral hydrogen atoms isnH = 0.05 cm−3 through-out the entire heliosphere (Fahr 1996; Frisch 1995). It is assumed that the temperature ofthe IG is∼ 8000 K (Lallement 1990) and the sound velocity for neutral hydrogen is thencH ≡

√2kBTH/mH ∼ 11.5 km/s.

7.1. Analytical Approach

Let us consider the following approximation: speed of a dust grain is much smaller than theinterstellar gas velocity in the stationary reference frame associated with the Sun (v vH ).In this case the drag coefficient reduces to a constantcD ≈ 2.6 withξ = 2. (Banaszkiewiczet al. 1994).

We can calculate the secular evolution of semimajor axisa, eccentricitye and argumentof perihelionω of the particle’s orbit under the nongravitational perturbation of interstellargas. Evolution of the osculating elements is given by Eqs. (60), i.e. central Keplerianacceleration is− µ(1 − β)~eR/r2. From the equation of motion (Eq. 113), Eqs. (61),relation~vH = vH [sin(ω + f) ~eR + cos(ω + f) ~eT ], and, using also the approximationv vH , we obtain radial and transversal components of perturbative acceleration

(aR)IG = − α vH2 − sin(ω + f)

+ ε [e sin f + e cosω sin(ω + f)+ sin(ω + f) cos(ω + f)] ,

(aT )IG = − α vH2 − cos(ω + f)

+ ε [1 + e cos f + e cos ω cos(ω + f)+ cos2(ω + f)

], (116)

where

α ≡ γH cD ,

α =2.4× 10−11 AU−1

R [m] ρ [kg/m3](117)

and

ε ≡ 1vH

√(1 − β)µ

p 1 ; (118)


R is radius of the particle andρ is mass density of the spherical particle. For the secularevolution of dust grain’s orbital elementsa, e, ω under the influence of the interstellar gaswe obtain

⟨da

dt

⟩

IG

= − α vH a

3 +

2e2

[√1 − e2 −

(1 − e2

2

)]cos(2ω)

,

⟨de

dt

⟩

IG

= − α vH

− 1

ε

32

cos ω

+1 − e2

e3

[√1 − e2 −

(1 − e2

2

)]cos(2ω)

,

⟨dω

dt

⟩

IG

= − α vH

1ε

1e

32

sinω

+1e4

[(1 − e2)3/2 −

(1 − 3

2e2 +

14

e4

)]sin(2ω)

. (119)

7.2. Numerical Results

In general, equation of motion used in this subsection is given by Eqs. (59) and (113):

d~v

dt= − (1 − β) µ

r2~eR − β

(1 +

η

Q′pr

)µ

r2

(2

vR

c~eR +

vT

c~eT

)

+ βη

Q′pr

µ

r2

− γT

vT

c~eR + γT

(u

c− vR

c

)~eT

+12

v2

uc~eR +

vR

c

~v

u

− γHcD |~v − ~vH | (~v − ~vH) . (120)

The numerical results for mean times for particle’s stay in the Edgeworth-Kuiper beltwithin the intervala ∈ (30 AU, 50 AU) are presented in Tab. 4. Initial values of orbitalelements of the particles are: semimajor axesain ∈ (30, 45) AU, eccentricitiesein ∈ (0,0.5). We consider (besides gravity of the Sun) the following cases: i) P-R effect + radialsolar wind, ii) P-R effect + radial solar wind + IG effect, iii) P-R effect + real solar wind, iv)P-R effect + real solar wind + IG effect. In Tab. 5 the ratios of the mean times of spirallingare presented.

The effect of neutral interstellar gas has some important consequences on the motion ofdust grains. Fig. 10 presents stable orbits for dust grains in the Edgeworth-Kuiper belt: theactions of nongravitational effects on the dust grain may be mutually compensated, mainlydue to the non-radial component of the solar wind velocity. Stable orbits are different forvariousQ′

pr (various radii or densities of dust grains - see Eq. 55). The stable orbitsindicate a possible existence of dust rings around the Sun. Corresponding evolutions foreccentricities and arguments of perihelia are depicted in Figs. 11 and 12. The influence ofplanet Neptune and trans-Neptunian objects (TNOs) is not considered in these numericalcalculations.

As for the orbital evolution of dust grains near the mean motion resonances with Nep-tune, the following result holds: if the effect of IG is taken into account, then there does not


Table 4. Mean times (years) of spiralling of dust particles within theEdgeworth-Kuiper belt: a ∈ (30 AU, 50 AU). Two values ofβ and Q′

pr are used. ThePoynting-Robertson effect, the effect of the solar wind (radial and non-radial) and theeffect of neural interstellar gas are considered. Mass of the particle does not change.

Forces β = 0.1 β = 0.01Q′

pr = 1 Q′pr = 1/2 Q′

pr = 1 Q′pr = 1/2

P-R + SW (R) 1.7E+06 1.3E+06 1.7E+07 1.3E+07P-R + SW (R)+IG 9.3E+05 6.3E+05 9.2E+06 6.2E+06P-R + SW (NR) 1.7E+07 3.0E+06 1.7E+08 3.1E+07

P-R + SW (NR)+IG 2.7E+06 4.3E+06 2.4E+07 3.4E+07

Table 5. Ratios of the mean times of spiralling within the Edgeworth-Kuiper belt.The values are obtained from the data presented in Tab. 4.

β = 0.1 β = 0.01Q′

pr = 1 Q′pr = 1/2 Q′

pr = 1 Q′pr = 1/2

τR+IG/τR 0.6 0.5 0.6 0.5τNR+IG/τNR 0.2 1.4 0.1 1.1

Figure 10. Evolution of semimajor axis of dust particle (β = 0.01) near the Edgeworth-Kuiper belt zone. Action of solar gravity, solar wind (γT = 0.05), neutral hydrogen gasand the P-R effect are considered. Initial eccentricity is close to zero. Results for severaloptical properties – various values ofQ′

pr – are depicted. Accelerations and decelerationsof the particle due to the nongravitational effects may be compensated and the particle mayremain in the Edgeworth-Kuiper belt.

exist any capture of the grains into an exterior mean motion resonance with Neptune fordiverging orbits (secular increase of semimajor axisa of the grains before capture). This isa different behavior from the case when only the P-R and real solar wind effects are consid-


Figure 11. Evolution of eccentricity of dust particle (β = 0.01) near the Edgeworth-Kuiperbelt zone. Action of solar gravity, solar wind (γT = 0.05), neutral hydrogen gas and theP-R effect are considered. Results for several optical properties – various values ofQ′

pr –are depicted. Corresponding evolutions for semimajor axes and arguments of perihelia aredepicted in Figs. 10 and 12.

Figure 12. Evolution of argument of perihelion of dust particle (β = 0.01) near theEdgeworth-Kuiper belt zone. Action of solar gravity, solar wind (γT = 0.05), neutralhydrogen gas and the P-R effect are considered. Results for several optical properties –various values ofQ′

pr – are depicted. Corresponding evolutions for semimajor axes andeccentricities are depicted in Figs. 10 and 11.

ered. As for the interior mean motion resonances with Neptune, the diverging orbits existalso for the case when all of the discussed nongravitational forces are taken into account.


7.3. Summary

On the basis of Eqs. (55), (64), (117) and (119) we can write for the comparison of theaction of interstellar gas and the P-R effect plus solar wind:

〈da/dt〉IG

〈da/dt〉P−R+SW

= 5.3× 10−4 (a [AU ])2

Q′pr × P

,

P = 1 +η

Q′pr

(1 −

γT u [km/s]√

a [AU ]30

), (121)

if terms of the orderO(e2) are neglected. If the secular semimajor axis does not change dueto the action of the solar gravity, solar wind, interstellar gas and the P-R effect, then the left-hand side of Eq. (121) should be equal to−1, approximately. Explanation follows from thefact that we require〈da/dt〉= 0, and, parallelly,〈da/dt〉 ≡ 〈da/dt〉IG + 〈da/dt〉P−R+SW .The exact result obtained from numerical solution of Eq. (120) is not equal to−1, since theapproximation defined by Eq. (118) is assumed in Eqs. (119). Comparison of the resultsobtained by Eq. (121) with the exact numerical calculations presented in Fig. 10 (see alsoFig. 11 –e2 are small) shows that Eq. (121) is consistent with Fig. 10 within 40 % accuracy.

As for the results presented in Tabs. 4 and 5, the most surprising results concern thevaluesτR+IG/τR andτNR+IG/τNR (see Tab. 5). While the values for the action of theradial solar wind (plus P-R effect) and interstellar gas are practically not sensitive to thevalues ofQ′

pr, this is not true for the action of non-radial solar wind (plus P-R effect) andinterstellar gas. We are not aware of any simple explanation of these numerical calculations.

8. Conclusion

Relativistically covariant equations of motion for arbitrarily shaped dust particle under theaction of solar wind and solar electromagnetic radiation are derived. Change of the parti-cle’s mass is an indespensable part of the space-time formulation of the equation of motionfor the action of the solar wind. If the particle of a spherical shape is considered, thenthe effect of electromagnetic radiation reduces to the Poynting-Robertson effect. Equationsfor the incoming and outgoing electromagnetic radiation are in physically correct forms, al-though not consistent with the conventionally presented statements (Poynting 1903, Robert-son 1937, Wyatt and Whipple 1950, Burnset al. 1979). The process of the relativisticcovariant derivations of equations of motion under the action of solar wind and solar elec-tromagnetic radiation for spherical dust particles exhibit several similar physical features.Also the final equations of motion for the radial solar wind and Poynting-Robertson effectscause qualitatively equal orbital evolutions of the interplanetary dust particles.

Orbital evolutions of interplanetary dust particles orbiting the Sun are calculated both inan analytical way (if it is possible) in terms of perturbation equations of celestial mechanics,and, also in a numerical way. As for the effect of the solar wind, the newest observationaldata on non-radial velocity of the wind (Brunoet al. 2003) are incorporated not only intothe relativistic equation of motion of the particle, but also into analytical and numericalcalculations on orbital evolutions of the particle. The non-radial solar wind velocity com-ponent enables:


i) A capture of spherical dust particle into a mean motion orbital resonance with planet Nep-tune for a diverging orbit of the particle (secular increase of semimajor axis of the particlebefore the capture into the resonance).ii) Qualitatively new behavior of secular eccentricity of the particle in the mean motionorbital resonance with Neptune, in comparison with the action of radial solar wind and thePoynting-Robertson effect.iii) Stabilization of the spherical interplanetary dust particle near the Edgeworth-Kuiperbelt, if a stream of interstellar hydrogen gas is taken into account.These results differ from a conventional idea that interplanetary dust particle spirals towardthe Sun, if solar electromagnetic radiation, solar wind, gravity of the Sun and a planet, and,interstellar hydrogen gas, are taken into account.

AcknowledgementsThe paper was supported by the Scientific Grant Agency VEGA (grant No. 1/3074/06).

References

[1] Banaszkiewicz M., Fahr H. J., Scherer K., 1994. Evolutionof dust particle orbits underthe influence of solar wind outflow asymmetries and the formation of the zodiacal dustcloud.Icarus 107, 358-374.

[2] Beauge C., Ferraz-Mello S., 1994. Capture in exterior mean-motion resonances dueto Poynting-Robertson drag.Icarus 110, 239-260.

[3] Bohren C. F., Huffman D. R., 1983.Absorption and Scattering of Light by SmallParticles John Wiley& Sons, Inc., New York.

[4] Brouwer D., Clemence G. M., 1961.Methods of Celestial Mechanics Academic Press,New York.

[5] Brownlee D. E., 1994. The ring around us.Nature 369, 706.

[6] Bruno R., Carbone V., Sorriso-Valvo L., Bavassano B.: 2003. Radial evolution of solarwind intermittency in the inner heliosphere.J. Geophys. Res. 108(A3), SSH8, arXiv:astro-ph/0303578.

[7] Burns J. A., Lamy P. L., Soter S., 1979. Radiation forces on small particles in theSolar System.Icarus 40, 1-48.

[8] Dermott S. F., Jayaraman S., Xu Y. L., Gustafson B. A. S., Liou J. C., 1994. A cir-cumsolar ring of asteroidal dust in resonant lock with the Earth.Nature 369, 719-723.

[9] Dermott S. F., Grogan K., Durda D. D., Jayaraman S., Kehoe T. J. J., Kortenkamp S. J.,Wyatt M. C., 2001. Orbital evolution of interplanetary dust. In:Interplanetary Dust,E. Grun, B. A. S. Gustafson, S. F. Dermott and H. Fechtig (eds.), Springer-Verlag,Berlin, pp. 569-639.


[10] Dohnanyi J. S., 1978. Particle dynamics. In:Cosmic Dust, J. A. M. McDonnell (ed.),Wiley-Interscience, Chichester, pp. 527-605.

[11] Einstein A., 1905. Zur Elektrodynamik der bewegter Korper.Annalen der Physik 17,891-920.

[12] Fahr H. J., 1996. The Interstellar Gas Flow Through the Heliospheric Interface Re-gion.Space Science Reviews 78, 199-212.

[13] Frisch P. C., 1995. Characteristics of Nearby Interstellar Matter.Space Science Re-views 72, 499-592.

[14] Grun E., 2007. Solar System dust. In:Encyclopedia of the Solar System , L.-A. Mc-Fadden, P. R., Weissmann and T. V. Johnson (eds.), Academic Press (Elsevier), SanDiego, 2nd ed., pp. 621-636.

[15] Grun E., Zook H. A., Fechtig H., Giese R. H., 1985. Collisional balance of the mete-oritic complex.Icarus 62 244-272.

[16] Grun E., Gustafson B., Mann I., Baguhl M., Morfill G. E., Staubach G., Taylor A.,Zook H. A., 1994. Interstellar dust in the heliosphere.Astron. Astrophys. 286, 915-925.

[17] Gustafson B. A. S., 1994. Physics of Zodiacal Dust.Annual Review of Earth andPlanetary Sciences 22, 553-595.

[18] Holmes E. K., Dermott S. F., Gustafson B.A. S., Grogan K., 2003. Resonant structurein the Kuiper disk: An asymmetric Plutino disk.Astrophys. J. 597, 1211-1236.

[19] van de Hulst H. C., 1981.Light Scattering by Small Particles Dover Publications, Inc.,New York, 470 pp. (originally published in 1957 by John Wiley & Sons, Inc., NewYork)

[20] Hundhausen A. J., 1972.Coronal Expansion and Solar Wind Springer-Verlag, Berlin.

[21] Jackson A. A., Zook H. A., 1989. A Solar System dust ring with the Earth as itsshepherd.Nature 337, 629-631.

[22] Kapisinsky I., 1984. Nongravitational effects affecting small meteoroids in interplan-etary space.Contr. Astron. Obs. Skalnate Pleso 12, 99-111.

[23] Kausch T., Fahr H. J., 1997. Interstellar gas filtration to the inner heliosphere underthe selfconsistent influence of a pick-up ion modulated termination shock.Astron.Astrophys. 325, 828-838.

[24] Kehoe T. J. J., Dermott S. F., Grogan K., 2002. Evolution of asteroidal dust particlesthrough resonance.Mem. S. A. It. 73, 684-687.

[25] Klacka J., 1994. Interplanetary dust particles and solar radiation.Earth, Moon, andPlanets 64, 125-132.


[26] Klacka J., 2004. Electromagnetic radiation and motion of a particle,Celestial Mech.and Dynam. Astron. 89, 1-61.

[27] Klacka J., 2008a. Mie, Einstein and the Poynting-Robertson effect. arXiv: astro-ph/0807.2795.

[28] Klacka J., 2008b. Electromagnetic radiation, motion of a particle and energy-massrelation. arXiv: astro-ph/0807.2915.

[29] Klacka J., Saniga M., 1993. Interplanetary dust particles and solar wind.Earth Moonand Planets 60, 23-29.

[30] Klacka J., Kocifaj M., Pastor P., 2005a. Motion of dust near exterior resonances withplanets.Journal of Physics: Conference Series 6, 126-131.

[31] Klacka J., Kocifaj M., Pastor P., 2005b. Effect of radiation on nonspherical particlesin resonances with large planets. In:8th Conference on Electromagnetic and LightScattering by Nonspherical Particles: Theory, Measurements and Applications , F.Moreno, J. J. Lopez-Moreno, O. Munoz and A. Molina (eds.), Instituto de Astrofisicade Granada, pp. 156-159.

[32] Klacka J., Kocifaj M., 2006a. Effect of electromagnetic radiation on dynamics of cos-mic dust particles. In:Space Science: New Research, Nick S. Maravell (ed.), NovaScience Publishers, Inc., pp. 245-285.

[33] Klacka J., Kocifaj M., 2006b. Effect of radiation on dust particles in orbital reso-nances.J. Quant. Spectrosc. Radiat. Transfer 100, 187-198.

[34] Klacka J., Kocifaj M., Pastor P., Petrzala J., 2007. Poynting-Robertson effect andperihelion motion,Astron. Astrophys. 464, 127-134.

[35] Klacka J., Komar L., Pastor P., Petrzala J., 2008. The non-radial component of thesolar wind and motion of dust near mean motion resonances with planets.Astron.Astrophys. (in press).

[36] Krauss O., Wurm G., 2004. Radiation pressure forces on individual micron-size dustparticles: a new experimental approach,J. Quant. Spectrosc. Radiat. Transfer 89, 179-189.

[37] Lallement R., 1990. Scattering of Solar UV on Local Neutral Gases. In:Physics ofthe Outer Heliosphere, COSPAR Colloquia Series, No. 1 , S. Grzedzielski and E. Page(eds.), Pergamon Press, London, pp. 49-60.

[38] Lallement R., 1996. Relations Between ISM Inside and Outside the Heliosphere.Space Science Reviews 78, 361-374.

[39] Leinert Ch., Grun E., 1990. Interplanetary dust. In:Physics of the Inner HeliosphereI, R. Schwen and E. Marsch (eds.), Spriger-Verlag, Berlin, pp. 207-275.

[40] Liou J.-Ch., Zook H. A., 1995. An asteroidal dust ring of micron-sized particlestrapped in the 1:1 mean motion resonance with Jupiter.Icarus 113, 403-414.


[41] Liou J.-Ch., Zook H. A., Jackson A. A., 1995. Radiation pressure, Poynting-Robertsondrag, and solar wind drag in the restricted three body problem.Icarus 116, 186-201.

[42] Liou J.-Ch., Zook H. A., 1997. Evolution of interplanetary dust particles in meanmotion resonances with planets.Icarus 128, 354-367.

[43] Liou J.-Ch., Zook H. A., Jackson A. A., 1999. Orbital Evolution of Retrograde In-terplanetary Dust Particles and Their Distribution in the Solar System.Icarus 141,13-28.

[44] Marzari F., Vanzani V., 1994. Dynamical evolution of interplanetary dust particles.Astron. Astrophys. 283, 275-286.

[45] Mie G., 1908. Beitrage zur Optik truber Medien speziell kolloidaler Metalosungen.Ann. Phys. 25, 377-445.

[46] Mishchenko M., 2001. Radiation force caused by scattering, absorption, and emissionof light by nonspherical particles.J. Quant. Spectrosc. Radiat. Transfer 70, 811-816.

[47] Mishchenko M., Travis L. D., Lacis A. A., 2002.Scattering, Absorption and Emissionof Light by Small Particles Cambridge University Press, Cambridge (UK), 445 pp.

[48] Pastor P., Klacka J., Komar L., 2008. Motion of dust in mean-motion resonances withplanets. arXiv: astro-ph/0807.1425.

[49] Poynting J. M., 1903. Radiation in the Solar System: its Effect on Temperature and itsPressure on Small Bodies.Philosophical Transactions of the Royal Society of LondonSeries A 202, 525-552.

[50] Reach W. T., Franz B. A., Welland J. L., Hauser M. G., Kelsall T. N., Wright E. L.,Rawley G., Stemwedel S. W., Splesman W. J., 1995. Observational confirmation of acircumsolar dust ring by the COBE satellite.Nature 374, 521-523.

[51] Robertson H. P., 1937. Dynamical effects of radiation in the Solar System.Mon. Not.R. Astron. Soc. 97, 423-438.

[52] Robertson H. P., Noonan T. W., 1968.Relativity and Cosmology Saunders, Philadel-phia, 456 pp.

[53] Scherer K., 2000. Drag forces on interplanetary dust grains induced by the interstellarneutral gas.Journal of Geophys. Research 105, A5, 10329.

[54] Sekanina Z., Hanner M. S., Jessberger E. K., Fomenkova M. N., 2001. Cometary dust.In: Interplanetary Dust, E. Grun, B. A. S. Gustafson, S. F. Dermott and H. Fechtig(eds.), Springer-Verlag, Berlin, pp. 95-161.

[55] Stix M., 2002.The Sun Springer-Verlag, Berlin.

[56] Sykes M. V., 2007. Infrared views of the Solar System from space. In:Encyclopediaof the Solar System, L.-A. McFadden, P. R. Weissmann and T. V. Johnson (eds.),Academic Press (Elsevier), San Diego, 2nd ed., pp. 681-694.


[57] Sidlichovsky M., Nesvorny D., 1994. Temporary capture of grains in exterior res-onances with Earth: Planar circular restricted three-body problem with Poynting-Robertson drag.Astron. Astrophys. 289, 972-982.

[58] Whipple F. L., 1955. A comet model III. The zodiacal light.Astrophys. J. 121, 750-770.

[59] Wisdom J., 1980. The resonance overlap criterion and the onset of stochastic behaviorin the restricted three-body problem.Astron. J. 85, 1122-1133.

[60] Witte M., Banaszkiewicz M., Rosenbauer H., 1996. Recent results on the parametersof the interstellar helium from the ULYSSES/GAS experiment.Space Science Reviews78, 289-296.

[61] Wyatt S. P., Whipple F. L., 1950. The Poynting-Robertson effect on meteor orbits.Astrophys. J. 111, 558-565.



Chapter 7

A ROLE OF THE SOLAR WIND IN DYNAMICS

OF INTERSTELLAR DUST IN THE SOLAR SYSTEM

M. Kocifaj1∗and J. Klacka2†1Department of Interplanetary Matter, Astronomical Institute

Slovak Academy of Sciences, Dubravska cesta 9, 845 04 BratislavaSlovak Republic

2Department of Astronomy, Physics of the Earth, and MeteorologyFaculty of Mathematics, Physics and Informatics

Comenius University, Mlynska dolina, 842 48 BratislavaSlovak Republic

Abstract

Interstellar dust grains have been detected by the dust detectors onboard theUlysses andGalileo spacecrafts. Motion of the interstellar dust particles in the So-lar System is driven by gravitational and nongravitational forces. As for gravity, theaction of the Sun is the dominant gravitational effect. Nongravitational forces are rep-resented by solar electromagnetic radiation force, similar effect of the solar wind, and,Lorentz force for submicrometer-sized dust grains. Lorentz force originates from theaction of interplanetary magnetic field on electrically charged grains and solar windvelocity plays a crucial role in this nongravitational force.

Keywords: interstellar dust particles, electromagnetic radiation, Poynting-Robertson ef-fect, solar wind, interplanetary magnetic field, Lorentz force

1. Introduction

Interstellar dust grains have been detected by the dust detector onboard theUlysses space-craft (Grunet al. 1993, Baguhlet al. 1995). The interstellar dust particles (IsDPs) enterthe Solar System with a speed of aboutv∞ = 26 km/s (Landgrafet al. 1999) and theyare arriving from direction ofλecl = 259 (heliocentric ecliptic longitude) andβecl = + 8

∗E-mail address: [email protected]†E-mail address: [email protected]

276 Kocifaj and Klacka

(heliocentric ecliptic latitude) (Landgrafet al. 2000). Masses of IsDPs detected byUlyssesand Galileo spacecrafts range from 10−18 kg to 10−13 kg (Sykeset al. 2004). Duringtheir motion in the Solar System, IsDPs are moving under the action of gravitational andnongravitational forces. The action of the Sun is the most important gravitational force.As for nongravitational forces, the effect of solar electromagnetic radiation influences themotion of IsDPs: the papers by Jackson (2001) and Kocifaj and Klacka (2003) discuss thecondition under which the IsDPs can be captured in the Solar System. While the paperby Jackson considers only spherical dust particles, the newer paper takes into account thatinterstellar dust particles are arbitrarily shaped, they are not spherical but rather have anelongated structure (Wurm and Schnaiter 2002). Bearing in mind that IsDPs are mainlysmaller than 1 micron, the electrical charge of the particles cannot be ignored and the ef-fect of interplanetary magnetic field plays an important role (e. g., Dermottet al. 2001).The orbital evolution of IsDPs in the Solar System, under the action of the gravity of theSun, solar electromagnetic radiation and Lorentz force due to the effect of interplanetarymagnetic field, was investigated by Kocifaj and Klacka (2004).

The effect of solar wind enters in two ways into the equation of motion of dust particleevolving in the Solar System. The first case is the effect similar to the Poynting-Robertsoneffect (Poynting 1903, Robertson 1937, Klacka 2004, 2008a, 2008b), when the solar windpartially decelarates the motion of the particle orbiting the Sun (the pressure generatedby the solar wind is in three orders of magnitude smaller than the solar electromagneticradiation pressure; see, e. g., Dohnanyi 1978). The second case is the effect of Lorentzforce, since the relevant velocity vector in the Lorentz force is given by the relative velocityof the particle with respect to the velocity of the solar wind. The effect of the solar wind isphysically justified in heliosphere. We will consider its effect on evolution of IsDPs if theirheliocentric distances are smaller than 150 AU (Opheret al. 2004).

2. Electrically Neutral Spherical Particles

The most simple case in treating the motion of IsDPs takes into account spherical dust grainsentering the Solar System with the speedv∞. The equation of motion of the spherical grainwith respect to the Sun is

d~v

dt= − GM

r3~r + β

GMr2

(1 − ~v · ~eR

c

)~eR − ~v

c

,

β = 5.76× 10−4Q′

pr

R[m] %[kg/m3], (1)

where~v is the heliocentric velocity of the grain,~r is its heliocentric position,~r = r ~eR, G isthe gravitational constant,M is mass of the Sun,c is the speed of light,R is the radius ofthe particle,% is mass density andQ′

pr is dimensionless efficiency factor of electromagneticradiation pressure (Mie 1908, van de Hulst 1981, Bohren and Huffman 1983) averaged overthe solar spectrum as follows

Q′pr =

∫∞0 I(λ) Q′

pr(λ) dλ∫∞0 I(λ) dλ

, (2)

Solar Wind and Dynamics of Dust Particles 277

whereI(λ) is the flux of monochromatic (λ is the wavelength) radiative energy. The firstpart of the acceleration on the right-hand side of Eq. (1) is the gravitational acceleration ofthe Sun, the second term is the P-R effect. If the gravity of the Sun would exist alone, thenthe interstellar dust particle would move on hyperbolic orbit and no capture in the SolarSystem could exist. However, there is an important part in Eq. (1): the term proportionalto − ~v/c enables capture of interstellar dust particles in the Solar System (Jackson 2001,Kocifaj and Klacka 2003).

It is easy to include also the effect of the solar wind, into Eq. (1). At first, the solarwind causes also deceleration of dust particle, in the form similar to the P-R effect. Thisterm can be easily added to the electromagnetic radiation force. The simultaneous actionof the solar electromagnetic and corpuscular (solar wind) radiation can be obtained by agentle substitutionβ → β (1 + η/Q′

pr), whereβ is the ratio between the radial componentof the electromagnetic radiation pressure force and the gravitational force of the Sun,η

.=1/3 (Dohnanyi 1978, Gustafson 1994). The equation of motion, including the effect of thesolar wind, for an electrically neutral spherical dust particle, is

d~v

dt= − GM (1 − β)

r3~r

− β

(1 +

η

Q′pr

)GM

r2

(~v · ~eR

c~eR +

~v

c

),

β = 5.76× 10−4Q′

pr

R[m] %[kg/m3],

η =13

. (3)

Eq. (3) yields acceleration of the spherical dust particle under the action of solar grav-ity, the P-R effect and the solar corpuscular effect, i.e., the effect of the solar wind in theconventional approach when the radial component of solar wind is considered.

2.1. Numerical Results

This section summarizes the most relevant results on orbital evolution of IsDPs. The equa-tion of motion of an interstellar dust particle is given by Eq. (3). The initial conditionsfor it are given for the heliocentric position vector~r0 and heliocentric velocity vector~v∞,|~v∞| = 26 km/s. The heliocentric radius vector~r0 is of effectively infinite radial heliocen-tric distance and the particle is moving at velocity~v∞ along a line that misses the centerof the Sun by a perpendicular distanceb. The quantityb is the impact parameter. As forthe material properties of the IsDPs, our calculations are limited to magnesium-rich silicateparticles as these could be representative for interstellar dust grains (Dorschneret al. 1995)and the mass density is% = 2.5 g/cm3. Particles of various radii are taken into account. Theimportant values of dimensionless efficiency factor for radiation pressure, averaged oversolar spectrum (see Eq. 2), are calculated from Mie’s solution of Maxwell’s equations (Mie2008, van de Hulst 1981, Bohren and Huffman 1983) and the results are presented in Fig.1.

As it follows from Eq. (3), the motion of an interplanetary dust particle is planar. Theplane is defined by its normal vector and this can be represented by angular momentum


Figure 1. Values of dimensionless efficiency factor for radiation pressure (averaged oversolar spectrum) as a function of radius of an interplanetary dust particle. The compositionof the particle corresponds to magnesium-rich silicate.

vector ~H = ~r0 × ~v∞, | ~H| = b |~v∞|. If the impact parameterb is less than a minimum valuebmin, then the particle hits the Sun. If the value ofb is greater than a valuebmax, then onlyhyperbolic motion of the particle exists. The valueb ∈ (bmin, bmax) corresponds to the casewhen the particle is orbiting the Sun, i. e., the particle is captured in the Solar System. Thiscase can really occur, as it is shown on Fig. 2 (moreover, such capture exists also for theparticle of radiusR = 0.1µm: b ∈ (8.1, 8.9) solar radii for the pure electromagnetic caseandb ∈ (8.1, 11.0) solar radii for the case when also solar wind is taken into account).

Fig. 2 shows that the IsDPs of radii between 0.3µm and 1.0µm can be captured inthe Solar System and it also documents the corresponding interval of impact parameter forwhich the capture exists:bmin < b < bmax. The dotted area denotes the pure electro-magnetic case, while the larger area corresponds to the more realistic case, when also theeffect of solar wind is taken into account. The pure electromagnetic case yields that onlyIsDPs of radii 0.3µm to 0.6µm can be captured by the Sun, but consideration of the solarwind yields that the IsDPs of radii 0.3µm to 1.0µm can be captured. As for the parti-cles of radii 0.4µm (the peak in size distribution of the detected particles on Ulysses andGalileo), the probability of the capture is 1.6-times larger for the solar wind case than forthe pure electromagnetic case. This follows from the ratio of ring areas: ([bmax(s.w.)]2

− [bmin(s.w.)]2)/([bmax(elmg)]2 − [bmin(elmg)]2) .= (18.52 − 14.12)/(17.02 − 14.12) .=1.6. Fig. 2 generalizes the results of Jackson (2001) and Kocifaj and Klacka (2003).

The capture of an interstellar dust particle by the Sun, the P-R effect and the effectof radial solar wind is depicted in Fig. 3. Fig. 3 shows orbital evolution of the particleincluding the first orbit around the Sun both for the pure electromagnetic case and the casewith solar wind. The velocity term− ~v/c present in Eq. (3) causes gradual spiralling of theparticle toward the Sun. Fig. 3 shows that the particle can move near the Sun for a shorttime interval. The length of this interval when particle’s heliocentric distance is smaller than3 solar radii (the area where the particle evaporates due to solar electromagnetic radiation)is presented in Fig. 4. There is practically no difference between the casesη = 0 andη =


Figure 2. Values of impact parameters (measured in solar radii) when an interstellar dustparticle is captured in the Solar System and the particle revolves the Sun. The smaller/dottedarea holds for the pure electromagnetic case (plus the gravity of the Sun):η = 0. The largearea holds for the case when also solar wind effect is considered:η = 1/3. Inclusionof the solar wind yields not only higher probability of the capture for particles of a givenradius, but also larger particles can be captured and move around the Sun than it is in pureelectromagnetic case.

Figure 3. Orbital evolution of an interplanetary dust particle (radius 0.4µm), captured inthe Solar System and orbiting the Sun. The pure electromagnetic case (plus gravity of theSun) and the case when also solar wind is taken into account, are depicted. The stay of theparticle in the evaporation zone requires 5.07 hours (0.0343 % of the total orbital period)for the electromagnetic case (η = 0), while it is 5.08 hours (0.0919 % of the total orbitalperiod) for the case when solar wind is also considered (η = 1/3). Real scale is depictedand given by the value of impact parameterb = 15RS (solar radii).


1/3 for particle radii 0.3µm - 0.6µm. The particles with radiiR > 0.6µm will revolve theSun only whenη = 1/3. The minimal heliocentric distances for the case of the capture inthe Solar System are depicted in Fig. 5: the difference between the pure electromagneticcase and inclusion of the solar wind is evident.

0.2 0.4 0.6 0.8 1particle radius R [µm]

2

4

6

8

10

time

spentin

eva

pora

tion

zone

[h]

η=0, η=1/3

Figure 4. Time interval which an interstellar dust particle captured in the Solar Systemorbits the Sun in its vicinity, in the evaporation zone. The time interval is given in hours.

Figure 5. Minimal heliocentric distance of an interstellar dust particle captured in the SolarSystem, corresponding to the first circulation around the Sun. The distances are smaller thanthe evaporation heliocentric distance 3 solar radii. The large polygonal domain correspondsto the caseη = 1/3.

2.2. Comparison of Numbers of IsDPs Orbiting the Sun

We have already found that the probability of the capture of IsDPs of radii 0.4µm is 1.6-times larger for the more realistic solar wind (SW) case than for the pure electromagnetic(ELMG) case (see also Fig. 2). Let us ignore the motion in the evaporation zone. The SW


case is characterized by smaller orbital periodsT and semimajor axesa than the ELMGcase:a(SW )/a(ELMG) = [T (SW )/T (ELMG)]κ .= (3.43/9.19)κ, according to Fig. 3.The value ofκ equals to 2/3 for the Keplerian motion. However, Fig. 3 shows that theSun is not situated in foci of the ellipses (approximation of the trajectory) and the ratio ofsemimajor axes is, approximately,a(SW )/a(ELMG) .= 1.78. Thus, Fig. 3 suggests thatκ = 0.59. Moreover, according to Eqs. (1) and (3), the rate of inspiralling toward the Sunis higher for the SW case than for the ELMG case. The ratio of the times of inspiralllingis τ(SW )/τ(ELMG) .= [a(SW )/a(ELMG)]2 / (1 + η/Q′

pr). Substituting from theratio a(SW )/a(ELMG), we obtainτ(SW )/τ(ELMG) .= [T (SW )/T (ELMG)]2κ / (1+ η/Q′

pr). The ratio of the number of IsDPs orbiting the Sun is 1.6× τ(SW )/τ(ELMG).= 0.3 for the Keplerian motion and 0.4 for the more realistic case corresponding to Fig. 3.In these calculations the valuesT (SW )/T (ELMG)= 3.43/9.19,η = 1/3 andQ′

pr = 1.14for the particle of radius 0.4µm were used.

When solar wind is considered, the probability of the capture of IsDPs is greater thanin the pure electromagnetic case (1.6-times for particles of radii 0.4µm). But the numberof particles orbiting the Sun is 3-times smaller for the solar wind case than for the pureelectromagnetic case. These results correspond to the situation when the motion in theevaporation zone is ignored.

3. Electrically Neutral Arbitrarily Shaped Particles

If the particle is not spherical, then one has to use a more general form of the interactionbetween dust particle and the incident electromagnetic radiation. The acceleration of theparticle with respect to the Sun, including solar gravity and solar wind, reads

d~v

dt= − GM (1 − β)

r3~r − β

(1 +

η

Q′pr

)GM

r2

(~v · ~eR

c~eR +

~v

c

)

+GM

r2

3∑

j=2

βj

[(1 − 2

~v · ~eR

c+

~v · ~ej

c

)~ej − ~v

c

],

β = 7.61× 10−4 C′pr[m2]

m[kg],

βj = 7.61× 10−4 C′pr,j [m2]m[kg]

, j = 2, 3 ,

η =13

, (4)

where also nonradial components of radiation pressure are considered and thermal emissionforce is neglected (Klacka 2004, 2008b). In agreement with Eq. (2) the spectrally averagedcross sections of radiation pressureC ′

pr, C′pr,1, C ′

pr,2 are obtained as weighted integral


quantities

C ′pr =

∫∞0 I(λ) C ′

pr(λ) dλ∫∞0 I(λ) dλ

,

C′pr,j =

∫∞0 I(λ) C ′

pr,j(λ) dλ∫∞0 I(λ) dλ

, j = 1, 2 , (5)

whereI(λ) is the flux of monochromatic radiation energy. Neckel’s and Labs’s (1981) datacan be taken into account when adequately accurate values ofI(λ) are required, especiallyin the spectral region 0.2µm≤ λ ≤ 0.6µm. The analytical functionAλ−% exp

−sλ−t

is

applicable to model the rest of theI(λ) curve in near-IR. Here the coefficientsA, %, s, andt are published in Kastrov (1979). The symbolm used in Eq. (5) denotes the mass of theparticle. Ifβ2 ≡ β3 ≡ 0, then Eq. (4) reduces to Eq. (3), i.e., the effect of electromagneticradiation reduces to the P-R effect.

In practically important cases it is necessary to evaluate cross sections for rapidly ro-tating particles. One has to take into account that orientation of the particle’s rotationalaxis is practically constant in space, during the particle’s motion (Krauss and Wurm 2004,Krauss 2005) and any wavelength-dependent cross sections for radiation pressure need tobe obtained from integral

〈 C′pr,i(λ) 〉 =

∫ Φmax

ΦmindΦ∫ θmin

θminsin θ dθ

∫ Ψmin

ΨminCpr,i(λ, Φ, θ, Ψ) dΨ

∫ Φmax

ΦmindΦ∫ θmin

θminsin θ dθ

∫ Ψmin

ΨmindΨ

, (6)

where Euler angles (Φ, θ, andΨ) characterize the orientation of the particle in respect tothe laboratory reference frame (Draine and Flatau 2004).

In respect to a nature of physical processes participating in formation of dust particles,the spherical or spheroidal obstacles almost never occur in the space. Thus, an approxi-mate formula forCpr,i(λ, Φ, θ, Ψ) (e.g. Mie- or Rayleigh-based model) can scarcely beemployed. The optical properties of homogeneous and compact particles may be efficientlydetermined by T-matrix method (Mishchenkoet al. 2002) which follows the Huygens prin-ciple. T-matrix approach decomposes the electromagnetic field on a basis of functionsadapted to the more-complex geometry of the scatterer. Once the T-matrix is determined,the numerical solution of electromagnetic scattering problem is straightforward and veryrapid because a change of direction of incidence and scattering and/or change of polariza-tion state of the incident field do not require the repetition of the entire set of calculations.However, T-matrix is limited in arbitrariness of the particle shape and composition. Thereare really great problems with coding the T-matrix for porous, inhomogeneous or verycomplex aggregates. To overcome these problems some kind of volume integral equationmethod can be adopted. One of the world-wide known techniques is so called Discretedipole approximation (DDA; Purcell and Pennypacker 1973, Draine 1998) which is appli-cable to various geometries and material configurations (Wriedt and Comberg 1998). Theprinciples of DDA are quite easy: any continuum target is replaced by an array of pointdipoles (Purcell and Pennypacker 1973) and the scattering is then solved for this dipolearray (Draine and Goodman 1993). A profit derived from automatic satisfaction of radi-ation condition is that arbitrarily shaped and, also, inhomogeneous particle can be used


for calculations. But the method is counterbalanced by a set of disadvantages. In particu-lar, extremely large number of dipoles is needed to guarantee the satisfactory accuracy ofscattering matrix elements. Thus, the DDA is time-consuming and very MEM and CPUintensive tool. In addition, the entire set of calculations needs to be repeated for each newgeometrical position or polarization state of the incident beam. In spite of these facts theattractiveness, publicity and simplicity of the physical idea of the DDA makes this toolwidely applied in solving many light scattering problems.

Whereas the interstellar grains are typically irregularly shaped and composite aggre-gates, there is no many alternatives for modeling the light scattering processes for suchobstacles. The DDA method appears to be one of the best choices. To accelerate the solu-tion of Eq. (4), it is convenient to precalculate the optical properties of a particle and keepobtained optical data in local database. Specifying the initial position and velocity vectorsof the particle, the differential equation Eq (4) can be solved (e. g., by the Runge-Kutta’smethod of the fourth order with adaptive step-size), i.e., new position and velocity vectorsof the particle can be determined. Dealing with the probability of the capture of the IsDPs,the impact parameterb, position angleα and orientation of the particle rotation axis need tobe specified (see Fig. 6). The capture probability for the particle depends on these param-eters. Thus, the situation for irregularly shaped dust particle is more complicated than forthe spherical interstellar dust grains treated in the previous section.

Figure 6. The scheme documents an interaction of interstellar dust particle with the SolarSystem (according to Kocifaj and Klacka, 2003). The initial position of the particle in duststream is deffined by the values of impact parameterb and position angleα. The orientationof the particle rotation axis with respect to the incident solar radiation corresponds to theanglesθ andφ.

The total massM(R) of the captured IsDPs with radiusR is proportional to the captureareaD(R, θ, φ)

M(R) ∼ N(R) m(R)∫ π

θ=0

∫ 2π

φ=0D(R, θ, φ) sin θ dθ dφ (7)

wherem(R) is a mass of single particle with radiusR, andN(R) is the number of inter-stellar particles crossing the unit area in a unit time. The anglesθ andφ characterize the


0 0.2 0.4 0.6 0.8 1

particle radius [µm]

0

0.2

0.4

0.6

0.8

1

rela

tive

mass

ofsu

rviv

ed

dust

[-]

Figure 7. Density function for the mass of non-spherical electrically neutral magnesium-rich silicate particles captured in the Solar System (η = 0).

orientation of the particle’s rotation axis in respect to the direction of incidence of solarelectromagnetic radiation (see Fig. 6). The capture areaD(R, θ, φ) is defined unambigu-ously as follows: all particles with radiusR intersecting this area are captured in the SolarSystem. Using Eq. (7) we calculated the normalized mass of captured magnesium-richparticles of the shape identical to cosmic dust grain U2015 B10 (Kocifajet al. 1999). Theaspect ratio of the particle U2015 B10 (archived in NASA catalogue; Clantonet al. 1984)coincides very well with typical aspect ratios obtained from mid-infrared spectropolarime-try (Hildebrand and Dragovan 1995). The results of numerical runs presented in Fig. 7document that non-spherical particles with effective radius 0.4µm are the most preferrablycaptured IsDPs in the Solar System if the solar wind is not taken into account (i.e.,η = 0).These results are, however, relevant only for electrically neutral particles. The incorpora-tion of the electric charge is important for generalization of the obtained results. This kindof investigation is presented in the following section.

4. Electrically Charged Arbitrarily Shaped Particles

If dust particle is smaller than 1 micron, and arbitrarily shaped, then one has to take intoaccount also the effect of Lorentz force, since the interplanetary magnetic field plays animportant role in motion of the particle. One has to add Lorentz force to Eq. (4). Theacceleration of the particle with respect to the Sun, including solar gravity, solar wind and


Lorentz force, is

d~v

dt= − GM (1 − β)

r3~r − β

(1 +

η

Q′pr

)GM

r2

(~v · ~eR

c~eR +

~v

c

)

+GM

r2

3∑

j=2

βj

[(1 − 2

~v · ~eR

c+

~v · ~ej

c

)~ej − ~v

c

]+

q

m(~v − ~u) × ~B ,

β = 7.61× 10−4 C′pr [m2]

m[kg],

βj = 7.61× 10−4 C′pr,j [m2]m[kg]

, j = 2, 3 ,

η =13

, (8)

~u = u ~eR is velocity of the solar wind (conventionally, the valueu = 400 km/s is used whendealing with motion of dust particles in the Solar System, e. g., Dohnanyi 1978, Gustafson1994) and the electric charge of the particle is given by relationq = 4 π ε0 U Reff , whereε0 is the permittivity of the vacuum,U is surface potential of the particle (Kimura and Mann1998) with effective radiusReff (volume of the particle equals volume of the sphere of theeffective radius). The magnetic field~B is (Grunet al. 1994):

~B = BR ~eR + BT ~eT ,

BR = BR0

(r0

r

)2cos (π × t[years]/11 + ϕ0) ,

BT = BT0r0

rcosϑ cos (π × t[years]/11 + ϕ0) ,

BR0 = BT0 = 3nT , r0 = 1AU , (9)

~eT = ~eA × ~eR,~eA defines magnetic axis of the Sun,ϑ is the heliographic latitude and differ-ent polarity of the magnetic field for northern and southern hemispheres is also considered.The phase angle of magnetic fieldϕ0 = 0 can be considered.

To recognize the influence of solar wind on capture probability of electrically chargeddust particles we performed the calculations equivalent to those discussed in Fig. 7. Theactual results are presented in Fig. 8 for two main solar wind components (Zirker, 1981;Hanslmeier, 2002), i.e. for slow (u = 400 km/s) and fast (u= 800 km/s) solar winds (butη = 0). Detail analysis shows that capture areaD(R, θ, φ) found in the case of fast solarwind is approximately two times larger than the corresponding capture area correspondingto the slow solar wind component. In contrary to this fact the mass of the surviving chargeddust particles for the fast solar wind is two times smaller than that for the slow solar wind– as it is documented in Fig. 8. One of extremely interesting findings of our numericalsimulations is that particles with radii 0.3µm – 0.6µm are unambiguosly captured in theSolar System, independent of whether they are charged or electrically neutral (compareFigs. 7 and 8). Such result shows sizes of particles contributing to the dust cloud in theSolar System. These theoretical resuls are consistent with experimental data which indicatethat characteristic radius of interstellar dust particles moving in Solar System is about 0.3 -0.4µm (Grunet al. 1997).


Figure 8. Density function for the mass of non-spherical charged magnesium-rich silicateparticles captured in the Solar System (according to Kocifaj and Klacka, 2004). The dashedcurve corresponds to slow solar wind component (400km s−1), the solid curve to fast solarwind component (800km s−1).

5. Conclusion

The effect of solar wind causes decrease (in 60 % – 70 %) of concentration of sphericalIsDPs orbiting the Sun in comparison with the action of the Poynting-Robertson effect.This holds for particles representing the most frequent IsDPs entering the Solar System(radii about 0.4µm). However, the solar wind also enriches the amount of spherical dustgrains orbiting the Sun: IsDPs of radii 0.6µm – 1.0µm can revolve around the Sun thanksto the effect of the solar wind, the pure P-R effect cannot generate such kind of behavior.In any case, spherical IsDPs can revolve around the Sun not far from the evaporation zone(not more than several tens of solar radii from the Sun).

As for non-spherical IsDPs rapidly rotating around fixed orientations of their rotationalaxes, the particles can be captured in the Solar System and orbit the Sun also in regionsfar from the evaporation zone of the Sun. The effect of solar wind corresponding toη= 1/3 in Eqs. (4) and (8) plays the less significant role in comparison with the effect ofsolar electromagnetic radiation, the greater is the aspect ratio of the non-spherical IsDPs(aspect ratio of a particle is defined as the ratio between the maximal and minimal size ofthe particle). If the aspect ratio is 1.4 or greater, then the effect of the solar wind is at leastin one order of magnitude less important that the effect of the electromagnetic radiation:the solar wind effect defined by the valueη = 1/3 in Eqs. (4) and (8) is negligible in secularevolution of orbital elements. However, the solar wind effect is important in equation ofmotion for IsDPs in the form of the Lorentz force. The capture of the IsDPs orbiting the Sunis most effective for dust particles of effective radii about 0.4µm, which also corresponds


to the peak of size distribution of IsDPs entering the Solar System.

Acknowledgement

This work has been supported by the Scientific Grant Agency VEGA (grant No. 2/0016/09)and by the Slovak Academy of Sciences (grant No. 350/OMS/Fun/07 - DAAD project Nr.D/07/01266).

References

[1] Baguhl M., Grun E., Hamilton D., Linkert G., Riemann R., Staubach P., 1995. Theflux of interstellar dust observed by Ulysses and Galileo.Space Sci. Rev. 72, 471-476.

[2] Bohren C. F., Huffman D. R., 1983. Absorption and Scattering of Light by SmallParticles, John Wiley& Sons, Inc., New York.

[3] Clanton V. S., Gooding J. L., McKay D. S., Robinson G. A., Warren J. L., Watts L. A.(Eds.), 1984. Picture In: Cosmic Dust Catalog (Particles from collection ¿ag U2015),Vol. 5/1 10. NASA Johnson Space Center, Houston, TX.

[4] Dermott S. F., Grogan K., Durda D. D., Jayaraman S., Kehoe T. J. J., Kortenkamp S. J.,Wyatt M. C., 2001. Orbital evolution of interplanetary dust. In: Interplanetary Dust.E. Grun, B. A. S. Gustafson, S. F. Dermott and H. Fechtig (eds.), Springer-Verlag,Berlin, 569-639.

[5] Dohnanyi J. S., 1978. Particle dynamics. In: Cosmic Dust, J. A. M. McDonnell (Ed.),Wiley-Interscience, Chichester, 527-605.

[6] Dorschner J., Begemann B., Henning Th., Jager C., Mutschke H., 1995. Steps towardinterstellar silicate mineralogy. II. Study of Mg-Fe-silicate glasses of variable compo-sition.Astron. Astrophys. 300, 503-520.

[7] Draine B. T., Flatau P. J., 2004. User Guide for the Discrete Dipole ApproximationCode DDSCAT.6.1. http://arxiv.org/abs/astro-ph/0409262

[8] Draine B. T., 1988. The discrete-dipole approximation and its application to interstel-lar graphite grains.Astrophys. J. 333, 848-872.

[9] Draine B. T., Goodman J., 1993. Beyond Clausius-Mossotti: wave propagation ona polarizable point lattice and the discrete dipole approximation.Astrophys. J. 405,685-697.

[10] Grun E., Zook H. A., Baguhl M., Balogh A., Bame S. J., Fechtig H., Forsyth R.,Nanner M. S., Horanyi M., Kissel J., Lindblad B.-A., Linkert D., Linkert G., Mann I.,McDonnell J. A. M., Morfill G. E., Phillips J. L., Polanskey C., Schwehm G., SiddiqueN., Staubach P., Svestka J., Taylor A., 1993. Discovery of jovian dust streams andinterstellar grains by the Ulysses spacecraft.Nature 362, 428-430.


[11] Grun E., Gustafson B., Mann I., Baguhl M., Morfill G. E., Staubach P., Taylor A.,Zook H. A., 1994. Interstellar dust in the heliosphere.Astron. Astrophys. 286, 915-925.

[12] Grun E., Staubach P., Baguhl M., Hamilton D. P., Zook H. A., Dermott S., GustafsonB. A., Fechtig H., Kissel J., Linkert D., Linkert G., Srama R., Hanner M. S., PolanskeyC., Horanyi M., Lindblad B. A., Mann I., McDonnell J. A. M., Morfill G. E., SchwehmG., 1997. Southnorth and radial traverses through the interplanetary dust cloud.Icarus129, 270-288.

[13] Gustafson, B. A. S., 1994. Physics of Zodiacal Dust.Ann. Rev. Earth and Planet. Sci.22, 553-595.

[14] Jackson A. A. 2001. The capture of interstellar dust: the pure Poynting-Robertsoncase.Planet. Space Sci. 49, 417-424.

[15] Hanslmeier A., 2002. The Sun and Space Weather. Kluwer Academic Publishers, Dor-drecht, 243pp.

[16] Hildebrand R. H., Dragovan M., 1995. The shapes and alignment properties of inter-stellar dust grains.Astrophys. J. 450, 663-666.

[17] Kastrov V. G., 1979. Selected papers on atmospheric physics, Gidrometeoizdat,Leningrad (in Russian).

[18] Klacka J., 2004. Electromagnetic radiation and motion of a particle,Celestial Mech.and Dynam. Astron. 89, 1-61.

[19] Klacka J., 2008a. Mie, Einstein and the Poynting-Robertson effect. arxiv:0807.2795

[20] Klacka J., 2008b. Electromagnetic radiation, motion of a particle and energy-massrelation. arxiv:0807.2915

[21] Kocifaj M. Klacka J., 2003. The capture of interstellar dust: the pure electromagneticradiation case.Planet. Space Sci. 51, 617-626.

[22] Kocifaj M. Klacka J., 2004. The capture of interstellar dust: the Lorentz force case.Planet. Space Sci. 52, 839-847.

[23] Kocifaj M., Kapissinsky I., Kundracık F., 1999. Optical effects on irregular cosmicdust particle U2015 B10.J. Quant. Spectrosc. Radiat. Transfer 63, 1-14.

[24] Kimura H., Mann I., 1998. The electric charging of interstellar dust in the solar systemand consequences for its dynamics.Astrophys. J. 499, 454-462.

[25] Krauss O., 2005. private communication

[26] Krauss O., Wurm G., 2004. Radiation pressure forces on individual micron-size dustparticles: a new experimental approachJ. Quant. Spectrosc. Radiat. Transfer 89, 179-189.


[27] Landgraf M., 2000. Modeling the motion and distribution of interstellar dust insidethe heliopshere.J. Geophys. Res. 105, 10302-10316.

[28] Landgraf M., Augustsson K., Grun E., Gustafson B. S., 1999. Deflection of the localinterstellar dust flow by solar radiation pressure.Science 286, 2319-2322.

[29] Mie G., 1908. Beitrage zur Optik truber Medien speziell kolloidaler Metalosungen.Ann. Phys. 25, 377-445.

[30] Mishchenko M. I., Travis L. D., Lacis A. A., 2002. Scattering, Absorption, and Emis-sion of Light by Small Particles, Cambridge University Press, Cambridge.

[31] Neckel H., Labs D., 1981. Improved data of solar spectral irradiance from 0.33 to 1.25microns.Solar Phys. 74, 231-249.

[32] Opher M., Liewer P. C., Velli M., Bettarini L., Gombosi T. I., Manchester W.,DeZeeuw D. L., Toth G., Sokolov I., 2004. Magnetic effects at the edge of the SolarSystem: MHD instabilities, the de Laval Nozzle effect, and an extended jet.Astrophys.J. 611, 575-586.

[33] Purcell E. M., Pennypacker C. R., 1973. Scattering and absorption of light by non-spherical dielectric grains.Astrophys. J. 186, 705-714.

[34] Poynting J. M., 1903. Radiation in the Solar System: its Effect on Temperature and itsPressure on Small Bodies.Philosophical Transactions of the Royal Society of LondonSeries A 202, 525-552.

[35] Robertson H. P., 1937. Dynamical effects of radiation in the Solar System.Mon. Not.R. Astron. Soc. 97, 423-438.

[36] Sykes M. V., 2007. Infrared Views of the Solar System from Space. In: Encyclopediaof the Solar System, L.-A. McFadden, P. R. Weissmann and T. V. Johnson (eds.),Academic Press (Elsevier), San Diego, 2nd ed., 681-694.

[37] Sykes M. V., Grun E., Reach W. T., Jenniskens P., 2004. The interplanetary dust com-plex and Comets. In: Comets II, M. C. Festou, H. U. Keller and H. A. Weaver (eds.),The University of Arizona Press, Tucson, in collaboration with Lunar and PlanetaryInstitute, Houston, 677-693.

[38] van de Hulst H. C., 1981. Light Scattering by Small Particles. Dover Publications, Inc.New York, 470 pp. (originally published in 1957 by John Wiley & Sons, Inc., NewYork)

[39] Wriedt T., Comberg U., 1998. Comparison of computational scattering methods.J.Quant. Spectrosc. Radiat. Transfer 60, 411-423.

[40] Wurm G., Schnaiter M., 2002. Fractal aggregates in space. In: Optics of Cosmic Dust,G. Videen and M. Kocifaj (eds.), Kluwer Academic Publishers, Dordrecht, 89-102.

[41] Zirker J. B., 1981. The solar corona and the solar wind. In: Jordan, S. (Ed.), The Sunas a Star. NASA, Washington, DC, pp. 135-162.



Chapter 8

SOLAR WIND, LARGE DIAMAGNETIC CAVITIES,AND ENERGETIC PARTICLES

Jiasheng ChenDepartment of Astronomy and Center for Space Physics,

Boston University, Boston, MA, USA

Abstract

The Earth’s magnetospheric cusp is a key region for transferring the solar wind en-ergy, mass, and momentum into the Earth’s magnetosphere. The solar wind particlescan directly access the dayside high-altitude cusp, creating large diamagnetic cavitieswith strong electromagnetic fluctuations. Different from magnetic reconnection, thecusp diamagnetic cavities are created by the interactions of the solar wind with the lo-cal magnetic field, which could depress the field from more than 200 nT into near zeronT, tearing wide and deep magnetic holes in the Earth’s magnetosphere. The powerspectral density of the electromagnetic fluctuations inside the cavities shows increasesby up to four orders of magnitude in comparison to adjacent regions. The strong elec-tric field fluctuations can efficiently energize the cusp charged particles by cyclotronresonant acceleration. The discovery of cusp energetic particle (CEP) events is a majorbreakthrough in space science. It is changing the traditional view about the structureand dynamics of the magnetosphere and has opened a great avenue for the Sun-Earthconnection investigations. The CEPs are detected in the high-altitude cusp region andare always there day after day. They have energies from 20 keV up to 15 MeV, whichis also the typical energies of the ring current and outer radiation belt populations. TheCEP intensities are observed to increase by as much as four orders of magnitude dur-ing cusp diamagnetic cavity crossings. These recentin situ observations reveal a new,broad and dynamic region of acceleration and trapped radiation in geospace, whichcenters at the Earth’s magnetospheric cusp and has a size of up to 10.5 Earth radii.The new region of radiation can extend to low-latitude region, and can reach 6.6 Earthradii from the Earth’s center, providing a direct particle source for the outer Van Allenradiation belt.

1. Introduction

For decades, the Earth’s magnetospheric cusp has been considered as only a sink - a verynarrow and small region of weak magnetic fields. No significant energetic particle fluxes

292 Jiasheng Chen

were expected to be detected there [Roederer,1970]. Therefore, it came as a big surprisewhen the POLAR spacecraft measured temporarily confined MeV charged particles in thehigh-altitude cusp region [Chen et al.,1997a, 1998;Sheldon et al.,1998]. The Earth’s mag-netospheric cusp, by definition [e.g., http://www.oulu.fi/∼spaceweb/textbook/cusp.html],is a near zero magnetic field magnitude and funnel-shaped region between the field linesthat map to the dayside and nightside of the outermost magnetospheric surface [Chapmanand Ferraro,1931;Roederer,1970]. Theoretically, for perfect shielding, the cusps are fo-cal points for the shielding currents confining the magnetosphere [Chapman and Ferraro,1931]; for not perfect shielding, the cusps become open funnels for direct entry of the solarwind plasma into the magnetosphere [e.g.,Reiff et al.,1977; Marklund et al.,1990; Ya-mauchi et al.,1996]. In practice, the cusp regions are identified either by minimum localmagnetic fields [Farrell and Van Allen,1990] or by a combination of magnetic field, plasmaflow, and plasma wave [e.g.,Chen et al.,1997b]. The solar wind particles inside the cusphad been measured a long time ago [Heikkila and Winningham,1971;Frank,1971]. Recentsatellite observations from POLAR and CLUSTER reveal in addition a broad and dynamicregion of acceleration and trapped radiation centered at the Earth’s magnetospheric cusp[Chen,2008], which is created by the solar wind.

2. Solar Wind and Frozen-in Field

2.1. Solar Wind

The solar wind is a fully ionized plasma flow consisting of electrons, protons, and somehigh charge state heavier ions such as He++ and O+6. It expands from the solar corona (aregion of the solar atmosphere, about 4000 km to several solar radii above the Sun’s visiblesurface) into interplanetary space and becomes supersonic a few solar radii from the Sunwhen the kinetic energy exceeds the thermal energy. The average of solar wind speed nearthe Earth over two sunspot cycles (1965-1987) is 445 km/s [Chen,1989;Chen et al., 1991].

Studies of the solar wind were actually started byChapmanin 1927 [Chapman, 1929;Pomerantz,1971]. Later, by considering the physics of comet tails,Biermann[1951, 1953,1957] recognized that the behavior of cometary tails could be explained only by the exis-tence of a particle outflow from the Sun. The original theoretical model of the supersonicsolar wind, dragging out with it magnetic field lines from the solar corona was proposed byParker[1958a, 1959, 1963].

Solar coronal holes, the coolest corona, are the source of high-speed solar wind [e.g.,Krieger et al.,1973]. Coronal mass ejections associated with flares and/or eruptive promi-nences are another source of solar wind, and are an important source of its variability. Thesolar wind continues to blow until it reaches a distance from the Sun at which its rampressure is balanced by that of the interstellar wind, which has been observed recently byVoyager 1 and Voyager 2 spacecraft [e.g.,Stone et al., 2008].

2.2. Frozen-in Magnetic Field

The solar corona has an extremely high conductivity, and the solar wind carries the magneticfield (B) away from the base of the corona. According to Ohm’s law and Faraday’s law,

Solar Wind, Large Diamagnetic Cavities, and Energetic Particles 293

this magnetic field is frozen-in in the solar wind plasma [e.g.,Cowling,1934;Alfven,1942,1950;Parker,1958b]. This can be understood by considering the change of magnetic flux(Φ) through a closed loop,l (surfaceS), moving with the plasma. There are two factors tocause the change: (i) The∂B

∂t during the time the loop moves froml(t) to l(t + dt), and (ii)the flux lost during the movements in the boundary of the loop. The area added to the loopby a line elementdl of the loop in timedt is dl×vdt, wherev is the plasma velocity; thus,

dΦ = d(∫ ∫

SB · dA) =

∫ ∫

S

∂B∂t

· dAdt−∫

lB · (dl× vdt). (1)

Since ∫

lB · (dl× vdt) =

∫

l(v× B) · dldt =

∫ ∫

S∇× (v×B) · dAdt, (2)

eq. (1) is equivalent to

dΦ =∫ ∫

S[∂B∂t

− ∇× (v× B)] · dAdt. (3)

Using Faraday’s law:

∇× E = −∂B∂t

(4)

and the steady state Ohm’s law in the moving frame:

J = σ(E + v× B) (5)

eq. (3) can be rewritten in the form

dΦdt

= −∫ ∫

SdA · (∇× J

σ) (6)

WhereE is the electric field;J, the current density; andσ, the electric conductivity. In theextremely high conductivity plasma, the current is to remain finite whileσ → ∞, whichrequiresdΦ/dt = 0. Therefore, the magnetic flux through any surface bounded by a loopmoving with the plasma does not change, which means that the magnetic field is frozen-in to the solar wind plasma and both are always constrained to move in unison. In otherwords, the solar wind plasma sees no spatial variation of the magnetic field, and the frozen-in condition is

E = −v ×B, (7)

which implies no parallel electric field.

3. Cusp Diamagnetic Cavities

When the solar wind plasma reaches the dayside Earth’s magnetosphere it sees spatialchanges of the local geomagnetic field that generate a parallel electric field in the solarwind frame and break the frozen-in condition shown in eq. (7). Figure 1 is the time pro-files of the thermalized solar wind plasma (bottom four panels) and the local geomagnetic

294 Jiasheng Chen

field strength (top panel) measured by the POLAR spacecraft in the high-altitude daysidecusp region on August 27, 1996. In Figure 1, the panels from top to bottom are the localmagnetic field strength, the energy spectra of the ions (mostly protons), the energy spectraof the electrons, the 1-1.15 keV proton energy flux, and the 244-281 eV electron energyflux, respectively. It shows the solar wind plasma has a peak value occurring at about 1keV for protons and at about 100 eV for elecrons. Figure 1 further shows that the depressedmagnetic field strength is associated with the increased intensities of the charged particles,suggesting a particle-field interaction.

Figure 1. The cusp diamagnetic cavities observed by POLAR on August 27, 1996. Thepanels show the variation of the local magnetic field strength, the energy spectra of the ions,the energy spectra of the electrons, the 1-1.15 keV proton energy flux, and the 244-281 eVelectron energy flux versus time, respectively.

Physically, the gyro-motions of charged particles (both electrons and ions) in an im-posed magnetic field can induce a magnetic field opposed to the imposed field; the result-ing magnetic field is depressed and is called a diamagnetic cavity. In this example, thediamagnetic cavity was produced by the solar wind plasma when the frozen-in conditionwas broken. At 8:00-10:36 UT on August 27, 1996, the POLAR spacecraft was about 9Re(Earth’s radius) from the Earth at' 65o magnetic latitude (MLAT) and' 15 hours mag-netic local time (MLT). Figure 1 indicates POLAR observed the cusp diamagnetic cavities(CDCs) during this period.


CDCs have also been observed by the CLUSTER mission. The CLUSTER missionconsists of four identical satellites (C1, C2, C3, and C4). Figure 2 is an example of theCDCs detected by the C1 satellite over 7:30-11:00 UT on March 5, 2001. The top panel ofFigure 2 is the enegy spectra of the thermalized solar wind He++ ions that shows a peakvalue at about 2 keV or 1 keV/e. The bottom panel is the local magnetic field strengthshowing a large depression characteristic of a diamagnetic effect. Figure 2 further showsthat inside the CDCs, the magnetic field strength could reach a very low value, some timeseven 0 nT.

Figure 2. The CDCs observed by the C1 satellite on March 5, 2001. The panels showthe variation of the the energy spectra of He++ (top) and the local magnetic field strength(bottom) versus time (UT).

Diamagnetic cavities are different from magnetic reconnection. The physical processfor magnetic reconnection is the annihilation of two magnetic field lines in opposite di-rections [Dungey, 1961; Petschek, 1963]. The magnetic reconnection has been thoughtas a major commonality of solar and magnetospheric plasma [e.g.,Buchner, 2006], butonly a few cases were observed directlyin situ. The physical process for the diamagneticcavities is the gyromotions of charged particles in an ambient magnetic field, where eachparticle (either ion or electron) forms a local ring current to generate a magnetic momentthat is always opposed to the ambient magnetic field direction, resulting a depressed mag-netic field. For space plasma with frozen-in magnetic field, breaking frozen-in (eq. (7)) isa necessary condition for magnetic reconnection to take place; however, it is a sufficientcondition for diamagnetic effect to occur. Therefore, diamgnetic effect is a more commonphysical phenomenno than magnetic reconnection. Diamgnetic cavity could occur beforeor without magnetic reconnection. The CDCs are produced by the solar wind plasma in thehigh-altitude dayside cusp regions when the “frozen-in” magnetic field condition (eq. (7))is broken, and are identified by a combination of low magnetic field strength and high solarwind plasma intensity.

296 Jiasheng Chen

3.1. Cusp Diamagnetic Cavities: A Broad Region

As mentioned before, one characteristic of solar wind in contrast to ionospheric plasma isa high charge state for heavy ions. On May 13, 1999 from 14 to 23:20 UT, the POLARspacecraft observed orders of magnitude enhancement of the high charge state ion intensi-ties in the high-altitude cusp region (top panel of Fig. 3). Associated with these ions werelarge diamagnetic cavities, where the measured local magnetic field strength showed a largedecrease with strong field turbulence (bottom panel of Fig. 3).

Figure 3. The CDCs measured by POLAR on May 13, 1999. The top panel shows thevariation of the 1-18 keV/e He++ (solid line) and 1-10 keV/e O+6 (dotted line) fluxes,while the bottom panel is the local magnetic field strength versus time. The distance ofPOLAR from the Earth (inRe), the magnetic latitude (MLAT), and the magnetic local time(MLT) are shown at the bottom. (AfterChen and Fritz[2004]).

Figure 4 is the POLAR 3-dimensional (3-D) orbit with respect to a model magneto-sphere from 14 UT to 23:00 UT on May 13, 1999 when POLAR was in a CDC, where themagnetospheric structure represents a shell of outermost field-lines. The POLAR orbit isplotted by the OVT (Orbit Visualization Tool) [Stasiewicz et al., 2003], and the magneticfield model includes the internal field model IGRF 1950-2000 and the external magneto-


spheric field model T96 [Tsyganenko and Stern, 1996]. Figure 4 indicates that on May 13,1999 the CDCs observed by POLAR were well inside the magnetosphere and were verybroad with a size of about 6Re in the latitudinal direction, much larger than that in thetraditional view [e.g.,Roederer, 1970].

Figure 4. POLAR 3-D orbit with respect to a model magnetosphere over 14-23 UT on5/13/99.

Broad diamagnetic cavities have been observed simultaneously by multiple satellites(POLAR and CLUSTER) as well. On May 4, 2006, while crossing through the dawnsidehigh-latitude region in the southern hemisphere, the CLUSTER satellites detected largediamagnetic cavities. The large diamagnetic cavities were also observed by the POLARsatellite near the dawnside in the southern hemisphere on the same day. Figure 5 displaysthe observations of the diamagnetic cavities by POLAR (10:30-15:12 UT), C2 (15:09-16:36UT) and C4 (15:09-17:20 UT) on May 4, 2006 (bottom panel) and the three componentsof the interplanetary magnetic field (IMF) measured by the WIND satellite after the cor-rections for the solar wind time delay (66 minutes) from WIND to POLAR, C2 and C4(top panel). During this period, the WIND satellite was located near the forward libra-tion point ∼ 209 Re from the Earth and observed a slow and stable solar wind velocitythat had a value of∼ 335 km/s in the Sun-Earth line direction. POLAR observed a largedecline of the geomagnetic field strength starting at 13 UT when the IMFBy turned pos-itive (duskward) ending at 17:04 UT (measured by C4) when the IMFBy turned negative

298 Jiasheng Chen

(dawnward). A positive IMFBy is expected to merge with the geomagnetic field in thehigh-latitude dawnside region in the southern hemisphere [Dungey,1961; Gonzalez andMozer,1974;Sonnerup,1974] causing the earth’s magnetosphere to open for direct entryof the solar wind charged particles and producing the observed diamagnetic cavities.

Figure 5. Top panel is the temporal variations of the IMFBx (aqua line), IMFBy (blackline), and IMFBz (green line) measured by WIND in the GSE coordinates. Bottom panelis the magnetic fields observed by POLAR (black line), C2 (red line), and C4 (blue line)during 10:30-17:30 UT on May 4, 2006.

Figures 6(a), 6(b) and 6(c) show three satellite positions, in the Geocentric Solar Ecliptic(GSE) coordinates, when they were in the diamagnetic cavities on May 4, 2006. Figure 5and 6 indicate that the diamagnetic cavities have a size of approximately 10.5Re, whichis comparable to the size of the entire dayside radiation belt. Figures 3, 4, 5 and 6 reveal atremendously broad diamagnetic cavity region can exist in geospace.

3.2. Cusp Diamagnetic Cavities: A Dynamic Region

One remarkable feature of diamagnetic cavities is the presence of the large magnetic fluctu-ations that are an indicator of the dynamic processes [Blecki et al.,1999]. Figure 7 presentsthe measurements of magnetic fluctuations by C3 in the high-altidute cusp during 18:45-20:28 UT on February 14, 2003. In addition to the large diamagnetic cavities (top panel)


Figure 6. Panels (a), (b) and (c) are three satellite positions projected into the X-Y, X-Z andY-Z planes in GSE when the satellites were in the diamagnetic cavities on May 4, 2006.

and the enhancement of the solar wind He++ intensity (bottom panel), there are broad band-width bursts of magnetic fluctuations extending from below 8 Hz up to about 1 kHz (middlepanel) which appear to associate with the helium intensity increases and the magnetic fielddepressions. In the middle panel of Figure 7, the power density of the magnetic fluctua-tions is displayed as frequency-time spectrograms with each color coded in blue throughred according to the color bar on the right. It shows two important features: (1) the spectraincrease significantly in intensity with decreasing frequency; and, (2) the magnetic fluctu-ation power is higher by orders of magnitude in the high-altitude CDCs than before 19:05UT (outside the diamagnetic cavities).

Figure 8 displays the observations of the magnetic fluctuations by POLAR on Septem-ber 18, 1996. The magnetic field intensity is displayed as frequency-time spectrograms witheach color coded in blue through red according to the color bar shown to the right. The whiteline shows the electron cyclotron frequency that is proportional to the local magnetic fieldstrength. Just like in Figure 7, Figure 8 exhibits orders of magnitude enhancement of themagnetic fluctuations extending from 5.6 Hz up to the electron cyclotron frequency, whichis correlated well with the local magnetic field depressions. This correlation has been foundfor other CDC crossings [Chen et al.,1998;Pickett et al.,1999;Blecki et al.,1999].

Figure 9 exhibits the cavity electric field (top) and magnetic field strength (bottom)measured by the POLAR satellite at 6:37-7:17 UT on May 4, 1998, during a part of the

300 Jiasheng Chen

Figure 7. CDCs measured by the C3 satellite on February 14, 2003. Panels from top tobottom are the local magnetic field strength, the magnetic power spectral density, and theHe++ energy spectra versus time.

Figure 8. Another example of the CDCs, showing enhanced power spectral density ofmagnetic fluctuations that were observed by POLAR on 18 September 1996. The whiteline shows the electron cyclotron frequency. The distance of POLAR from the Earth (inRe), the magnetic latitude (MLAT), and the magnetic local time (MLT) are shown at thebottom of the figure. (Courtesy ofJ. S. Pickett).

magnetospheric cusp crossing, when POLAR was located at∼ 6.8Re, 32o MLAT, and 11MLT [Chen and Fritz, 1999, 2001a]. It displays large electromagnetic fluctuations. Thecavity’s magnetic field strength varied between 220 nT and 0 nT, which could generate aninductive electric field. The measured cavity electric field peaked at 150 mV/m. Comparedto the reported equatorial convection electric field of less than 0.16 mV/m [Kosik, 1979],the measured cavity electric field of 150 mV/m is much higher by about three orders ofmagnitude, and its power (proportional to square of the electric field) is larger by six orders


of magnitude. These cavity electric fields can change the charged particle energy. Figures7, 8 and 9 reveal that the large diamagnetic cavities are an extraordinarily dynamic region.

Figure 9. The time variations of the cusp electric field (top panel), and the local magneticfield strength (bottom) measured by POLAR on May 4, 1998.

3.3. Cusp Diamagnetic Cavities: A New Radiation Region

One major discovery during the space era is the cusp energetic particles (CEP) [Chen et al.,1997a, 1998;Sheldon et al.,1998]. These CEPs have energies from 20 keV up to 15 MeV[Chen et al.,2005;Chen and Fritz,2005]. They are detected in the CDCs and are alwaysthere day after day [Chen et al.,1998; Chen and Fritz,2000, 2005;Fritz et al., 2003].One example shown in Figure 10 displays the 20-200 keV electrons (top panel) and 0.52-1.15 MeV helium ions (bottom panel) with the local magnetic field strength (middle panel)measured by POLAR over 7:30-11:00 UT on August 27, 1996. It shows the increasedintensities of the energetic charged particles associated with large diamagnetic cavities.Since electrons and the helium ions drift in opposite directions, it is not expected to detectthem simultaneously in the CDCs for several hours.

302 Jiasheng Chen

Figure 10. The CEP events measured by POLAR on August 27, 1996. Panels are thetime profiles of the cusp relativistic electrons (top panel), the local magnetic field strength(middle panel), and the cusp MeV helium, where the vertical dashed lines mark the fourdifferent CEP events. The distance of POLAR from the Earth (inRe), the magnetic latitude(MLAT), and the magnetic local time (MLT) are shown at the bottom of the figure. (AfterChen et al.[1997a, 1998]).

POLAR CEP observations have been confirmed by the INTERBALL-1, CLUSTER,and ISEE-1/ISEE-2 spacecraft [e.g.,Pissarenko et al.,2001;Chen and Fritz,2004, 2005;Whitaker et al.,2006, 2007;Walsh et al.,2007]. Figure 11 is another example of the CEPsmeasured by the C3 satellite in the southern hemisphere. In Figure 11, the panels from topto bottom are the time variations of the energy spectra of the thermalized solar wind He++

energy flux, the local magnetic field strength, the energy spectra of the energetic electronflux, the energetic helium flux, and the power spectral density of the magnetic fluctuations,respectively. Figure 11 shows that the power spectral density of the magnetic fluctuationsin the diamagnetic cavities increased by up to four orders of magnitude in comparison toan adjacent region at 18:05-18:10 UT on that day (bottom panel). The enhancements ofthe energetic particles have also been detected at an energy of about 200 keV for electrons


(middle panel) and 1 MeV for helium (panel 4 from top). These observational results arealso true for the other three CLUSTER satellites (C1, C2 and C4). Orders of magnitudeincreases of the energetic particle intensities in the large diamagnetic cavities have beenmeasured by CLUSTER for other CEP events, including the three examples shown in Figs.2 (3/5/01), 5 (5/4/06) and 7 (2/14/03).

Figure 11. The CEP events observed by the C3 satellite on December 28, 2002. Panels(from top to bottom) are the time variation of the energy spectra of the thermalized solarwind He++ energy flux, the local magnetic field strength, the energy spectra of the 35-337keV electron flux, the 30 keV - 1.7 MeV helium flux, and the power spectral density of themagnetic fluctuations over a frequency range of 8-1000 Hz, respectively.

Figure 12 plots the energy spectrum of the CEPs that were associated with the largediamagnetic cavities shown in Figure 9 on May 4, 1998. In Figure 12, the cusp energeticions have an energy up to 15 MeV and can be represented by a power-law form (straight linein Fig. 12) over 7 keV - 15 MeV. For comparison, a Maxwellian distribution curve peakedat 1 keV is also plotted in Figure 12. This Maxwellian curve represents approximately the

304 Jiasheng Chen

thermalized solar wind plasma energy distribution with a typical energy of 1 keV for ions(dominated by protons). The figure shows that the higher the ion energy, the larger thedifference of the ion energy spectrum from the Maxwellian distribution.

Figure 12. The measured CEP ion energy spectrum at 6:50-7:50 UT on May 4, 1998, wherethe MICS (open diamonds), IPS (solid circles) and HIT (open sqares) are three sensorsonboard POLAR. The measured spectrum can be represented by a power-law form (straightline). The curve is the 1 keV Maxwellian energy distribution for thermalized solar windions.

The abovein situ observations show that the CDCs are filled with energetic (keV up to15 MeV) charged particles, including MeV ions and relativistic electrons, which reveals anew region of radiation centered at the Earth’s magnetospheric cusp.

3.4. Cusp Diamagnetic Cavities: A New Trapping Region

Trajectory calculations show that the high-altitude cusp has a large trapping geometry that,in a static geomagnetic field model, can trap the tens of keV to MeV charged particles[Sheldon et al., 1998;Delcourt and Sauvaud, 1999;Blake, 1999;Antonova et al., 2000;Pugachevac et al., 2005; Gusev et al., 2006]. Figure 13 shows examples of orbits for 1MeV electrons at three different locations in a static cusp geometry in Geocentric SolarMagnetospheric (GSM) coordinates [Sheldon et al.,1998]. The charged particles are mir-roring around the minimum magnetic field near the cusp center, and drifting in closed drift


shells around the cusp field line. It is noted that the cusp has a locally outward magneticgradient in contrast to the typical inward (to the Earth) gradient in the Van Allen radiationbelt. Figure 13 suggests that the cusp trapping region has a broad size of about 10Re in Zdirection, 6Re in X, and 11Re in Y, consistent with the spacecraft observations shown inFigures 3, 4, 5 and 6.

Figure 13. Trajectories of trapped 1 MeV electrons in the polar cusp, projected into theGSM X-Z and Y-Z planes. Dashed lines are magnetic field lines, and black lines are con-tours of|B| in nT (from Sheldon et al.[1998]).

It has been reported that the CEPs show a peak intensity around 90o pitch angle (theangle between the particle velocity and the local magnetic field direction) [Chen et al.,1997a, 2005;Sheldon et al.,1998; Chen and Fritz, 2000; Whitaker et al.,2006, 2007;Walsh et al.,2007], indicating a trapped population. In fact, in the real geomagnetic field,

306 Jiasheng Chen

the solar wind pressure changes the dipole into quadrupolar, and the solar plasma injectioncan create a diamagnetic cavity to form a trapping geometry with two local maxima ofmagnetic field intensities and a local minimum field intensity in the cusp [Chen et al.,1997a, 1998]. POLAR and CLUSTER measurements reveal that the cusp magnetic fieldis very turbulent, so that the CDCs are not a stable trapping region but rather a dynamictrapping region that can only temporarily confine charged particles [Chen et al.,1997a].

In summary, the CEP observations reveal a new, broad and dynamic region of trappedradiation that is characterized by (i) a more than three sigma increase in intensity abovebackground for> 30 keV charged particles, (ii) a more than one order of magnitude en-hancement in intensity for the 1-10 keV solar wind ions, and (iii) diamagnetic cavities. Thediamagnetic cavities are created by the interactions of the charged particles (dominated bysolar wind) with the local magnetic field, which could depress the geomagnetic field frommore than 200 nT into near zero nT, tearing wide and deep magnetic holes in the Earth’smagnetosphere. This new region of trapped radiation is centered at the Earth’s magneto-spheric cusp and is filled with energetic particles and large electromagnetic fluctuations. Itis different from the Van Allen radiation belt that is centered at the Earth’s magnetic equatorwith stable magnetic field. The recognition of the new trapped radiation region representsa conceptual revolution in magnetospheric physics and a crucial step in understanding theradiation environment in geospace.

4. Origin of Cusp Energetic Particles

The origin of cusp energetic particles is a fundamental issue to space science, which can beaddressed by using both charged particle and field data. The field and particle data can beused to identify mechanisms by which these particles are energized and transported fromtheir source populations.

4.1. Two Seed Populations

Since He++ and O+6 ions are of solar origin [Gloeckler et al., 1986] while O+ ions areof ionospheric origin, ion charge states can be used to determine seed populations of theenergetic ions in the new, dynamic trapping region of radiation. On 20 April 1999, whenPOLAR was crossing through the dayside high-altitude cusp, it observed three basic fea-tures: (1) large diamagnetic cavities with strong field turbulence (bottom panel of Fig. 14);(2) elevated intensities of the lower energy (1-10 keV/e) O+6 and 1-18 keV/e He++ of solarwind origin (middle panel); and, (3) high, variable fluxes of the high-energy particles (toppanel).

Of particular interest is the top panel, in which an unexpected energetic O+ (70-200keV/e) population (solid line) was observed in the high-altitude dayside cusp. Figure 14reveals that the seed populations of the energetic ions in the new trapping region of radia-tion are a mixture of ionospheric and solar wind particles [Chen and Fritz,2001b, 2002a,2002b]. It is noticed that the time profiles of the energetic (55-200 keV/e) cusp He++ aresimilar to those of the energetic (70-200 keV/e) O+. The key point here is that since theseed population of the cusp energetic O+ is of ionospheric origin, and since the seed popu-lation of the cusp energetic He++ is solar wind plasma, the similarity of their time-intensity


profiles suggests that either both seed populations have been energized by a common accel-eration mechanism [Fritz et al., 2003] or a consequence of the trap.

Figure 14. The CEPs observed by POLAR on April 20, 1999. The panels show the variationof the 70-200 keV/e O+ (solid line) and the 55-200 keV/e He++ (dotted line) fluxes (toppanel), the 1-10 keV/e O+6 (solid line) and 1-18 keV/e He++ (dotted line) fluxes (middle),and the magnetic field (bottom) versus time, respectively. The distance of POLAR fromthe Earth (inRE), the magnetic latitude (MLAT), and the magnetic local time (MLT) areshown at the bottom. (AfterChen and Fritz[2002a]).

4.2. Evidence of Local Acceleration

Time-intensity profiles of the charged particles over different energy ranges will provideinformation about their transportation from their source. Figure 15 displays the March 5,2001 CEP event observed by the C2 satellite over 7:30-11:00 UT when C2 was crossingthrough the dayside high-altitude cusp region in the northern hemisphere. The figure showsthe local magnetic field strength (top panel) and the measurements of the energetic electrons

308 Jiasheng Chen

at eight different energy channels from 35 keV to 337 keV, protons from 28 keV to 4 MeV,and helium ions from 30 keV to 3.8 MeV (bottom three panels), respectively. From 8 to10 UT, C2 was located at X=2.43-5.40Re, Y=3.00-3.13Re, Z=7.81-8.73Re in GSE, andit detected simultaneous enhancements of the energetic electron and ion fluxes that wereassociated with the large diamagnetic cavities. Note that from 8:50-10:00 UT the 28-92keV proton flux in the cusp was about three to four orders of magnitude higher than thatbefore 7:40 UT and after 10:45 UT when C2 was outside the cusp region.

Figure 15. The CEP event observed by the C2 satellite on 5 March 2001. The panels showthe variation of the local magnetic field strength (top panel), and the fluxes of the 35-337keV electrons, the 28 keV - 4 MeV protons, and the 30 keV - 3.8 MeV helium ions at eightdifferent energy channels (bottom three panels) versus time, respectively.

Figure 15 further reveals no obvious energy dispersion signatures for the energetic par-ticles (bottom three panels). Because electrons and ions drift in opposite directions andbecause charged particles with different energies drift/transport at different velocities, si-multaneous enhancements of the energetic electron and ion fluxes with no obvious energydispersion signatures imply a local dynamic process, a trap, or a local accerelation mecha-nism that must be extremely efficient.

On February 12, 2003, the four CLUSTER satellites were in a tetrahedral configurationwith a separation distance of 5000 km between the spacecraft. Figure 16 is the CLUS-TER 3-D orbit plot on that day over 8-13 UT when the four CLUSTER satellites traveled


from the nightside toward the dayside high-altitudehigh-latitude cusp region in the northernhemisphere. It shows that C4 (blue) was the leading satellite and C3 (green) was the onebehind.

Figure 16. The 3-D orbits of CLUSTER C1 (black), C2 (red), C3 (green) and C4 (blue)with respect to a model magnetosphere from 8 UT to 13 UT on February 12, 2003.

Figure 17 presents the simultaneous measurements of the> 100 keV and 30-100 keVrelativistic electrons and 30-100 keV protons (top three panels) with the local magneticfield strength (bottom panel) by the C1 (black lines), C2 (red lines), C3 (green lines) andC4 (blue lines) satellites over 8:00-13:00 UT on February 12, 2003. In Figure 17, Theleading satellite C4 detected a more than one order of magnitude increase of the 30-100keV proton intensity first at 8:12 UT, followed by C1 and C2 at 8:30 UT, and finally by C3at 8:40 UT. The orders of magnitude enhancements of the energetic proton intensity endedat 11:47 UT as measured by C2, at 11:50 UT by C4, at 11:55 UT by C1, and at 12:45 UTby C3.

These observational results shown in Figure 17 together with the CLUSTER positionsshown in Figure 16 reveal an energetic proton source region centered at the magnetosphericcusp. This conclusion is also true for energetic electrons. The 30-100 keV and> 100keV relativistic electrons (top two panels of Fig. 17) move at 32-55% and> 55% of thespeed of light, respectively. After 11:50 UT, C1, C2 and C4 were outside the new trappedradiation region and saw no enhancement of the relativistic electrons, while C3 was inside

310 Jiasheng Chen

Figure 17. The new trapping region of radiation observed simultaneously by C1 (black),C2 (red), C3 (green) and C4 (blue) on February 12, 2003. Panels from top to bottom are thetime-intensity profiles of the> 100 keV electrons, the 30-100 keV electrons, the 30-100keV protons, and the magnetic field strength, respectively.

the region and observed significant relativistic electron flux until 12:45 UT when it movedout of this source region. In other words, there is an energetic particle gradient pointing tothe new trapped radiation region, which is a local energetic particle source. Therefore, thesimultaneous observations shown in Figure 17 provide the most striking evidence that thereis an energetic particle source located in the broad diamagnetic cavities. These CEPs haveto be energized locally in the cusp from their seed populations. The trapping properties ofCDCs permit charged particles inside them to be accelerated [Sheldon et al., 2005].

On the other hand, large fluctuations of electric fields have been observed in the broadCDCs (see Fig. 9). The varying electric field can change the energies of the cusp chargedparticles with some of them being accelerated locally. Particle acceleration signatures lo-cally in the cusp have also been reported by other research groups [Pfaff et al.,1998;Ya-mauchi et al.,2001;Pissarenko et al.,2001;Savin et al.,2002;Delcourt et al.,2005]. Thecusp boundary as a particle emitting boundary has been reported recently [Whitaker et al.,2007].


4.3. Resonant Acceleration

As shown in the Section 3.2, large diamagnetic cavities are always associated with strongmagnetic fluctuation power. The correlation of the magnetic fluctuation power with the cuspMeV helium intensity has been reported previously [Chen and Fritz, 1998]. On September10, 1996, POLAR detected the large diamagnetic cavities with MeV particles in the daysidehigh-altitude cusp region between 13.1-14.5 MLT at 6:12-9:30 UT [Chen et al.,1998].The measured diamagnetic cavities were associated with large magnetic fluctuations. Aninnovative difference method of spectral analysis [Chen,1989; Bieber et al.,1993] wasused to determine the power spectra of the magnetic field for fluctuations in the ultra lowfrequency (ULF) range of 0.02 to 3 Hz over one 60-second period and one 120-secondperiod. The results were plotted in Figure 18. POLAR was inside the diamagnetic cavitiesat 8:36-8:37 UT and outside the cavities at 6:06-6:08 UT. When compared to 6:06-6:08UT, the ULF power spectral density of the cavity magnetic field at 8:36-8:37 UT increasesby more than four orders of magnitude. Figure 18 further shows that at O+, He++, andproton gyro-frequencies, as depicted by arrows, the magnetic power density was about fiveorders of magnitude larger at 8:36-8:37 UT inside the cusp than at 6:06-6:08 UT outsidethe cusp. The power spectral densities also exhibit notable enhancements around the He++

and proton gyro-frequencies of∼ 0.48 Hz and 0.96 Hz. The 60-second interval covers∼ 29 and 58 gyro-periods for He++ and protons, respectively. It is a permanent featurethat the magnetic power density in the CDCs exhibits orders of magnitude enhancementwhen compared to the adjacent regions. Such magnetic power enhancements in the CDCshave also been detected at higher frequencies from 6 Hz to several kHz (the electron gyro-frequency) (e.g., Figs. 7 and 8) [Chen et al.,1998;Pickett et al.,1999;Blecki et al.,1999].

The magnetic power spectra with peaks at the ion gyro-frequencies shown in Figure 18suggest a resonant interaction of the field with the charged particles. As shown in Figure 9the cusp magnetic field strength varied between 220 nT and 0 nT, which will generate aninductive and varying electric field. Since the gyro-frequency of a charged particle is pro-portional to the magnetic field strength, some of the cusp charged particles have to undergoa resonant or partial resonant acceleration with the varying electric field. In fact, POLARhas measured a strong perpendicular electric field that varied between -300 mV/m and 350mV/m in a large CDC, and has detected a left-hand circular polarization of the cusp electricfield over a period near the ion gyro-period [Chen,2008]. It can energize the ions by acyclotron resonant acceleration mechanism.

The energization rate of cyclotron resonant acceleration can be expressed analytically.The rate of change of the ion perpendicular kinetic energy by ion cyclotron resonant accel-eration is [Chen,2008]:

dK⊥/dt = (2K⊥(0)/m)1/2qE + q2E2t/m, (8)

where theK⊥(0) is the ion perpendicular kinetic energy at time (t) = 0;m, the ion mass;q,the ion charge; andE, the left-hand polarization perpendicular electric field at the ion gyro-frequency. Over an ion gyro-period (Ti), the energy increase due to ion cyclotron resonantacceleration can be obtained by integrating eq. (8); that is,

∆K⊥ = (2K⊥(0)/m)1/2qETi + q2E2Ti2/(2m). (9)

312 Jiasheng Chen

Figure 18. The total magnetic power spectra for fluctuations in the ULF range at 8:36-8:37UT (inside the cusp, black line) and at 6:06-6:08 UT (outside the cusp, blue line) on 10September 1996.

The significance of eq. (9) is that all terms on its right side are measurable and areindependent of models and simulations. Eq. (9) indicates that an ion energy enhancedby the gyro-resonant acceleration is a function of the initial perpendicular kinetic energy,charge/mass ratio, gyro-period of the ion and the left-hand polarization perpendicular elec-tric field. Taking He++ ion as an example. Assuming its initial perpendicular kinetic energy= 2 keV (the solar wind as seed population), the enhanced energy by the gyro-resonant ac-celeration for the He++ ion will be 101.4 keV, 0.54 MeV, and 2.04 MeV over a two-secondgyro-period for the perpendicular electric field of 20 mV/m, 50 mV/m, and 100 mV/m,respectively. Similarly, a right-hand polarization perpendicular electric field at the electrongyro-frequency (see Fig. 8) will energize the electrons by the gyro-resonant acceleration.

5. CEP: A Source of Outer Van Allen Radiation Belt

It has been fifty years of intensive research since the discovery of the Earth’s Van Allenradiation belt in 1958 [Van Allen and Frank,1959a, 1959b;Yoshida et al.,1960], yet the


origin of the charged particles in the outer radiation belt is still a mystery. The Earth’s VanAllen radiation belt consists of inner and outer zones [e.g.,Van Allen, 1959]. The outerzone (or the outer radiation belt) centers at the geomagnetic equator and∼ 3.5-11Re fromthe Earth’s center, and the inner zone (or the inner radiation belt) locates at< 2.4Re fromthe Earth’s center [e.g.,Spjeldvik and Rothwell,1985]. The origin of the inner radiationbelt is primarily from the decay of the neutrons sputtered from cosmic ray interaction inthe upper atmosphere [e.g.,Singer, 1958]. The origin of the outer radiation belt remains agreat mystery. The discovery of the broad and dynamic region of radiation centered at theEarth’s magnetospheric cusp provides the key to open the mysterious door of the origin ofthe outer Van Allen radiation belt.

Figure 5 suggests the IMF has a great impact on the configuration of diamagnetic cavi-ties. When IMF varies, the diamagnetic cavities are reconfigured, which releases the CEPsthat are temporarily confined in the diamagnetic cavity region.

The phase space density (PSD) of charged particles in the magnetosphere provides im-portant information about their source. For the same species at different locations, thegradient of the PSD profile reveals the particle transport direction, and the peak of the PSDwill point to the source region. Generally, the measured PSD is a function of the particle’skinetic energy, the pitch angle, and the position.

There are two ways to compare the PSD in different locations. The first one is simulta-neous PSD observations by two or more spacecraft at different locations as shown in Figs.16 and 17; the second one is observations by one or more spacecraft at different times(thus different locations) when the time variation effect is negligible. Figure 19 provides anexample of the latter one. It shows that the charged particles in the broad diamagnetic cav-ities could be a source of the charged particle populations in the outer Van Allen radiationbelt/ring current.

On April 20, 1999, POLAR was in the dayside outer radiation belt at 8-11:42 UT andin the high-altitude cusp at 12-18:30 UT (Fig. 14). Simultaneous observations of threegeosynchronous satellites (1994-084, LANL-97A, and 1991-080) on that day showed thatthe measured 50-250 keV proton fluxes at geosynchronous orbit (6.6Re from the Earth’scenter) varied by a factor of less than 2 at the time [Chen et al., 2005]. Figure 19 dispays thePSD observed by POLAR for five time intervals with three (8:00-9:00 UT, open triangles;9:24-10:24 UT, solid circles; 10:42-11:42 UT, open squares) in the dayside outer radiationbelt and two (12-13 UT, crosses; 16-17 UT, open diamonds) in the cusp regions on April20, 1999 over 1-200 keV energy ranges for protons (left panel) and over 41-200 keV/e forO+ (right panel).

The left panel of Figure 19 shows that even if the protons in the outer radiation belt weremeasured at different latitudes, different local times, and different altitudes, their PSDs werenearly overlapping with each other. This demonstrates that the proton phase space densityin the outer radiation belt is organized by magnetic moment (=K⊥/B). Only over the range0.2-1 keV/nT was the proton intensity in the outer radiation belt roughly the same as thatin the cusps, while over 0.02-0.2 KeV/nT and> 1 keV/nT, the proton phase space densityin the outer radiation belt was lower than that in the high-altitude cusp at a given magneticmoment. The right panel of Figure 19 shows that the observed O+ phase space densitiesin the cusp are orders of magnitude higher than those measured in the outer radiation belt.This observational result is significant and very surprising. Since the energetic ions in the

314 Jiasheng Chen

outer radiation belt are stably trapped and have much longer trapping times than in thediamagnetic cavities, while for locally accelerated particles the PSD is proportional to thetrapping time, one would expect much higher ion flux in the radiation belt. This higherparticle flux in the diamagnetic cavities at a given magnetic moment was also reportedpreviously for the energetic electrons [Sheldon et al.,1998] and O≤+2 ions [Chen andFritz, 2001b, 2002b]. Figure 19 implys that the direction of charged particle transport isfrom the new trapping region of radiation to the outer radiation belt/ring current.

Figure 19. Proton (left panel) and O+ (right panel) phase space densities observed bythe POLAR for five time intervals with three (8:00-9:00 UT, open triangles; 9:24-10:24UT, solid circles; 10:42-11:42 UT, open squares) in the outer radiation belt (RB) and two(12:00-13:00 UT, crosses; 16:00-17:00 UT, open diamonds) in the cusp regions on April20, 1999. (AfterChen et al.[2005]).

Furthermore, Figures 3, 6, 8 and 9 indicate that the diamagnetic cavities could reach6.6 Re from the Earth’s center in low latitude, overlapping part of the traditional outerradiation belt region and allowing the cusp energetic particles a direct access to the outerVan Allen radiation belt/ring current. According to Figure 4, POLAR was well inside theEarth’s magnetosphere at the time on May 13, 1999, and the diamagnetic cavities wereoccurred in both open and closed geomagnetic field lines. The energetic charged particlesin the diamagnetic cavities with closed field lines ought to experience scattering, diffusion,and magnetic gradient curvature drift which would provide a direct source for the outerradiation belt/ring current particles [Chen and Fritz, 2000].

6. Conclusion

Recent satellite observations reveal a new, broad and dynamic region of trapped radiationcentered at the Earth’s magnetospheric cusp, distinct from the Van Allen radiation belt thatis centered on the geomagnetic equator. The solar wind particles can directly get access


to this region, creating large diamagnetic cavities with strong electromagnetic fluctuationsand tearing wide and deep magnetic holes in the Earth’s magnetosphere. The diamagneticcavities are different from and more common than magnetic reconnection. This new regionof radiation has a size of up to 10.5 Earth radii, which is filled with the energetic chargedparticles, large diamagnetic cavities, and strong electromagnetic fluctuations. Inside thecavities, both the energetic particle intensity and the power spectral density of the magneticfluctuations show increases by up to four orders of magnitude in comparison to adjacentregions. Peak power spectral densities at the ion gyro-frequencies have been measured.The fluctuations of the cavity electric fields have an amplitude of up to 350 mV/m thatcan efficiently accelerate the charged particles by cyclotron resonant acceleration. Thecyclotron resonant acceleration can energize ions from keV to MeV in seconds. Higherphase space density in the new region of radiation at a given magnetic moment suggeststhat the energetic particles transport from the new region of radiation to the outer Van Allenradiation belt. The extension of the new region of radiation to low-latitude region and to 6.6Earth radii from the Earth’s center provides a direct particle source for the outer Van Allenradiation belt.

Acknowledgments

My sincere appreciation is to J. W. Bieber for his enlightening discussion on the cyclotronresonant acceleration. Special thanks go to R. B. Sheldon for his many constructive sug-gestions. I am grateful to J. B. Blake, J. Blecki, C. Z. Cheng, J. F. Fennell, T. A. Fritz, S. A.Fuselier, W. J. Heikkila, K. Kudela, C.-I. Meng, P. T. Newell, G. K. Parks, W. K. Peterson,J. Roeder, S. P. Savin, M. Schulz, D. Sibeck, G. L. Siscoe, H. E. Spence, W. N. Spjeldvik,J. D. Sullivan, K. J. Trattner and B. M. Walsh for helpful discussions. I cordially thank F. S.Mozer for providing the POLAR electric field data, J. S. Pickett for plasma wave data, C. T.Russell for the magnetic field data, and J. D. Scudder for the POLAR HYDRA data. I amgrateful for the POLAR, CLUSTER and WIND instrument teams, the ESA Cluster ActiveArchive, and the NASA’s open data policy that make the spacecraft data accessible for thepresent study.

References

Alfven, H. Nature1942, 150, 405.

Alfven, H. Cosmical electrodynamics;Clarendon Press, Oxford, 1950.

Antonova, A. E.; Gubar, Yu. I.; Kropotlin, A. P.Phys. Cham. Earth (C)2000, 25(1-2),47-50.

Bieber, J. W.; Chen, J.; Matthaeus, W. H.; Smith, C. W.; Pomerantz, M. A.J. Geophys.Res.1993, 98(A3), 3585-3603.

Biermann L.Z. Astrophys.1951, 29, 274.

Biermann L.Mem. Sco. Roy. Liege Quar., Ser.1953, 13, 291.

316 Jiasheng Chen

Biermann L.Observatory1957, 77, 109-110.

Blake, J. B.Czech. J. Phys.1999, 49(4a), 675-677.

Blecki, J.; Kossacki, K.; Wronowski, R. et al.Adv. Space Res.1999, 23(10), 1765-1768.

Buchner, J.Space Sci. Rev.2006, 124, 345-360.

Chapman, S.Mon. Not. R. Astr. Soc.1929, 89, 456-470.

Chapman, S.; Ferraro, V. C. A.J. Geophys. Res.1931, 36, 171-186.

Chen, J.Long-term modulation of cosmic rays in interplanetary magnetic turbulence;Ph.D. thesis, Univ. of Del., Newark, DE, 1989.

Chen, J.Ann. Geophys.2008, 26(7), 1993-1997.

Chen J.; Fritz, T. A.Geophys. Res. Lett.1998, 25(22), 4113-4116.

Chen J.; Fritz, T. A.Geophys. Res. Lett.1999, 26(19), 2921-2924.

Chen J.; Fritz, T. A.Int. J. Geomagnetism and Aeronomy2000, 2(1), 31-44.

Chen J.; Fritz, T. A.J. Atmospheric and Solar-Terrestrial Phys.2001a, 63(5), 463-472.

Chen J.; Fritz, T. A.Geophys. Res. Lett.2001b, 28(8), 1459-1462.

Chen J.; Fritz, T. A. InSolar-Terrestrial Magnetic Activity and Space Environment;Wang,H. N.; Xu, R. L.; Ed.; COSPAR Colloquia Series; Pergamon: Oxford, 2002a; Vol.14, 239-249.

Chen J.; Fritz, T. A.Adv. Space Res.2002b, 30(7), 1741-1748.

Chen J.; Fritz, T. A. InMultiscale processes in the Earth’s magnetosphere: From INTER-BALL to CLUSTER;Sauvaud, J.-A.; Nemecek, Z.; Ed.; NATO Science Series II.Mathematics, Physics and Chenistry; Kluwer Academic Publishers: Dordrecht, TheNetherlands, 2004; Vol. 178, pp 175-194.

Chen J.; Fritz, T. A.Surveys in Geophysics2005, 26(1-3), 71-93.

Chen J.; Bieber, J. W.; Pomerantz, M. A.J. Geophys. Res.1991, 96, 11569-11585.

Chen, J.; Fritz, T. A.; Sheldon, R. B.J. Geophys. Res. 2005, 110, A12219,doi:10.1029/2004JA010718.

Chen, J; Fritz, T. A.; Sheldon, R. B. et al.Geophys. Res. Lett.1997a, 24(12), 1447-1450.

Chen, J; Fritz, T. A.; Sheldon, R. B. et al.J. Geophys. Res.1998, 103(A1), 69-78.

Chen, S.-H.; Boardsen, S. A.; S. F. Fung, S. F. et al.J. Geophys. Res.1997b, 102(A6),11335-11347.

Cowling, T. G.Mon. Not. R. Astr. Soc.1934, 94, 39-48.


Delcourt, D. C.; Sauvaud, J.-A.J. Geophys. Res.1999, 104, 22635-22648.

Delcourt, D. C.;, H. V. Malova, H. V.; Zelenyi, L. M. et al.Earth, Planets and Space2005,57(2), 125-130.

Dungey, J. W.Phys. Rev. Lett.1961, 6, 47-48.

Farrell, W. M.; Van Allen, J. A.J. Geophys. Res.1990, 95(A12), 20945-20958.

Frank, L. A.J. Geophys. Res.1971, 76(22), 5202-5219.

Fritz, T. A.; Chen, J.; Siscoe, G. L.J. Geophys. Res.2003, 108(A1), 1028-1036.

Gloeckler G.; Ipavich, F. M.; Hamilton, D. C. et al.Geophys. Res. Lett.1986, 13(8),793-796.

Gonzalez, W. D.; Mozer, F. S.J. Geophys. Res.1974, 79(28), 41864194.

Gusev, A. A.; Jayanthia, U. B.; Pugachevac, G. I.; N.J. Schuchc, N. I.; Martind, I. M.;Spjeldvike, W. N.Advances Space Res.2006, 37(8), 1532-1537.

Heikkila, W. J.; Winningham, J. D.J. Geophys. Res.1971, 76(4), 883-891.

Kosik, J. C. InQuantitative Modeling of Magnetospheric Processes;Olson, W. P.; Ed.;Geophys. Monogr. Series, 1979; Vol. 21, pp 569-581.

Krieger, A. S.; Timothy, A. F.; Roelof, E. C.Sol. Phys.1973, 29(2), 505-525.

Marklund, G. T.; Blomberg, L. G.; C.-G. Falthammar, C.-G.; Erlandson, R. E.; Potemra,T. A. J. Geophys. Res.1990, 95(A5), 57675780, 1990.

Parker, E. N.Astrophys. J.1958a, 128, 664-676.

Parker, E. N.Rev. Mod. Phys.1958b, 30, 955-965.

Parker, E.J. Geophys. Res.1959, 64(11), 1675-1681.

Parker, E. N.Interplanetary dynamical processes;Interscience Publishers, New York,1963.

Petschek, H. E.;Proc. AAS-NASA Symp. Phys. Solar Flares, NASA-SP-50, 1963, p.425.

Pfaff, R.; Clemmons, J.; Carlson, C. et al.Geophys. Res. Lett.1998, 25(12) 2037-2040.

Pickett, J. S.; Gurnett, D. A.; Menietti, J. D. et al.Adv. Space Res.1999, 24, 23-33.

Pissarenko, N. E.; Kirpichev, I. P.; Lutsenko, V. N. et al.Phys. Chem. Earth (C)2001,26(1-3), 241-245.

Pomerantz, M. A.Cosmic rays;Van Nostrand Reinhold Company, New York, 1971.

Pugacheva, G. I.; Gusev, A. A.; Jayanthi, U. B.; Schuch, N. J.; Spjeldvik, W. N.J. Atmo-spheric and Solar-Terrestrial Phys.2005, 67(5), 479-487.

318 Jiasheng Chen

Reiff, P. H.; T. W. Hill, T. W.; Burch J. L.J. Geophys. Res.1977, 82(4), 479-491.

Roederer, J. G.Dynamics of Geomagnetically Trapped Radiation;Springer, New York,1970.

Savin, S.; Blecki, J.; Pissarenko, N. et al.Adv. Space Res.2002, 30(7), 1723-1730.

Sheldon R. B.; Spence, H. E.; Sullivan, J. S.; Fritz, T. A.; Chen, J.Geophys. Res. Lett.1998, 25(11), 1825-1828.

Sheldon R. B.; Fritz, T. A.; Chen, J. InParticle Acceleration in Astrophysical Plasmas:Geospace and Beyond;Gallagher, D.; Horwitz, J.; Perez, J.; Preece, R.; Quenby, J.;Ed; Geophys. Monogr. Series, 2005, Vol. 156, pp 197-204, DOI: 10.1029/156GM22.

Singer, S. F.Phys. Rev. Lett.1958, 1, 171-173.

Sonnerup, B. U. . InMagnetospheric Physics;McCormac, B. M.; Ed.; Astrophysics andSpace Science Library, Dordrecht: Reidel, Dordrecht-Holland, 1974; Vol. 44, p.23.

Spjeldvik W. N.; Rothwell, P. L. InHandbook of Geophysics and the Space Environment;Jursa, A. S.; Ed.; ADA 167000; Air Force Geophysics Laboratory: MA, 1985; pp5-34.

Stasiewicz, K.; Khotyaintsev, M.; Khotyaintsev, Y. (2003). Orbit Visualization Tool.http://ovt.irfu.se.

Stone, E. C.; Cummings, A. C.; McDonald, F. B.; Heikkila, B. C.; Lal, N.; Webber, W. R.Nature2008, 454, 71-74.

Tsyganenko, N. A.; Stern, D. P.J. Geophys. Res.1996, 101(A12), 27187-27198.

Van Allen, J. A.J. Geophys. Res.1959, 64(11), 1683-1689.

Van Allen, J. A.; Frank, L. A.Nature1959a, 183, 430-434.

Van Allen, J. A.; Frank, L. A.Nature1959b, 184, 219-224.

Walsh, B. M.; Fritz, T. A.; Lender, N.; Chen, J.; Whitaker, K. E.Ann. Geophys.2007,25(12), 2633-2640.

Whitaker, K. E.; Chen, J.; Fritz, T. A.Geophys. Res. Lett.2006, 33, L23105,doi:10.1029/2006GL027731.

Whitaker, K. E.; Fritz, T. A.; Chen, J.; Klida, M.Ann. Geophys.2007, 25(5), 1175-1182.

Yamauchi, M.; Andersson, L.; P.-A. Lindqvist, P.-A. et al.Phys. Chem. Earth (C)2001,26(1-3), 195-200.

Yamauchi, M.; Nilsson, H.; Eliasson, L. et al.J. Geophys. Res.1996, 101(A11), 24675-24687.

Yoshida, S.; Ludwig, G. H.; Van Allen, J. A.J. Geophys. Res.1960, 65(3), 807-813.

Reviewed by Robert B. Sheldon, NASA/MSFC/NSSTC/XD12, 320 Sparkman, Huntsville,AL 35805 USA.



Chapter 9

SOLAR WIND INTERACTION WITH ARTIFICIAL

ATMOSPHERES

L. Gargate1,∗, R.A. Fonseca1,2, R. Bamford3, R. Bingham3,4 and L.O. Silva1

1GoLP/Instituto de Plasmas e Fusao Nuclear,Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

2DCTI, Instituto Superior de Ciencias do Trabalho e da Empresa,Av. Forcas Armadas, 1649-026 Lisbon, Portugal

3Space Science & Technology Dept, Science & Technology Facilities Council,Rutherford Appleton Laboratory, Harwell Science and Innovation Campus,

Didcot, Oxon, OX11 0QX, UK4Physics Department, University of Strathclyde, Glasgow G4 0NG, UK

Abstract

Active experiments in space involving artificial atmospheres began with theAMPTE releases. In these seminal experiments, a cloud of Barium or Lithium wasreleased and photoionized by the UV radiation from the sun. The cloud expanded andinteracted with flowing solar wind, thus providing important data about pick-up ionbehaviour, diamagnetic cavity formation, and shock formation. More recently, sys-tems consisting of a dipole magnetic field and a plasma source are being consideredand studied in spacecraft propulsion, and as a spacecraft shield from Solar EnergeticParticles (SEP) from the sun [1].

We use a 3D massively parallel hybrid code to analyze the behaviour of such sys-tems in the presence of a plasma flow. The model is ideal to study artificial atmo-spheres interacting with the solar wind, covering the relevant physical scales, and al-lowing a kinetic treatment of the ions. Arbitrary density distributions, and arbitraryinitial velocity distributions can be set, while dynamic load balancing algorithms areused to guarantee parallel efficiency.

We focus our analysis in the differences between two distinct scenarios: the un-magnetized scenario of a plasma cloud expanding in the solar wind in the presence ofthe Interplanetary Magnetic Field (IMF), and the magnetized scenario of a laboratoryplasma flow shock against a dipole magnetic field structure. Our results show thatboth configurations effectively deflect the incoming plasma. The nature of the shocks

∗E-mail address: [email protected]

320 L. Gargate, R.A. Fonseca, R. Bingham et al.

formed in both situations is different, with a bow shock being formed in the first case,while in the second case there is a compression of the magnetic field, but no bow shockis observed. In the unmagnetized case, the diamagnetic cavity formation is the mostsignificant aspect, with the cloud particles producing the diamagnetic currents as theyexpand outwards due to their temperature. The dependency of the plasma standoffdistance with the plasma density, velocity, and with the dipole field intensity in themagnetized case is highlighted, and the relevance of these scenarios for the shieldingof spacecrafts is also addressed.

Key Words: artificial magnetospheres, solar wind, shocks, numerical simulations

1. Introduction

Active space experiments and in-situ measurements by satellites in space are important tounderstand the solar wind, the solar wind interaction with magnetospheres or planetary exo-spheres, and the space environment in general. Important phenomena like the rarefaction ofthe Martian atmosphere, the onset of geomagnetic storms, and the interaction of large-scalestructures (e.g. Coronal Mass Ejections, Interplanetary Shocks) with the Earth’s magne-tosphere, are better understood today thanks to numerous space missions, and to manydevelopments in theoretical knowledge, computing power, and simulation techniques.

The increase of computing power and the improvement of the simulation techniques hasled to a renewed interest in specific space plasma problems that can now be tackled withMHD codes, hybrid codes (with kinetic ions and fluid electrons), and fully kinetic codes.Simulations covering larger spatial and temporal scales, with increased resolution, can nowbe performed. One of the most interesting problems is the interaction of the solar wind withartificial magnetospheres, either in the traditional sense of a magnetosphere dominated by adipole magnetic field, or of a plasma cloud expanding in the solar wind. Of particular inter-est is the possibility of using such artificial magnetospheres to protect spacecrafts againsthigh-energy particles, mostly SEPs, motivated by recent results in the field suggesting theviability of such strategies [1].

Solar Energetic Particles are charged particles originating from the sun, mostly protonsand electrons, that can reach energies up to hundreds ofMeV or evenGeV in some extremescenarios. These SEP particles are hazardous to both spacecrafts (e.g. electronics, externalpanels), and to astronauts in space. The concept of spacecraft protection using artificialmagnetospheres is then an attempt to emulate what the Earth magnetosphere does naturallyfor our planet, using a small scale dipole field and a plasma source to create a shield againstcharged particles.

Similar plasma cloud and magnetic field configurations have also been considered forspacecraft propulsion in the Solar System [2, 3, 4]. In that context, experimental [5, 6, 7, 8]and simulation work has recently been performed, including detailed numerical simulationsof the expansion of a magnetic bubble in the absence of a plasma flow[9, 10].

A comprehensive study of how high energy particles are deflected by a magnetospherehas not yet been completed. It is an intricate problem, and even in the well studied case ofthe Earth, a full understanding of the mechanisms responsible for effective SEP deflectionis lacking: while it is known that some very energetic particles (tens of MeVs) penetrate themagnetopause and are trapped in the Earth radiation belt for very long periods, the physical

Solar Wind Interaction with Artificial Atmospheres 321

processes relevant for particle transport across the magnetopause are still a central objectof investigation. For a better understanding of the physics of the interaction of a plasmaflow with a magnetosphere, and with the objective of studying the feasibility of using mini-magnetospheres for spacecraft protection, we perform hybrid simulations of two relatedinteraction scenarios.

For the first part of our study, we focus on the analysis of the interaction of the solarwind with an unmagnetized plasma cloud, adopting parameters that allow for a comparisonof our results with the measurements from the AMPTE release experiments, as well as withprevious results from the numerical modeling of these experiments [11, 12, 13, 14, 15, 16].The AMPTE experiments consisted of several gas (Lithium and Barium) releases in the up-stream solar wind by a spacecraft orbiting the Earth [17, 18, 19]. After the release, the ex-panding cloud of atoms is photoionized by the solar ultraviolet radiation, thus producing anexpanding plasma and forming an obstacle to the flowing solar wind. In-situ measurementswere made by two additional spacecrafts and observations from ground-based stations werealso performed. Modeling the ion kinetics correctly is essential to understand how the solarwind ions are deflected around the plasma cloud and, furthermore, the problem is intrin-sically kinetic in nature due to the fact that the Larmor radius of the ions is of the orderof magnitude of the plasma cloud size. While MHD simulations do not capture kinetic ef-fects, fully kinetic simulations are computationally too demanding. In this sense, the hybridtechnique is ideal to model the problem, since the relevant ion kinetics is captured, whilehigh electron-scale frequencies and associated phenomena are neglected. We describe themost important features of the interaction, including the magnetic field buildup in front ofthe shock, the formation of a diamagnetic cavity, the solar wind behavior around the cloudexpansion zone, and the main distinctive features of the cloud expansion itself.

The second part of our study focuses on the deflection of a plasma beam by a mini-magnetosphere in the laboratory, and is directly comparable to laboratory experiments cur-rently underway [8]. In these experiments, a plasma beam, guided by an axial magnetic fieldin a cylindric chamber, hits a dipole magnetic field created by a permanent magnet. Recentexperimental and simulation results reveal the formation of a very sharp shock structure,and provide evidence of the beam deflection out of the magnetized cavity [1]. Modelingthe ion kinetics is crucial in this case too, although the plasma can become magnetized inthe regions adjacent to the dipole magnetic field origin, due to the sharp gradient in themagnetic field intensity of a dipoleB ∼ r−3. In order to understand the key parametersthat determine the mini-magnetosphere features, a parameter scan of the plasma density, theflow velocity and the dipole magnetic field intensity has been performed, giving a particularemphasis to the shock behavior, the distance of the magnetopause to the dipole field origin,and the behavior of the beam around the plasma-depleted region of the magnetic dipole.

A particle-in-cell [20, 21] hybrid code,dHybrid [22], is used for the modeling of the twointeraction scenarios. The code is a massively parallel three-dimensional kinetic ion, mass-less fluid electron code [24], allowing for arbitrary plasma configurations, external fields,and implementing a particle tracking algorithm that enables the individual particle informa-tion to be stored and analyzed. Resorting to the state-of-the-art visualization package of theosiris framework [23], we analyze and compare the features of both systems.

This paper is organized as follows. In the next section we describe the hybrid simulationmodel in detail, including the implementation indHybrid, and the main features of the code.


In section 3. we present the results of the unmagnetized plasma cloud expanding in the solarwind, and in section 4. we present the results of the magnetized laboratory scenario. Finally,in section 5., we present the conclusions.

2. The Hybrid Simulation Model

2.1. The Hybrid Model

Hybrid models are commonly used in many problems in plasma physics, and can includedifferent types of approximations, depending on the specific physical system considered[24]. The main assumption of hybrid models with kinetic ions and fluid electrons is that thedynamic scales of interest are those of the ions, while the dynamics of the electrons can beneglected to a lesser or higher degree. This translates in neglecting the displacement currentin Ampere’s Law, thus suppressing the propagation of electromagnetic waves traveling atthe speed of light, and considering an MHD model for the electrons, as well as assumingquasi-neutrality. Differences between various hybrid approximations depend mainly onwhether the effects of finite electron mass, resistivity, and electron pressure need to beincluded in the MHD equations. For the sake of completeness we present the main steps inthe derivation of the hybrid model implemented indHybrid.

We start from the Vlasov equation for the electrons,

∂ fe

∂ t+ ~ve · ~∇rfe −

e

m

(~E + ~ve × ~B

)· ~∇vefe = 0 (1)

wherefe is the electron distribution function,~ve is the electron velocity,~E the electric field,~B the magnetic field,e andm the electron charge and the electron mass, and~∇r and~∇ve

denote the gradients in physical space and in velocity space, respectively. The zeroth ordermoment is calculated by integrating eq. (1) in velocity space, the first term from the leftyielding ∂ n

∂ t , with n =∫

fed~ve the electron density, the second term yielding~∇r·∫

~vefed~ve,and the last term vanishing if we integrate by parts and make the usual assumptionfe → 0at±∞.

In the current version ofdHybrid, the effects of finite electron mass, resistivity andelectron pressure are not considered, although the code is already structured so as to makesuch generalization straightforward. In them → 0 limit, eq. (1), which yields the continuityequation for the zeroth order moment, reduces to

(~E + ~ve × ~B

)· ~∇vefe = 0 (2)

and its zeroth order moment is identically zero. The first order moment of eq. (2) is∫

~ve

(~E + ~ve × ~B

)· ~∇vefed~ve = 0

∫~ve

~∇ve ·[fe

(~E + ~ve × ~B

)]d~ve −

∫~vefe

~∇ve ·(

~E + ~ve × ~B)

d~ve = 0 (3)

where we have used the vector identity~∇ ·(f ~A

)= ~A · ~∇f + f ~∇ · ~A. The second integral

of eq. (3) vanishes since~∇ve ·(

~E + ~ve × ~B)

= 0, while the first integral of eq. (3) is


calculated by parts, the non-vanishing term yielding

∫fe

(~E + ~ve × ~B

)d~ve = 0

~E = −~Ve × ~B (4)

with ~Ve = 1n

∫fe~ved~v the electron fluid velocity. This last equation indicates that the

electric field is perpendicular to the local magnetic field, and arises from considering zeroinertia electrons that instantaneously short-circuit any parallel component of the electricfield.

In the hybrid approximation we now consider Ampere’s law without the displacementcurrent

~∇× ~B = µ0~J (5)

whereµ0 is the magnetic permeability,~J is the current density, and where~∇ is the usualgradient in physical space, to be used instead of~∇r from now on. The current is given by

~J = −n e ~Ve +nsp∑

i=1

qi

∫fi~vid~vi (6)

with qi the charge of speciesi, and where the sum is over all ion species present in thesystem. Substituting~Ve from eq. (6) in eq. (4), and~J from eq. 5 in eq. (6), the electric fieldbecomes

~E = −~Vi × ~B +1

neµ0

(∇× ~B

)× ~B (7)

where~Vi = 1n

∑nsp

j=1 Zj

∫fj~vjd~vj is the ion fluid velocity,Zj = qj/e is the relative charge

of the ion speciesj, and where we have assumed quasi-neutrality,n =∑nsp

j=1 Zjnj .Finally, the magnetic field can be obtained straightforwardly from Faraday’s law

∂ ~B

∂ t= −~∇ × ~E (8)

while the ion velocities are determined by the Lorentz force equation

d~vi

d t=

qi

M

(~E + ~vi × ~B

)(9)

and the ion positions are determined from

d~x

d t= ~vi (10)

whereM is the mass of the ions and~x the position of the ions. Equations (4) through (10)form the basis of the hybrid model implemented indHybrid; the numerical method for thesolution of this set of equations is described in the next paragraphs.


2.2. Implementation in dHybrid

The ion species indHybrid are represented by finite sized computational particles to bepushed in a 3D simulation box. The fields and fluid quantities, such as the densityn andthe ion fluid velocity~Vi, are interpolated from the particles using quadratic splines [25] anddefined on two 3D regular staggered grids [26]. The fields and fluid quantities are theninterpolated back to the position of the particles in order to push the ions using quadraticsplines, in a self-consistent manner.

All quantities are expresseed in normalized units: time is normalized to the inversecyclotron frequencyω−1

ci , space is normalized toc/ωpi, with ωpi = (n0 e2/(ε0 M))1/2 theion plasma frequency, charge is normalized to the proton chargee, the mass is normalizedto the proton massmp, and the velocities are normalized to the Alfven velocityvA =B0/

√µ0n0mp, whereB0 is the normalizing magnetic field, andn0 the normalizing density.

In these units, eq. (7) through eq. (10) can be rewritten, dropping the indexi for the ions,as

~E = −~V × ~B + 1n

(∇× ~B

)× ~B (11)

∂ ~B

∂ t= −~∇ × ~E (12)

d~v

d t= q

M

(~E + ~v × ~B

)(13)

d~x

d t= ~v (14)

The equations are advanced in time in finite steps∆t, and are discretized in space onthe two staggered grids, grid1/2 being displaced from grid1 by half cell size in each spatialdirection (∆x/2, ∆y/2, and∆z/2). Any quantityA can be transposed from one grid to theother by spatial averaging:

Ai+1/2,j+1/2,k+1/2 =18

(Ai,j,k + Ai+1,j,k + Ai,j+1,k + Ai+1,j+1,k+

Ai,j,k+1 + Ai+1,j,k+1 + Ai,j+1,k+1 + Ai+1,j+1,k+1) (15)

Derivatives are calculated by the finite differences method in order to be space centered;hence, calculating∂ A

∂ x , would yield

(∂ A

∂ x

)

i+1/2,j+1/2,k+1/2

=

=1

4∆x(Ai+1,j,k − Ai,j,k + Ai+1,j+1,k − Ai,j+1,k

+Ai+1,j,k+1 − Ai,j,k+1 + Ai+1,j+1,k+1 − Ai,j+1,k+1 ) (16)

meaning that a given quantity and its derivative are defined on different grids [24]. Fol-lowing this approach, the field equations (11) and (12) are solved numerically by the Lax-Wendroff algorithm [21, 24], which is then second order accurate in space and time, and is


space and time centered. The electric field is calculated in two steps:

~En+1/21/2 = −~V

n+1/21/2 × ~B

n+1/21/2 + 1

nn+1/21/2

(~∇× ~B

n+1/21

)1/2

× ~Bn+1/21/2 (17)

~En+11 = 2 ~E

n+1/21 − ~En

1 (18)

the superscriptsn + 1/2 andn + 1 denoting quantities calculated at timestn+1/2 = tn +∆t/2, and at timestn+1 = tn+∆t, and the subscripts1 and1/2 denoting quantities definedon grid 1 at the pointi, j, k and on grid1/2 at the pointi + 1/2, j + 1/2, k + 1/2. Whileeq. (17) is a direct discretization of eq. (11), eq. (18) uses values from eq. (17) displacedfrom grid1/2, and uses the electric field from the previous time step. The magnetic field isadvanced in time through

~Bn+1/21/2

= ~Bn1/2 −

∆t2

(~∇× ~En

1

)1/2

(19)

~Bn+11 = ~Bn

1 − ∆t(

~∇× ~En+1/21/2

)1

(20)

Finally, the Boris pusher scheme [27, 21] is used to advance the velocities in time; eq.(13) becomes

~v− = ~vn+1/2 + ~En+11/2

(∆t q

2M

)(21a)

~v′= ~v− + ~v− × ~Bn+1

1/2

(∆t q

2M

)(21b)

~v+ = ~v− + ~v′ × ~Bn+1

1/2

∆t q

2M

2

1 +∣∣∣ ~Bn+1

1/2

∣∣∣2 (

∆tq2M

)2

(21c)

~vn+3/2 = ~v+ + ~En+11/2

(∆t q

2M

)(21d)

and the discretization of eq. (14), for the position update, yields

~xn+3/2 = ~xn+1/2 + ∆t ~vn+1 (22)

where~vn+1 = 1/2(~vn+1/2 + ~vn+3/2

).

The numerical implementation of the hybrid model described above indHybrid is basedon the Message Passing Interface (MPI) routines [28]; the use of standard particle-in-cellalgorithm optimization schemes [25] along with state-of-the-art dynamic load balancingtechniques guarantees excellent parallel scalability up to hundreds of CPUs [22]. The 3Dsimulation space is divided across processes, and 1D, 2D and 3D domain decompositionsare possible. Using the dynamic load balancing capabilities ofdHybrid, the simulationspace is redistributed across processes during any simulation, in order to maintain similarcomputing loads across nodes; speedups of up to 40% are observed for runs with unevenparticle distributions, as in the present case.

The code can simulate an arbitrary number of particle species with arbitrary charge tomass ratios, arbitrary initial thermal velocity and drift velocity distributions, as well as ar-bitrary spatial configurations. Periodic boundary conditions, open boundary conditions and


Figure 1. Magnetic field vectors, magnetic field iso-surfaces, and magnetic field projectionsat a)t = 2.22 ω−1

ci , b) t = 11.08 ω−1ci , and c)t = 19.94 ω−1

ci .

configurable particle injectors can be used for the particles, and periodic boundary condi-tions are used for the fields. The code also includes particle tracking capabilities, which areof particular relevance for the problem at hand. To take full advantage of particle tracking,a simulation is typically ran twice: the first time all usual diagnostics can be analyzed (e.g.electric field, magnetic field, fluid phase spaces), and a special kind of diagnostics, the rawdiagnostics, are produced. In these raw diagnostics, a sample of raw simulation particles isstored at given intervals, including the positions, the velocities, and the charge. A sample ofthese particles is then chosen according to specific, problem-dependent criteria (e.g., parti-cles within a given energy interval and/or spatial region), and the list of particles is suppliedas an input for the second run, which then provides a detailed time-resolved information onthe phase-space dynamics of the selected particles.

In the physical scenarios considered here, particle tracking allows for the determinationof how particles behave near the shock structures formed by the plasma cloud expansion,and by the dipole magnetic field in the laboratory phase.

3. Plasma Cloud Interaction with the Solar Wind

In the AMPTE release experiments, clouds of Lithium or Barium were released in theupstream solar wind, which is essentially a proton/electron plasma. The gas cloud expandeddue to its temperature, while particles were photo-ionized by solar UV radiation. For theLithium releases, the cloud expands much farther into the solar wind than the Barium cloud,since the Lithium atoms take much more time to ionize than the Barium atoms. The IMFfrom the sun was the only external magnetic field source in this case. In our 3D simulationbox, the solar wind propagates in the+x direction, the magnetic field is oriented in the+zdirection, and a pre-ionized Lithium cloud expands from a point at40% the box size in thex direction, and centered in they andz directions.

Results are presented in normalized units, the density normalized ton0 = 5 cm−3, thespatial dimensions normalized toc/ωpi ≈ 102 km, the time normalized toω−1

ci ≈ 4.53 s,


Figure 2. Magnetic field intensity cut along thex y plane atz = 75 c/ωpi for: a) t =2.22 ω−1

ci , b) t = 11.08 ω−1ci , and c)t = 19.94 ω−1

ci .

Figure 3. Electric field vectors, electric field iso-surfaces, and electric field projections at a)t = 2.22 ω−1

ci , b) t = 11.08 ω−1ci , and c)t = 19.94 ω−1

ci .

the velocities normalized tovA ≈ 22.5 km s−1, the magnetic field normalized toB0 =2.3 nT, and the electric field normalized toB0 vA ≈ 0.0516 mVm−1. The box size isL = 150 c/ωpi ≈ 15000 km ≈ 41 rLsw in each dimension, withrLsw the solar windLarmor radius, and(300)3 grid cells are used, yielding a cell size of∆ = 0.5 c/ωpi ≈51 km ≈ 0.14 rLsw. The time step is∆t ≈ 0.0022 ω−1

ci ≈ 0.01 s ≈ 3.5 × 10−4 TLsw,whereTLsw is the solar wind ion gyro period, and the simulation is run up to10000 timesteps, which results in a total simulation timeT ≈ 22 ω−1

ci ≈ 100 s ≈ 3.51 TLsw. We use8 particles per cell to model the solar wind plasma, and around 2 million particles to modelthe Lithium cloud.

The background magnetic field in the simulation isB = 1 (≈ 2.3 nT), and the solarwind plasma is distributed uniformly across the box with a densitynsw = 1

(≈ 5 cm−3

), a

drift velocity of Vsw = 3.59(≈ 80.5 km s−1

), and a temperature ofT = 0.78 eV, yielding

a kinetic to magnetic pressure ratioβ ≈ 0.3. The Lithium ions in the plasma cloud aresingly ionized and are initialized in a sphere of radiusrLi = 4 c/ωpi with a gaussian densityprofile with peak densitynLi ≈ 56000 n0e, and a temperatureT = 15.5 eV.

The most striking feature of the system is the magnetic field behavior as the cloud ex-


Figure 4. Electric field intensity cut along thex y plane atz = 75 c/ωpi for: a) t =2.22 ω−1

ci , b) t = 11.08 ω−1ci , and c)t = 19.94 ω−1

ci .

Figure 5. Fluid velocity vectors, fluid velocity iso-surfaces, and fluid velocity projectionsat a)t = 2.22 ω−1

ci , b) t = 11.08 ω−1ci , and c)t = 19.94 ω−1

ci .

Figure 6. Fluid velocity intensity cut along thex y plane atz = 75 c/ωpi for: a) t =2.22 ω−1

ci , b) t = 11.08 ω−1ci , and c)t = 19.94 ω−1

ci .


Figure 7. Charge density slice along thex y plane atz = 75 c/ωpi at a)t = 2.22 ω−1ci , b)

t = 11.08 ω−1ci , and c)t = 19.94 ω−1

ci . The solar wind charge density is represented in blue,and the Lithium plasma cloud charge density is represented in red.

pands. Figure 1 shows the magnetic field evolution including the magnetic field vectors,iso-surfaces and projections, and figure 2 shows ax y plane cut of the magnetic field inten-sity at z = 75. The magnetic field present at the beginning (frame a) is mostly the IMFfield. As the cloud expands, the IMF is pushed out of the cloud expansion zone; the mag-netic field vectors are bent, a compression zone is formed in the upstream side of the shock,and a low magnetic field zone, a diamagnetic cavity, is formed in the downstream side ofthe shock. Figure 2 at later time steps, frames b and c, shows a clear asymmetry betweenthe +y side of the expansion and the−y side of the expansion, and with the maximummagnetic field intensity over1.8, while the minimum magnetic field intensity is below0.5.

To understand the overall behavior of the system we analyze the evolution of both theelectric field and the fluid velocity of the ions. From the inspection of the electric field infigure 3 and in figure 4, we see that outside of the cloud expansion zone the electric fieldvectors point in the+y direction. This is in agreement with eq. (7), since the plasma isflowing in the+x direction so that−~Vi × ~B points in the+y direction, and the magneticfield in this zone is uniform so that~J = ~∇× ~B, in the second term of the same equation, ismostly zero.

The electric field vectors in the plasma cloud dominated zone are curved in the counter-clockwise direction (figure 4), and the electric field intensity grows from the center of thecloud outwards. This is associated with the temperature-driven expansion of the plasmacloud. Figures 5 and 6 show an increase of the ion fluid velocity from the center of thecloud outwards, which is due to the fact that hotter ions diffuse outwards faster from theirinitial positions. Hence, the−~Vi × ~B term once again explains both the counter-clockwisedirection of the electric field and the electric field intensity growth outwards.

The spatial uniformity of the electric field, magnetic field, and plasma flow velocity anddensity, in the solar wind dominated zone, contrasts with the non-uniformity of the electricfield in the plasma cloud expansion zone. In the later case, the spatial variation of theelectric field yields a non-vanishing~∇× ~E that drives the evolution of the magnetic field intime according to Faraday’s law, eq. (12). The time evolution of the magnetic field resultsin the spatial non-uniformity of~B: the magnetic field enhancement in the−x side and themagnetic field depletion on the+x side. The~B field non-uniformity in the cloud zone canthen be interpreted as a current system, owing to~J = ~∇ × ~B, that acts as a diamagnetic


Figure 8. Slice along thex y plane atz = 75 c/ωpi showing the magnetic field intensity,and a representative sample of particle tracks from the solar wind (red color table), andfrom the Lithium plasma cloud ions (blue color table). The line colors represent the energyof the particles.

current on the downstream side of the cloud.

The solar wind ions are affected by the electromagnetic structures formed by the cloudexpansion, and the most visible effect is the asymmetry along they axis, which can beexplained by the electric field configuration outside of the cloud zone and at the boundariesbetween the two zones. Looking at the electric field from figure 4, and at the charge densityfrom figure 7, it can be seen that ions escape from the cloud mainly in the+y side due tothe IMF-generated electric field that points in this direction. Also, the electric field pointsin opposite directions at the shock front boundary, leading to turbulence.

Figure 7 also shows that the solar wind plasma is pushed out of the region where theLithium plasma cloud dominates, forming a density bump that propagates outwards just infront of the plasma cloud expansion. This outer shock drives a smaller electric field presentjust outside the cloud boundary, seen in figure 4 to point in the+x direction on the−y sideof the cloud. This electric field accelerates the solar wind ions present in this region, as canbe observed in figure 6, while in the opposite side of the cloud it has a decelerating effect.

The trajectories of a sample of particles from the solar wind and from the Lithium cloudcan be observed in figure 8. They axis asymmetry is evident once more in the solar windparticle trajectories that stream along the−y side of the cloud, while particles impacting athighery are decelerated or back-scattered. The Lithium ions, on the other hand, escape thecloud in the+y side, are picked up by the solar wind, and start to drift downstream.

These results demonstrate that the solar wind is effectively stopped from entering theLithium dominated zone. This would not be expected if we reasoned that a charged particlewould be deflected only when its Larmor radius is small compared with the distance to thecentral object. In fact, in the unmagnetized scenario where the Larmor orbits are of the same


Figure 9. Density slice in thex y plane atz = 0.335 c/ωpi, in the middle of the simulationbox, for times a)t = 0.0952 ω−1

ci , b) t = 0.238 ω−1ci , and c)t = 0.381 ω−1

ci .

order of magnitude of the central object (the cloud in this case, or the magnetic dipole fieldin the case described in the next section), this over-simplistic view must be abandoned. Thisaspect will be further explored in the next section, where we relate plasma flow deflectiondistances to the magnetic field intensity and plasma parameters such as the density and theplasma flow velocity.

4. Mini-magnetosphere in the Laboratory

Recent laboratory experiments were setup with the specific aim of studying particle de-flection mechanisms, and studying the feasibility of protecting a spacecraft using a mini-magnetosphere [8]. In the final proposed configuration, the mini-magnetoshpere consists ofa dipole magnetic field and a plasma source; the purpose of the plasma source is to expandthe dipole magnetic field, which usually decays asr−3, so that the decay isr−α with α ∼ 1,thus increasing the efficiency of particle deflection [1].

In the current phase of the laboratory experiments, the dipole magnetic field is generatedby a permanent magnet, and there is no plasma source inflating the magnetic field. Acylindrical magnet with radiusrM = 13.5 mm is placed in a vacuum chamber, where itproduces a magnetic field with a peak intensity ofBmax ≈ 0.2 T at the edge of the magnet.A quasi-neutral proton/electron plasma beam with a number density ofnb = 1012 cm−3, abulk velocity of Vb = 400 km s−1, and a ion temperature ofTb = 5 eV, is then guided byan axial background magnetic field of intensityBb = 0.02 T towards the magnet.

For these reference parameters, the plasma flow has an acoustic Mach number ofMac =12.91, an Alfvenic Mach number ofMa = 0.92, and the Larmor radius of the ions isrLb ∼ 11.4 mm, which corresponds torLb/rM = 0.85. The hybrid simulation method isthen ideal for this configuration, since the ions are mostly unmagnetized in regions far fromthe magnet, and thus require a kinetic treatment.

Three sets of simulations were run in order to scan the dependency of the plasma stand-off distance, at the nose of the magnetopause in the beam propagation direction, withvarying magnetic field intensity, beam plasma density, and plasma flow velocity. Sim-ple MHD theory considers that the total pressure is conserved across the magnetopause,[p + B2/2

]= 0, where the first term is the plasma kinetic pressure and the second term is


Figure 10. Density slice (top panel), and fluid velocity slice (bottom panel), in thex y planeat z = 0.355 c/ωpi, in the middle of the simulation box, for timet = 0.2 ω−1

ci . The leftframes show the results for the reference simulation run, withVb = 0.92, and the rightframes show the results for a run with the same parameters but withVb = 2.84.

the magnetic pressure, and predicts that the distance from the magnetopause to the dipoleorigin is given by

rmp =(

K B2

2 n M V 2

)1/6

(23)

whereB is the magnetic field intensity at the edge of the magnet,n is the density,M isthe ion mass (protons),V is the flow velocity of the plasma, and the parameterK is afree parameter of the theory accounting for the non-ideal specular reflection of the particleswhen hitting the magnetopause and deviations of the magnetic field intensity from its dipolefield values [1, 29].

In our simulations the plasma flows along the background magnetic field in the+xdirection, and the magnetic dipole is centered in the middle of the simulation box, withthe magnetic moment vector aligned along the+z direction. The results presented arenormalized to the simulation units, the density normalized ton0 = 1012 cm−3, the spatialdimensions normalized toc/ωpi ≈ 22.76 cm, the time normalized toω−1

ci ≈ 0.52 µs, thevelocities normalized tovA ≈ 436 km s−1, the magnetic field normalized toB0 = 0.02 T,


Figure 11. Distance of the mangetopause to the dipole origin,rmp, as a function of themagnetic field intensity at the edge of the permanent magnet. The solid line representsthe theoretical prediction, eq. (23). The triangles represent the values measured in thesimulations, with the error bars describing the resolution of the simulation. Reproducedfrom [1], courtesy of IOP publishing.

and the electric field normalized toB0 vA ≈ 8732 Vm−1. The box size is0.89 c/ωpi ≈20.35 cm ≈ 17.83 rLb in thex direction,0.67 c/ωpi ≈ 15.26 cm ≈ 13.37 rLb in they andz directions, and80×60×60 grid cells are used, yielding a cell size of∆ ≈ 0.011 c/ωpi ≈2.5 mm ≈ 0.22 rLb. The time step is∆t ≈ 9.52× 10−7 ω−1

ci ≈ 0.5 ps ≈ 1.52× 10−7 TLb,and the simulation is run up to400 k time steps, which results in a total simulation timeT ≈ 0.38 ω−1

ci ≈ 0.2 µs ≈ 0.06 TLb. We use27 particles per cell to model the beam.

The reference simulation for our parameter scans is the run reproducing the laboratoryparameters. We can see in figure 9 a cut of the density evolution of the plasma beam forthis run. At early times, the magnetic dipole field acts as a magnetic piston, and the plasmais expelled from the most intense magnetic field region near the dipole origin. Here, thedipole magnetic field plays the role of the Lithium cloud in the previous section, while theplasma beam plays the role of the solar wind. At some point during the early stages ofthe simulation, the beam kinetic pressure equalizes the outward magnetic pressure, and themagnetopause is formed according to eq. (23). A direct measurement ofrmp in the labora-tory yieldedrmp = 28.5 mm, and the same measurement in the reference simulation yieldsrmp = 26.7 mm± 2.5 mm, showing a good agreement between the two. The uncertaintyin the simulation measurement is due to the simulation grid cell size.

Figure 10 shows a comparison between the reference run, and a run with the sameparameters butVb = 2.84 vA, highlighting the bow shock shape and the fluid velocityvectors. The width of the bow shock is narrowed in the transverse direction, in the secondrun, comparing to the reference run, but the qualitative behavior of the two scenarios is


Figure 12. Dependence of the distance of the magnetopause to the dipole origin,rmp, on thedensity of the plasma flow, for the baseline simulation parameters. The solid line representsthe theoretical prediction, eq. (23). The triangles denote the simulation results, with theerror bars describing the resolution of the simulation. Reproduced from [1], courtesy ofIOP publishing.

very similar. In particular, there is a particle flow, present in both cases, that penetrates tosome degree the bow shock boundary and that enables some particles to enter the density-depleted zone. Looking at the velocity vectors in the central region also indicates that thislow density plasma is turbulent, and the observation of the same behavior in both casesindicates that the phenomenon represents a characteristic feature of the problem, and not anumerical artifact due to the specific plasma parameters used. A similar effect is observed inthe laboratory experiment [1], where particles penetrate the bow shock through a magneticcusp; however, as a definite physical explanation for the phenomena is lacking, it is nottrivial to infer a relation between the two observations.

In the first simulation scenario, we have scanned the magnetic field intensity, with themagnetic field on the edge of the magnet varying from0.01 T to 0.4 T, while keeping thereference run plasma parameters fixed. In figure 11,rmp measured in the simulation is com-pared with the theoretical prediction from eq. (23). The qualitative behavior is obtained,but some quantitative discrepancies are visible, with better agreement being obtained forlower magnetic pressures.

Scanning the distancermp as a function of the plasma density, figure 12, the qualitativebehavior is recovered, with a slight deviation from the theoretical model, as in the previousscenario. For the plasma densities scanned, theβ’s range from0.005 to 0.5. The scalingrmp ∝ n−1/6, from eq. (23), indicates thatrmp depends weakly on the density, while itis strongly affected by variations of the magnetic field,rmp ∝ B1/3, and by variations ofvelocity, rmp ∝ v−1/3, which means that more significant changes ofrmp are observed in


Figure 13. Distance of the magnetopause to the dipole origin,rmp, as a function of theplasma flow velocity, for the baseline simulation parameters. The solid line represents thetheoretical prediction, eq. (23). The triangles denote the simulation results, with the errorbars describing the resolution of the simulation. Reproduced from [1], courtesy of IOPpublishing.

these cases for our parameter scan, and for our numerical parameters.Finally, in the third scenario, the velocity of the solar wind was varied from30.97 km/s

up to1548 km/s, corresponding to acoustic Mach numbers fromMac = 1 to Mac = 50and Alfvenic Mach numbers fromMa = 0.07 to Ma = 3.5. The results, depicted in figure13, follow the same behavior as in the previous scenarios, with a small deviation from thetheoretical values for most of the measured points. For all the simulation scenarios the valuefor K, in eq. (23), wasK = 6.09 × 10−12 m6 adjusted from the data. This value forK

implies that the particles are mostly specularly reflected at the nose of the magnetopause.A thorough discussion of the meaning of this value forK can be found in [1].

The discrepancies between measured simulation values and the theoretical values of eq.(23) are associated with the simplifying assumptions of the theoretical model. In particular,in the derivation of eq. (23), the thermal pressure is neglected, and the Rankine-Hugoniotshock jump conditions are implicitly used [29]. Neglecting the thermal pressure causesdeviations for low values of the velocityV observed in figure 13, and the use of the Rankine-Hugoniot jump conditions implies considering a simple one fluid magnetohydrodynamicsmodel, which has limited applicability in this problem, as finite Larmor radius effects arenot negligible.

5. Discussion and Conclusions

We have analyzed two different plasma interaction scenarios, relevant for ongoing researchon spacecraft protection against energetic charged particles. Unlike the case of the solar


wind interaction with a planetary magnetosphere, such as the Earth magnetosphere whererLsw/r⊕ ∼ 0.01 (r⊕ ≡ radius of the Earth), the Larmor radius of the solar wind ions andthe Larmor radius of the beam protons are of the same order of magnitude of the systemsizes. While in the Earth/solar wind case MHD simulations can model most phenomena ofinterest on a global scale, the same does not hold true for these smaller systems [30].

The numerical modeling of the AMPTE release experiments, as analyzed in section3., shows that a thermally expanding plasma cloud is capable of effectively deflecting thesolar wind. The expansion of the cloud against the incoming solar wind compresses andenhances the magnetic field at the shock interface, while the magnetic field downstream isdepleted and a diamagnetic cavity is formed. The solar wind particles are deflected mostlysideways, in the−y direction, and some of these particles are accelerated up to twice theirinitial bulk velocity, due to the electric field generated by the radially propagating plasmacloud.

In the laboratory scenario, the dipole magnetic field acts as a magnetic piston to create aplasma depleted cavity, as in the cloud expansion case. In this case the differences betweenthe experimental setup and typical space plasma parameters should be considered. The twomain differences reside in the number density of the solar wind, typically≈ 5 cm−3 at 1AU, and in the typical value for the IMF which is≈ 10 nT at 1 AU, representing muchlower values than the ones used in the laboratory. These differences result in a plasmaβ ∼ 0.4, and a typical acoustic Mach number ofMac ∼ 7.3, and an Alfvenic MachnumberMa ∼ 4.6, that should be compared with values ofβ ∼ 0.005, Mac ∼ 12.9, andMa ∼ 0.9, respectively, for the laboratory case. Assuming that the magnetic field intensitiesof a system on-board of a spacecraft can be of the order of magnitude of the ones tested inthe laboratory, the system should stop the incoming solar wind at longerrmp, according toeq. (23), by a factor of(n/nsw)1/6 ∼ 76 resulting in a standoff distance of a few meters.

In order to push the concept of the mini-magnetosphere further, the injection of plasmain the region of the dipole field to expand the magnetic field has to be considered. Thisplasma injection can result in a change of the decay law fromr−3 to r−α, with α ∼ 1, asoutlined before. An estimate of operating parameters for this configuration is calculatedbased on the requirement of deflecting1 MeV protons and considering a magnetic fieldintensity decay ofr−1. For efficient reflection, we require the Larmor radius to be a fraction,f ∼ 20%, of the distance of the proton to the spacecraft, yielding a magnetic field intensityof 0.72 T generated by a current loop withr = 1 m, corresponding to a magnetic momentM ∼ 7.2× 106 A m2.

The above estimates provide only a crude approximation; our results indicate that therequirements for the magnetic field intensity can be relaxed in the self-consistent configu-ration. As observed in both simulation scenarios, even whenrLsw andrLb are comparable,respectively, to the radius of the cloud and tormp, the incoming plasma is efficiently de-flected.

Future work on the subject will focus on the behavior of a mini-magnetosphere in aspace plasma environment, accounting for the much lower density of the solar wind. Theinjection of plasma and the expansion of the dipolar magnetic in the presence of the solarwind flow will also be tested. The deflection of energetic particles by these systems will beconsidered, resorting to test particles and following particle trajectories in time, thus provid-ing information that will allow for a detailed assessment of the role of mini-magnetospheres


in the space environment.

Acknowledgments

This work was supported by Fundacao para a Ciencia e a Tecnologia (FCT/Portugal) undergrants SFRH/BD/17750/2004 and POCI/66823/2006. The simulations presented in thispaper were produced using the IST Cluster (IST/Portugal).

References

[1] L. Gargate, R. Bingham, R. A. Fonseca, R. Bamford, A. Thornton, K. Gibson, J.Bradford, L. O. Silva,Plasma Phys. Control. Fusion 50, 074017, 2008

[2] R. M.Winglee, J. Slough, T. Ziemba, A. Goodson,J. Geophys. Res., 105(A9), 21067,2000

[3] J. T. Mendonca, A. L. Brinca, R. Fonseca, J. Loureiro. L. O. Silva, I. Vieira,J. ofPlasma Phys. 71, 4, 495, 2005

[4] J. Loureiro, J. T. Mendonca, A. L. Brinca, R. Fonseca, L. O. Silva, I. Vieira,J. ofAtmosph. and Solar-Terrestrial Phys. 67, 14, 1315, 2005

[5] T. Ziemba, R. Winglee, P. Euripides, J. Slough,43rd APS DPP meeting, KP1.061,2001

[6] R. M. Winglee, T. Ziemba, P. Euripides, J. Slough,AIP Conference Proceedings, 608,433, 2002

[7] I. Funaki, H. Kojima, H. Yamakawa, Y. Nakayama, Y. Shimizu,Astrophysics andSpace Science, 307, 1-3, 63, 2007

[8] R. Bamford, K. J. Gibson, A. T. Thornton, J. Bradford, R. Bingham, L. Gargate, L.O. Silva, R. A. Fonseca, M. Hapgood, C. Norberg, T. Todd, R. Stamper,35th EPSConference Proceedings,Plasma Phys. Control Fusion , in press

[9] D. Winske, N. Omidi,Phys. of Plasmas 12, 072514, 2005

[10] H. Tang, J. Yao, H. Wang, Y. Liu,Phys. of Plasmas 14, 053502, 2007

[11] F. Kazeminezhad,Hybrid Modeling of Plasmas and Applications to Fusion and SpacePhysics, UCLA PhD thesis, 1989

[12] A. Valenzuela, G. Haerendel, H. Foeppl, F. Melzner, H. Neuss,Nature, 320, 700, 1986

[13] G. Haerendel, G. Paschmann, W. Baumjohann, C. W. Calrson,Nature, 320, 720, 1986

[14] S. C. Chapman, S. J. Schwartz,J. Geophys. Res. 92(A10), 11059, 1987

[15] J. B. Harold, A. B. Hassam,Geophys. Res. Letters 18 (2), 135, 1991


[16] P. A. Delamere, D. W. Swift, H. C. Stenbaek-Nielsen,Geophys. Res. Letters 26 (18),2837, 1999

[17] P. A. Bernhardt, R. A. Roussel-Dupre, M. B. Pongratz, G. Haerendel, A. Valenzuela,D. A. Gurnett and R. R. Anderson,J. Geophys. Res. 92(A6), 5777, 1987

[18] A. B. Hassam and J. D. Huba,Geophys. Res. Letters 14, 60, 1987

[19] R. Bingham, V. D. Shapiro, V. N. Tsytovich, U. de Angelis, M. Gilman and V. I.Shevchenko,Phys. Fluids B 3, 1728, 1991

[20] J. M. Dawson,Rev. Mod. Phys. 55, 403, 1983

[21] C. K. Birdsall, A. B. Langdon,Plasma Physics Via Computer Simulation, Institute ofPhysics Publishing , Bristol and Philadelphia, 1998

[22] L. Gargate, R. Bingham, R. A. Fonseca, L. O. Silva,Comp. Phys. Commun., 176, 419,2007

[23] R. A. Fonseca, L. O. Silva, F. S. Tsung, V. K. Decyk, W. Lu, C. Ren, W. B. Mori, S.deng, S. Lee, T. katsouleas, J. C. Adam,Lecture Notes on Computer Science 2331,342, Springer-Verlag, Heidelberg, 2002

[24] A. S. Lipatov, The Hybrid Multiscale Simulation Technology, Springer, 2002

[25] V. K. Decyk, S. R. Karmesin, A. de Boer, P. C. Liewer,Comp. in Phys., 10 (3), 1996

[26] K. S. Yee,IEEE Trans. Ant. Prop. 14 (3), 302, 1966

[27] J. P. Boris,Proc. Fourth Conf. Num. Sim. Plasmas, Naval Res. Lab, 3-67, 1970

[28] M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra,MPI - The CompleteReference, MIT press, 1999

[29] W. Baumjohann, R. A. Treumann,Basic Space Plasma Physics , Imperial CollegePress, 2004

[30] F. Kazeminezhad, J. M. Dawson, R. Bingham,J. Geophys. Res. 98 (A6), 9493, 1993

SHORT COMMUNICATIONS


Short Communication A

SOLAR RADIATION OVER DONGOLA, NORTHERN SUDAN

Abdeen Mustafa Omer1 Nottingham, Nottinghamshire, United Kingdom

Abstract

A number of years worth of data concerning the solar radiation on a horizontal surface and sunshine duration at Dongola, Northern Sudan have been compiled, evaluated and presented in this short communication. Measurements of global solar radiation on a horizontal surface at Dongola for a whole year are compared with predictions made by several independent methods. In the first method, Angstrom formula was used to correlate relative global solar irradiance to the corresponding relative duration of bright sunshine. Regression coefficient are obtained and used for prediction of global solar irradiance. The predicted values were consistent with measured value (±6% variation). In the second method, by Barbaro et al. (1978) sunshine duration and minimum air mass were used to derive an empirical correlation for the global radiation. The predicted values compared well with measured values (±6% variation). The diffuse solar irradiance is estimated using Page’s, Lui and Jordan’s correlations. The results of the two formulas have a close agreement. The annual daily mean global radiation ranges from 5.27 to 7.65 kW h m-2 per day. It is concluded that Northern Sudan is enjoyed with abundant solar energy.

Keywords: Dongola, Sudan, global solar radiation, diffuse radiation prediction

Abbreviations

H The monthly mean daily global irradiance on a horizontal surface Ho Extraterrestrial irradiation on a horizontal plane

1 Correspondence to: 17 Juniper Court, Forest Road West, Nottingham NG7 4EU, Nottinghamshire, United

Kingdom, Tel.: (0115) 9787179, Fax: (0115) 9513159, E-Mail: [email protected]

Abdeen Mustafa Omer

342

a and b Regression constant ‘‘Empirical constants’’ Angstrom coefficients calculated from regression technique

n Monthly average of daily hours of bright sunshine duration N The maximum possible daily hours of bright sunshine (i.e., the length of the

average day of the month) n/N The fraction of the maximum possible number of bright sunshine hours H/Ho The atmospheric transmission coefficient Φ The latitude, and δ the solar declination ω The sunset, sunrise hour angle, in degrees Is The solar constant (1367 W/m2) KT The ratio of cloudiness index or transmission coefficient Sn The solar elevation at noon

1. Introduction

Solar radiation arriving on earth is the most fundamental renewable energy source in nature. It powers the bio-system, the ocean and atmospheric current system and affects the global climate. Reliable radiation information is needed to provide input data in modelling solar energy devices and a good database is required in the work of energy planners, engineers and agricultural scientists (Sayigh, 1987). In general, it is not easy to design solar energy conversion systems when they have to be installed in remote locations. Firstly, in most cases, solar radiation measurements are not available for these sites. Secondly, the radiation nature of solar radiation makes difficult the computation of the size of such systems.

While solar energy data are recognised as very important, their acquisition is by no means straightforward. The measurement of solar radiation requires the use of costly equipment such as pyrheliometers and pyranometers. Consequently, adequate facilities are often not available in developing countries (Sudan is no exception) to mount viable monitoring programmes. This partly due to the equipment cost and also the cost of technical manpower. Several attempts have, however, been made to estimate solar radiation through the use of meteorological and other physical parameter in order to avoid the use of expensive network of measuring instruments.

In recent years, solar energy utilisation in various applications (both solar thermal and photovoltaics (PVs)) has increased significantly. Applications involving solar thermal energy include air and water heating whilst solar PV systems have been installed to provide electricity for households mainly in rural areas. In Sudan, several research institutions have initiated research at various stages on the applications of solar energy in various industrial processes (NEA, 1985; ERI, 1997). However, the availability of monthly global solar radiation data required in solar thermal designs is very limited. The high cost of solar radiation equipment is still unaffordable by most institutions involved in solar energy research and development activities. Hence, adequate and relatively accurate solar radiation data are often not readily available in locations of interest. As a consequence, the solar systems installed often do not reflect the optimum designs.

The design and estimation of the performance of all solar energy systems require the knowledge of solar radiation data, which have been measured over a long period of time. The solar radiation measurements are very important in order to establish a complete solar map for

Solar Radiation over Dongola, Northern Sudan

343

Sudan. These data are not only useful for the country under consideration but also for many other countries. This is needed for two main reasons: (1) The possibility of plotting solar radiation maps for the whole world through the availability of the required data for all countries of the world, and (2) The manufacturers of solar devices require the knowledge of solar radiation data in the different locations. This is most important in order to design such devices to suit the climate and to open new markets accordingly.

Solar radiation data are not easily available for many countries. Many countries cannot afford the measurement equipments and techniques involved. The solar equipments needed for these purposes are expensive and require maintenance as well as frequent calibrations (Omer, 2007). Moreover, it is almost impossible to scan all the country and get reliable day-by-day solar radiation data. Therefore, this work is an effort to find out reliable methods for prediction of solar radiation data with minimum possible measurements.

For the sizing of a solar system using total solar radiation (flat plate thermal solar collector or photovoltaic (PV) modules), or to estimate its productivity, many engineers use daily or hourly solar irradiation data. But, in many cases as for instance mathematical simulation of solar energy processes, these values are not sufficient because they do not provide a precise idea of the different energy phenomena, which take place in the heart of the production system (inertia phenomenon, shadowing masks, etc.). For example, for the sizing of a stand-alone PV system, knowledge of the load is required and this load is sometimes known with a time step interior to one hour; it is then necessary to transform this load profile into hourly data, which leads to the loss of information (Omer, 1990).

In various studies of solar energy systems (sizing and estimation of production), solar irradiation data collected is needed. The work presented in this study is discussing the prediction of the global solar radiation at Dongola town (latitude 19o 10’N, longitude 30o 29’E and altitude 225 m), using measured data. It discusses also the estimation of the diffuse solar radiation out of the global values. Dongola was selected as a representative site due to its location in the north of Sudan where there is no mountains and clouds. In this study the monthly average daily global solar radiation correlation applicable to the Sudanese climatic region is presented. The correlation used is based on the meteorological data collected from Meteorological Department-Khartoum.

The data presented herein are in good agreement, but still needed extensive data collection. The data presented at this stage can serve as a good indicator for researchers and policy makers in planning the utilisation of solar energy in northern Sudan. The need for solar information is essential in the design and study of solar energy conversion devices. Other uses of such information include agricultural studies, meteorological forecasting, environment and energy conservation (Omer, 2005).

2. Prediction Formulae

2.1. Prediction of Global Solar Radiation, H

Many methods have been devised for the prediction of the amount of solar energy incident on a horizontal plane at the earth’s surface. The simplest models are the empirical formulas presented by Goldberg et al. (1979). The first relation which have used is Angstrom correlation (Angstrom, 1924; 1956):

Abdeen Mustafa Omer

344

H/Ho = a+ b.n/N (1)

Where Ho and N are cloudless daily global irradiation received on a horizontal surface at ground level, i.e., extraterrestrial and maximum possible sunshine duration; both a and b are model parameters. This equation has been used most often all over the world in order to calculate the global irradiation at locations of sunshine duration measurements and extrapolate the global solar irradiation estimations from measured short-term solar irradiation data. Later this equation has been modified by taking into account some other relevant meteorological variables (Prescott, 1940). The Angstrom model is an empirical relation between the ratios of the daily insolation, H, to the extraterrestrial radiation, Ho, above the earth’s atmosphere and the daily fraction of possible hours, (n/N), where n is the measured sunshine duration in a day and N is the theoretical day-length of that day. The constant a and b are obtained by regression analysis, using H and n data from many years. The constants have been found depend on the latitude, climate of the site and the season of the year. In order to estimate the ratios of n/N and H/Ho monthly mean extraterrestrial radiation Ho, day-length N, were calculated using monthly mean declination angle from eqns (2 and 4), respectively, for each month. Computations of extraterrestrial radiation were based on the new solar constant of 1367 W/m2. All over the world, the coefficients are estimated from available solar irradiation and sunshine duration data at a location by the use of statistical regression technique. However, in such an approach there are implied assumptions as follows: (1) The Angstrom’s approach provides estimations of the global solar irradiation on horizontal surfaces, but unfortunately it does not give clues about global solar irradiation on a tilted surface because diffuse and direct irradiations do not appear in the Angstrom model. (2) Whatever the scatter diagram of H versus N, the regression line is automatically fitted leading to constant a and b estimates for the given data (Dogniaux et al., 1983). In fact, these coefficients depend on the variations in the sunshine duration during any particular time interval and since sunshine duration records have inherently random variabilities.

The values of N are computed from Cooper’s formula (Cooper, 1969): N = 2/15 cos-1 (-tan Φ tan δ) (2)

Where Φ the latitude and δ the solar declination. The value of declination can be found from the equation of Cooper (Cooper, 1969): δ = 23.45 sin [365 (284+m)/365] (3)

Where m is the number of the day in the year (1-365). While extraterrestrial radiation on horizontal surface at any time between sunrises and

sunset is given by Duffie et al. (1980): Ho = [(24x3600xIs/π) (1+0.33 cos (360xm)/365)] [cos Φ cos δ sin w + (2xπxw/360) sin

Φ sin δ] (4)

Where w is the sunset and sunrises hour angle (in degrees) and Is the solar constant 1367 W/m2.


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Another method, which requires only hours of sunshine and minimum air mass as input parameters, was proposed by Sivkov (1964) for latitudes 35o-65o North in the form:

Hm = 4.9 (nm)1.31 + 10500 (sin Sn)2.1 (5)

Where Hm is the monthly global irradiance, Cal cm-2, nm is the monthly sunshine hours and Sn is the noon altitude of the sun at the 15th of the month [90-(Φ-δ)] (Collares-Pereira et al., 1979). Barbaro et al. (1978) modified the formula to make it fit 31 Italian stations, which they divided into three zones according to their climatological characteristics. The modified formula used is:

Hm = K(nm)1.24 (Sn)-0.19 + 10550 (sin Sn)2.1 (6)

Where K is the zone parameter (8, 9.5, 11) for three different regions in Italy.

Relations (5 and 6), which were proposed for high latitudes (35-65oN), were tested by Khogali (1992) for low latitudes (4-19oN). It was found applicable with a good degree of accuracy provided that the parameter K is appropriately adjusted.

2.2. Prediction of Diffuse Solar Irradiance

As no information is available on the diffuse solar irradiance at Dongola, the theoretical methods were used for evaluation. A well-known relation for this purpose is the Page correlation (Page, 1964):

Hd/Hm = 1.00–1.13KT (7)

Where Hd is the monthly mean daily diffuse solar irradiance, Hm is the monthly mean daily total global irradiance and KT is the ratio of cloudiness index or transmission coefficient.

KT = Hm/Ho avg (8)

Where Ho avg is the average value of Ho over the whole month under consideration. Another commonly used correlation is Liu and Jordan (1977), which was developed by

Klein (1977), to take the form, Hd/Hm = 1.390-4.027KT+5.531K2

T-3.108K3T (9)

The numerical coefficients in eqns (7) and (9) are empirical. These two correlations are

used for the prediction of the diffuse solar irradiance. The direct beam component Ib can be deduced from the relation (Spencer, 1982): Hm = Hd + Ib sin (Sn) (10)

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Where Ib sin (Sn) is the average horizontal beam component and Sn is defined as the solar elevation at noon. This is useful for the various types of solar concentrating systems.

3. Results and Discussion

3.1. Prediction of H

The measured values of the monthly mean daily global solar radiation H, were obtained from the measured daily values (measured data provided by the Meteorological Department – Khartoum). The monthly mean daily global solar radiation was calculated from eqn (1). The values of the monthly mean daily extraterrestrial radiation Ho were calculated for each month from eqn (4), as outlined previously. The measured monthly mean daily numbers of bright sunshine hours n were also obtained from the data provided by the Meteorological Department – Khartoum. The monthly mean daily theoretical values of sunshine hours N were calculated from eqn (2). Values of (H/Ho) and (n/N) for each month were determined as shown in Table 1. Accordingly, 12 equations (one for each month) may be written. The least square method was then used to calculate the regression coefficients a and b of eqn (1) for Dongola.

Table 1. Solar radiation at Dongola

Month n N H Ho n/N H/Ho January 10.10 10.96 20.10 26.92 0.92 0.75 February 10.50 11.37 22.87 30.76 0.92 0.74 March 10.40 11.87 25.54 34.57 0.88 0.74 April 10.80 12.44 27.17 37.19 0.87 0.73 May 10.00 12.91 27.55 37.79 0.77 0.73 June 11.30 13.15 27.42 37.59 0.86 0.73 July 11.00 13.05 26.09 37.55 0.84 0.69 August 10.60 12.65 25.21 37.27 0.84 0.68 September 9.80 12.10 24.07 35.48 0.81 0.68 October 10.40 11.55 22.90 31.93 0.90 0.72 November 10.60 11.08 20.77 27.84 0.96 0.75 December 10.20 10.85 18.97 25.75 0.94 0.74 Yearly Average 10.48 24.06 0.88 0.72

Dongola, which is exposed to the Sahara Desert climate has the highest solar insolation

H/Ho=0.72, n/N=0.88. The regression coefficients a and b for Dongola were 0.21 and 0.57 respectively. The value of a+b=0.78 constitutes an atmospheric transparency index, and an annual average of daily irradiance of 24.1 MJ/m2. Table 2 and Figure 1 present the results obtained for Dongola during the period 1973-2000. The percentage errors between the measured and estimated values of the monthly mean daily global solar radiation have been calculated and are also given in Table 2. It is evident from Table (2) that the agreement with measurements during each month is better than 5.5% except for March, which is 5.9%, while that for the annual average of daily solar radiation is ±2%. Routinely recorded daily global irradiation and sunshine duration values are used by the regression technique for determining


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the coefficients in eqn (1). The use of such a deterministic linear model provides unique predictions of global solar irradiation given the sunshine duration.

Table 2. Comparison between measured and estimated monthly mean daily global radiation

Month H H1 E1 H2 E2 January 20.10 19.40 -3.48% 19.80 -1.49% February 22.87 22.30 -2.49% 22.40 -2.06% March 25.54 24.10 -5.64% 24.10 -5.64% April 27.17 25.80 -5.04% 25.80 -5.04% May 27.55 26.60 -3.45% 26.60 -3.45% June 27.42 26.80 -2.26% 26.80 -2.26% July 26.09 26.10 0.04% 26.20 0.42% August 25.21 25.70 1.94% 25.90 2.74% September 24.07 23.60 -1.95% 24.20 0.54% October 22.90 22.90 0.00% 23.00 0.44% November 20.77 20.60 -0.82% 21.00 1.11% December 18.97 19.10 0.69% 19.80 4.38% Yearly Average 24.06 23.58 -1.87% 23.80 -0.86%

H Measured monthly mean daily global radiation, MJ/m2 Day-1. H1 Computed monthly mean daily global radiation, MJ/m2 Day-1 (method 1). E1 Percent difference between estimated and measured values, % (method 1). H2 Computed monthly mean daily global radiation, MJ/m2 (method 2). E2 Percent difference between estimated and measured values, % (method 2).

Another method to predict H was employed. In this method an empirical relation due to

Barabaro et al. (1978), which used sunshine duration and minimum air mass as inputs, was tried. Deviation of ±5.98% between estimated and measured values of H was recorded.

3.2. Estimation of Diffuse Solar Radiation

Values of the monthly average of the daily diffuse solar radiation at Dongola have been computed by two correlations (7) and (9), and the results are presented in Table 3, and Figure 2. It is clear that Page’s correlation gives consistently lower estimates, compared to those computed on the basis of Liu, Jordan and Klein correlation. In the absence of experimental data of diffuse radiation at Dongola, Shambat station data (1975-2000) has been used. Shambat is located at latitude 15o 40’N, longitude 32o 32’E and it is at an altitude of 380 m above sea level. It is the only station in which diffuse solar radiation is measured in Sudan, to know which method is better. The predicted values compared well with measured values (±5.88%). The results of two formulas have close agreement. Future measurements of diffuse solar radiation are therefore desperately needed.

In order to consider effects of unexplained part, it is necessary to estimate coefficients from the successive data pairs ‘‘locally’’ rather than ‘‘globally’’ as in the classical regression approach. Angstrom’s approach provides estimations of the global solar irradiation on horizontal surfaces, but unfortunately it does not give clues about global solar irradiation on a

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tilted surface because diffuse and direct irradiations do not appear in the Angstrom model. The method evaluates statistics on the basis of daily values.

17

19

21

23

25

27

29

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

Months

Sola

r ra

diat

ion

(MJ/

m2 /D

ay)

H H1 H2 H Measured monthly mean daily global radiation, MJ/m2 Day-1. H1 Computed monthly mean daily global radiation, MJ/m2 Day-1 (method 1). H2 Computed monthly mean daily global radiation, MJ/m2 (method 2).

Figure 1. Comparison between predicted and measured values of global radiation over Dongola, Sudan

3.3. Computation of the Beam Component of Solar Radiation

Values of the monthly average of the daily beam component Ib are deduced from eqn (10) and Tables (2 and 3). Table 4 presented the computed values of Ib. A linear relationship between global radiation levels and number of sunshine hours was tried, but failed to give meaningful results. A linear regression between daily values of H/Ho vs n/N suggested by Duffie and Beckman (1980) failed to meet any goodness of fit, where H and Ho are the ground and extraterrestrial radiation, respectively, and n and N are the sunshine duration and the maximum possible sunshine duration, respectively. The reasons may be attributed to: (1) Augmentation of global radiation by multiple reflectors between ground and clouds; (2) Measurement error related to the Campbell-Stokes sunshine records; (3) Measurement error associated with bimetallic global radiation records.

The model parameters are assumed invariant with time on the average as if the same sunshine duration appears on the same days or months of the year in a particular location. The physical meanings of the model coefficients are not considered in most of the application studies but only the statistical linear regression line fit and parameters estimations are


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obtained directly and then incorporated into eqn (1) for global solar irradiation estimation from the sunshine duration records.

Table 3. Estimation of monthly mean daily diffuse solar radiation by two correlation methods

Month Hd1 Hd2 Hmd E3 E4 January 3.30 3.60 3.40 2.94 -5.88 February 3.50 3.90 3.70 5.41 -5.41 March 4.20 4.60 4.40 4.55 -4.55 April 5.00 5.30 5.10 1.96 -3.92 May 5.40 5.70 5.40 0.00 -5.56 June 5.60 5.80 5.70 1.75 -1.75 July 6.20 6.20 6.20 0.00 0.00 August 6.20 6.10 6.10 -1.64 0.00 September 5.60 5.60 5.60 0.00 0.00 October 4.20 4.40 4.30 2.33 -2.33 November 3.20 3.60 3.40 5.88 -5.88 December 3.30 3.60 3.40 2.94 -5.88 Yearly Average 4.64 4.87 4.75 1.76 -3.00

Hmd Measured monthly mean daily diffuse radiation at Shambat Station – Khartoum North, MJ/m2 Day-1. Hd1 Computed monthly mean daily diffuse radiation, MJ/m2 Day-1 (method 1). E3 Percent difference between estimated and measured values, % (method 1). Hd2 Computed monthly mean daily diffuse radiation, MJ/m2 (method 2). E4 Percent difference between estimated and measured values, % (method 2).

Table 4. Computed monthly mean daily values of beam solar radiation

Month H Hd avg Ib January 20.10 3.45 16.65 February 22.87 3.70 19.17 March 25.54 4.40 21.14 April 27.17 5.15 22.02 May 27.55 5.55 22.00 June 27.42 5.70 21.72 July 26.09 6.20 19.89 August 25.21 6.15 19.06 September 24.07 5.60 18.47 October 22.90 4.30 18.60 November 20.77 3.40 17.37 December 18.97 3.45 15.52 Yearly Average 24.06 4.75 19.30

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2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.Months

Sola

r ra

diat

ion

(MJ/

m2 /D

ay)

Hd1 Hd2 Hmd H Measured monthly mean daily global radiation, MJ/m2 Day-1. Hd avg Average diffuse solar irradiance of the two methods (MJ m-2 Day-1). Hmd Measured monthly mean daily diffuse radiation at Shambat Station – Khartoum North, MJ/m2 Day-1. Hd1 Computed monthly mean daily diffuse radiation, MJ/m2 Day-1 (method 1). Hd2 Computed monthly mean daily diffuse radiation, MJ/m2 (method 2).

Figure 2. Comparison of the two methods for predicting diffuse radiation with Shambat

4. Conclusion

Global solar radiation data at Dongola station measured over 25 years, has been collected, investigated and used as a base for estimated values. Angstrom correlation relation and Barbaro et al., formulas were used for the prediction of the monthly mean daily global solar radiation at Dongola. The predicted values using these two different empirical approaches were in good agreement with the measured values with percentage error less than ±6%. Therefore these two empirical correlations could be used to predict the solar radiation intensity in Sudan. The diffuse components of the monthly mean daily solar radiation were estimated using two different correlations. The first was the Page’s correlation relation while the other was Liu and Jordan relation. The percentage errors of the results obtained by those two methods were less than ±11%. These two correlations could be accepted for estimation of the diffuse component of the solar radiation with an error of ±10%. However predicted measurements are needed to confirm the results and most solar technologies do require the averages and variances of solar radiation for design purposes. The main purpose of this study is to provide a simple statistical technique to take into account random behaviours in model coefficients. This is because the regression method does not provide dynamic estimation of the coefficients from available data.


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References

Barabaro S., Coppolino S., Leone C., and Sinagra E. (1978) Global solar radiation in Italy. Solar Energy 20 (5): 431-38.

Sayigh, A.A.M. (1987) The iso-radiation map of the Arab World. Solar and Wind Technology 4: 163-177.

National Energy Administration (NEA) (1985) The national energy plan 1985-2000. Khartoum: Sudan.

Energy Research Institute (ERI) (1997) Renewable energy resources potential in Sudan. Khartoum: Sudan.

Omer, A.M. (2007) Renewable energy resources for electricity generation in Sudan. Renewable and Sustainable Energy Review 11 (7): 1481-1497.

Omer, A.M. (1990) Solar Atlas for Sudan. M.Sc Thesis. University of Khartoum. Omer, A.M. (2005) Solar energy in Sudan: PV application in developing countries, In:

Proceedings of the 15th International Photovoltaic Science and Engineering Conference and Solar Energy Exhibition (PVSEC-15), Impacts on Photovoltaic Industry and Market Development in China, Paper No. PV0013-O9i, Shanghai, China, 10-15 October 2005.

Goldberg B., Klein W.H., and McCartney R.D. (1979) A comparison of some simple models to predict irradiance on a horizontal surface. Solar Energy 23, 81-85.

Angstrom A. (1924) Solar and terrestrial and radiation. Q.J.R. Met. Soc. 50- 121. Angstrom A. (1956) On computation of global radiation from records of sunshine. Arkiv.

Geophisk 3, 551. Prescott J.A. (1940) Evaporation from water surface in relation to solar radiation. Trans. R.

Soc. S. Austr. 46- 114. Dogniaux, Lemoine (1983) Solar radiation data. Solar energy R&D in the European

Community Series 2, 94-107; W. Palz Editor, Reidel. Cooper P.I. (1969) The absorption of solar radiation in solar stills. Solar Energy 12 (3): 333-

346. Duffie J.A., and Beckman W.A. (1980) Solar Engineering of Thermal Processes. J. Wiley and

Sons, New York. Sivkov S.I. (1964) To the methods of computing possible radiation in Italy. Trans. Main

Geophys. Obs. 160: 12-20. Collares-Pereira, M., and Rabl, A. (1979) Average distribution of solar radiation correlations

between diffuse and hemispherical and between daily and hourly insolation values. Solar Energy 22: 155-160.

Khogali A., and Al-bar, O.F. (1992) A study of solar ultraviolet radiation at Makkah solar station. Solar Energy 48: 79-87.

Page J.K. (1964) The estimation of monthly mean values of daily total short wave radiation on vertical and inclined surfaces from sunshine records for latitudes 40oN to 40oS. UN New Sources of Energy 4: 378-85.

Lui M.Y., and Jordan R.C. (1977) The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4(3): 1-19.

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Klein S.A. (1977) Calculation of monthly average insolation on tilted surfaces. Solar Energy 19: 325-30.

Spencer J.W. (1982) Comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Solar Energy 29(1): 19-32.


Short Communication B

ELECTROSTATIC SOLAR LIGHT-WIND SAIL


Abstract

The solar sail has become well-known after much discussion in the scientific literature as a thin continuous plastic film, covered by sunlight-reflecting appliquéd aluminum. The Solar wind propulsion also has many researches. Any solar sail simultaneously is the solar wind sail because the light and solar wind have a same direction and adsorb by a sail material. Earlier, there were attempts to launch and operate solar light and solar wind sails in near-Earth space and there are experimental projects planned for long powered space voyages. However, as currently envisioned, the solar light-wind sail has essential disadvantages. Solar light-wind pressure in space is very low and consequently the solar light-wind sail has to be very large in area. Also it is difficult to unfold and unfurl the solar sail in space. In addition it is necessary to have a rigid framework to support the thin material. Such frameworks usually have great mass and, therefore, the spacecraft’s acceleration is small. Here, the author proposes to discard standard solar light-wind sail technology (continuous plastic aluminum-coated film) with the intention instead of using millions of small, very thin aluminum charged plates and to release these plates from a spacecraft, instigated by an electrostatic field. Using this new technology, the solar sail composed of millions of plates can be made gigantic area but have very low mass. The acceleration of this new kind of solar sail may be as much as 300 times that achieves by an ordinary solar sail. The electrostatic solar sail can even reach a speed of about 300 km/s (in a special maneuver up to 600–800 km/sec). The electrostatic solar sail may be used to move a large spaceship or to act as an artificial Moon illuminating a huge region of the Earth’s surface.

Key words: Solar wind propulsion, solar sail.

1 Correspondence to: C&R, A.Bolonkin, 1310 Avenue R, #F-6, Brooklyn, NY 11229, USA, T/F 718-339-4563,


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Introduction

Description of Conventional Light-Wind Solar Sail and Its Short History

Conventional solar sails are composed of large flat smooth sheets of very thin film, supported by ultra-lightweight structures. The side of the film which faces the sun is coated with a highly reflective material so that the resulting product is a huge mirror, typically about the size of a football field (see Figure 1). The force generated by the sun shining on this surface is about equal to the weight of a letter sent via first class mail. Even though this is a very tiny force, it is perpetual, and over days, weeks, and months, this snail-paced acceleration results in the achievement of velocities large enough to overtake and pass the Voyagers and Pioneers that are now speeding away through the outer reaches of our solar system.

NASA has a program in place to develop solar sail technology to a point where it can be used to implement important space exploration missions. There are a number of missions on the NASA strategic roadmap that require this type of propellantless propulsion to achieve their objectives. There are other classes of missions that are greatly enhanced by solar sails because these vehicles are inexpensive to construct and can deliver such high performance propulsion.

There are important applications for solar sails beyond the science missions that NASA has planned. The National Oceanic and Atmospheric Administration (NOAA) needs this technology to create a new class of space and earth weather monitoring stations that can provide greater coverage of the earth and provide better advance warning of the solar storms that sometimes plague communications and electrical power grids. There are also a number of military missions in earth orbit that can be enabled by low cost sailcraft.

Figure.1. NASA Light-wind Solar sail. 280K.

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Solar sailing is a method of converting light-wind energy from the sun into a source of propulsion for spacecraft. In essence, a solar sail is a giant mirror that reflects sunlight in order to transfer the momentum from light-wind particles (photons-protons) to the object one is interested in propelling. Since the phrase "solar sails" is often confused with "solar cells", which is a technology for converting solar light into electrical energy, we will use the term "light sail" for the purpose of this discussion.

Solar radiation pressure = 9.12 µN/m2 at the Earth’s orbit. The light sail material must be as thin and lightweight as possible. Conventional light sail film has comprised 5 micron thick aluminized mylar or kapton with a thin film aluminum layer (approximately 100 nm thick) deposited on one side to form a mirror surface with 90% reflectivity.

For 5 micron thick mylar, which has an area density of 7 g/m2, the acceleration would be 1.2 mm/s2. This acceleration results in a daily velocity increase of about 100 m/s, a velocity which is useful for maneuvering around the solar system. Although mylar is inexpensive and readily available in 0.5 micron thickness, it is not ideal sail film material because it is easily degraded by the sun's ultraviolet radiation. The other key contender, kapton, can withstand ultraviolet radiation but isn't available in layers much thinner than 8 µm, with a resulting area density of 12 grams per square meter.

A conventional solar sail is a spacecraft with a large, lightweight mirror attached to it that moves by being pushed by light reflecting off the mirror instead of using rockets. The light to push a sail can come from the Sun or large lasers we could build. Satellites in orbit around the Earth can survive for many years without any maintenance while using only a small amount of rocket propellant to hold their positions. Solar sails can be made to survive in space for many years as well. But, because solar sails use sunlight that never runs out like rocket propellant, during those years the sail can move around as much as you want it to, such as from the Earth to Mars and back, possibly several times if the sail remains in good condition. A similarly equipped rocket would either be ridiculously huge because it has to carry the fuel for each trip, or would need to be refueled regularly.

Sunlight exerts a very gentle force. The power of sunlight in space at the Earth's distance from the Sun is between 1.3–1.4 kilowatts per square meter. When you divide 1.4 kilowatts by the speed of light, about 300 million meters per second, the result is very small. A square mirror of side 1 kilometer would only receive about 9 newtons.

Light pressure is P = E/c if the light is absorbed (black surface) and P = 2E/c if the light is reflected (mirror). Here E is light energy, c = 3×108 m/s is light speed.

There are three major designs used for conventional light sail construction (Figure 2): • Three axis stabilized sails which require booms to support the sail material. • Heliogyro sails, which are bladed like a helicopter and must be rotated for stability. • Disk sails which must be controlled by moving the center of mass relative to the

center of pressure.

A practical sail places great demands on our physical construction capabilities. The sail must be as large as possible so that it can collect enough light to gain a useful thrust. At the same time it must be as light weight as possible. This implies an extremely thin sail film with minimal mass. Finally, it must be durable enough to with stand a wide range of temperature

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changes, charged particles, and micrometeoroid hazards. A laser beam may be used for moving the solar sail2-9.

Figure 2. Design of Solar sail

The description of solar sail is in [1] chapter 16. Solar radiation pressure equals 9.12 µN/m2 at distance 1 AU from the Sun. Solar wind pressure is significantly less, but solar wind (protons) may be collected from large area by electrostatic and magnetic fields. Any solar sail has also pressure from Solar wind.

No solar sails have been successfully deployed as primary propulsion systems, but research into this technology is continuing. On 9 August , 2004 the Japanese ISAS successfully deployed two prototype solar sails in low Earth orbit. A clover-shped sail was deployed at 122 km altitude and a fan-shaped type sail at 169 km. Both sails used 7.5 micrometer thick film.

A joint private project between the Planetary Society, Cosmos Studios and the Russian Academy of Science launched Cosmos 1, the first solar sail spaceship, on 21 June, 2005. The rocket was supposed to push the 124 kg spacecraft into 800 km orbit where it was intended to unfurl the 15 meter sails (with a total area of 600 m2). Unfortunately, the launch was unsuccesful. A suborbital prototype test by the group also did not succeed in 2001 because of rocket failure.

Brief Information about Solar Wind

The Sun emits plasma which is a continuous outward flow (solar Wind) of ionized solar gas through out our solar system. The solar wind contains about 90% protons and electrons and some quantities of ionized α-particles and gases. It attains speeds in the range of 300–750 km/s and has a flow density of 5×107 – 5×108 protons/ electrons/cm2s. The observed speed rises systematically from low values a 300–400 km/s to high values of 650–700 km/s in 1 or 2 days and then returns to low values during the next 3 to 5 days (Figure 3). Each of these high-speed streams tends to appeal at approximately 27-day intervals or to recur with the rotation period of the Sun. On days of high Sun activity the solar wind speed reaches 1000 (and more) km/s and its flow density 109 – 1010 protons/electrons/ cm2s, 8–70 particles in cm3. The Sun has high activity periods some days each year.


10 ÷ 6.3×10–9 N/m2. This value is double when the particles have full reflection. The interstellar medium also has high energy particles. Their density is about 1 particle/cm3.


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Figure 3. Speed and density variations in solar wind. The speed is in km/s, the density is in protons/cm3.

Description of the Innovations

A conventional solar sail is a dielectric thin film (thickness 5 mkm = 5000 nm) with an aluminum layer 100 nm thick, and it has 90% reflectivity. The weight of one square meter is 5–7 g/m2. If it accelerates by itself the maximum acceleration is about 1 mm/s2. However, the gigantic thin film needs a rigid structure to support the very thin film in an unfolded position and to anable it to be contrilled. This rigid structure has a large weight, so it is very difficult to launch and to unfurl the structure in space. All attempts to do this (for example, to unfurl the inflatable radio-antennas in space) have failed.

The author proposes to use small thin charged aluminium plates (petals) supported by a central electrostatic ball and rotated around the ball (Figure4). They rotate also around their own axis and main thin a direction perpendicular to the solar rays. The diameter of the plate-petals is small, about 1 mm or less, and, it is not a necessity to use the dialectric film. The aluminium film may be very thin because the individual petal size is small.

Figure 4. The proposed electrostatic solar light-wind AB-sail. a. Side view; b. Front view; c. Side and front views of square petal; d. Side and front views of round petal. Notation: 1 – spaceship, 2 – charged

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ball, 3 – charged plate-petals, 4 – cable connecting the ship and the ball, 5 – solar rays, 6 – reflected rays, 7 – charged petals, 8 – thrust (drag).

The electrostatic sail can be controlled by changing charge on the ball (diameter of the mirror) and by the positioning of an additional charged ball, 9 (Figure 5), which turns the mirror. Additional charge collects the charged particle of solar wind from very large area (in many times more then mirror area). That increases the trust of light-wind sail in comparison with conventional only light sail.

Figure 5. Guidance and control of the electrostatic solar sail. Notation: 9 – charged ball for control. All other notations are the same as Figure 4.

The unfurling of the sail may be done using a rotated charged head 10 (Figure 6). The head is detached from the apparatus in the radius of sail, and is rotated around it’s axis (parallel to the solar rays) and around the ball. The head emits the negativity charged petals. The speed of the petals may be controlled by the head charge (voltage). The same charge stretches the petals3 and repels them from the others. The sail can be collected back by the head, through the head changing the opposite charge.

Figure 6. Unfurling of the electrostatic solar sail. Notation: 10 – rotating mobile charged head connected by a variable cable to the central ball, 11 – variable cable connecting the head and the ball. All other notations are same as Figure 4.


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The proposed solar sail has many unique advantages in comparison with the conventional solar sail or a space mirror:

1. The proposed sail (made only of film) is easier to use (has less mass) in 50–100 times

because of the absence of a support substrate (dielectric film of 5000 nm thickness) and the aluminum film used can be of minimum thickness (6–15 nm, not 100 nm).

2. A rigid support structure giving a large additional mass is unnecessary. 3. The size of the reflected mirror is not limited and may be more than 1 km. This

means the proposed sail can accelerate a large spaceship with a mass of 1 ton or more.

4. There are no big problems with the unfurling and collection of the sail. 5. The electrostatic sail may be collected (furled) to the head. 6. The increasing of charge alloys to collect protons of solar wing with very large area.

That increases the trust of electrostatic AB-sail.

Theory of Estimation and Computation of Light-Wind Solar Sail

1. Estimation of the Space Sail

The spectrum of solar radiation is presented in Figure 7 (or Figure 19.111). If we want to use the most energy, the sail must reflect or absorb all waves having the wavelength less than λ = 1–2 μm (mkm).

The amount of light that can pass capability through metal depends on its thickness2:

,4

)/ln(),/4exp( 00 kn

IIddknIIπ

λλπ −=−= (1)

where I – light intensity after passing through metal film, I0 – initial light intensity, I/I0 – coefficient of clarity, n – refraction coefficient, k – absorption coefficient, d – metal thickness [m], λ – wavelength [m].

The refraction and absorption coefficients of aluminum are equal (see Reference11, p. 639):

for λ = 0.5 μm, coefficient n = 0.5, k = 9.18, nk = 4.59 ; λ/nk = 0.109×10–6 ; for λ = 5 μm, coefficient n = 6.7, k = 5.61, nk = 37.59 ; λ/nk = 0.133×10–6 ,

For other values the product nk can be found using linear interpolation: λ = 1 μm, nk = 8.26; λ = 2 μm, nk = 15.59 .

The computation of the metal film thickness versus the coefficient of clarity I/I0 is presented in Figure 8.

The weight of the sail is computed using the equation: SdW ρ= , (2)

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where W – sail weight (mass) [kg], ρ = 2700 kg/m3 is the density of aluminum, S – sail area [m2], d – sail (aluminum) thickness [m].

Figure 7. Spectrum of solar radiation. Horizontal axis is the wavelength λ, vertical axis is the energy density.

Figure 8. The sail film thickness via clarity coefficient I/I0 for the wavelength λ = 2 μm.

The mass of a 1 m2 sail of thickness d = 10 nm is W = 2700×10–8 = 0.027 g/m2. Compared with 5–7 g/m2 for the conventional sail this is 185–260 times less. Clarity correction makes this value 110–150 times less.

The acceleration, a, of a spaceship with a sail can be computed using the equation:

( ) ( )( )nk

IISM

IISPWM

IISPa

πλρ

4/ln

/1/10

0000

−

−=

−−

= , (3)


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where P0 is light pressure [N], M is useful mass (of the ship without sail) [kg]. If we take solar radiation pressure for 88% reflection at 1 AU, it is about P0 = 8×10–6 [N/m2]. This works out at 8 N for a sail with a radius of 564 m (area 106 m2). The mass of our sail is 27 kg, the mass of a conventional sail (without the support structures) is 5 tons. However, the unbiased comparison is of sail acceleration for M = 0.

The result of computation for equation (3) are presented in Figure 9. As you can see, the acceleration of the proposed sail reaches as much as a ≈ 0.3 m/s2 = 300 mm/s2. In comparison, acceleration of the conventional solar sail without a useful load is 1 mm/s2. If our sail spacecraft has an additional useful mass (the ship, the ball, and other devices) of 100 kg, the acceleration is 45 mm/s2; for a useful mass of 500 kg, the acceleration is 13 mm/s2.

Figure 9. Apparatus acceleration via relative clarity of sail film and additional apparatus mass.

The maximum speed of a solar-sail spacecraft can be estimated using the equation:

,112,,,,0

200

22

00

20

0 ⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛===

sssaVds

ssaVdV

ssaa

VsdtadtdV (4)

where V is the apparatus speed [m/s], a is acceleration [m/s2], t is time [seconds], a0 is acceleration at distance 1 AU (astronautic unit, for an Earth orbit of radius s0 = 15×1010 m), s is distance from the Sun [m].

If s >> s0, the maximum apparatus speed is

00max 2 saV = . (5)

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The proposed solar sail without a load reaches a maximum speed of 295 km/s ≈ 300 km/s whereas the conventional sail without a load reaches only 55 km/s. With a load of 100 kg the new sail reaches a speed of 116 km/s. If the apparatus makes a maneuver and starts at s0 = 30 million km from the Sun (a = 25a0) the maximum speed reaches 660 km/s.

We can find the tangent speed of the petals (aluminum plates) around the charged ball from the following equations:

,,,,2

2 SrdkQv

NSdm

NQq

rmv

rqQkF

ρρ

===== (6)

where F – the electrostatic force between the central ball and the petal [N], k = 9×109 – electrostatic coefficient, q – charge of a petal [C], Q – charge of the ball [C], r – distance between the petal and the center of ball [m], m – mass of a petal [kg], v – tangent speed of a petal (around the ball) [m/s], N – number of petals.

If ρ = 2700 kg/m3 (for aluminum), S = 106 m2 , r = 600 m, d = 10–8 m, then v = 745Q. For Q = 0.01 C the speed v = 7.45 m/s.

Figure 10. Possible form of Solar Sail. Credit NASA/JPL, 63K

2. Estimation of the Initial Expenditure of Electrical Energy to Charge of the Ball

The ball has to be charged with electrical energy of high voltage (millions of volts). Let us estimate the minimum energy, when the charged device has 100% efficiency. This energy


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equals the work done to move of the ball charge to infinity. It can be computed using the equation

,2

,,,2

2322

kEaW

kaC

kEaQ

CQW bb ==== (7)

where Wb – ball charge energy [J]; C – ball capacitance [F]; Q – ball charge [C]; a – radius of ball [m]; E – electric intensity [V/m].

For our charge Q = 0.01C and electrical intensity (safe for a vacuum) E = 108 V/m the required ball radius is a = 0.95 m ≈1 m [equation (7)], the required charge energy is Wb = 0.154 kWh [equation (7)]. This energy is not great, and it may be returned when the ball discharged by emitting the charge into space using a sharp edge.

3. Estimation of the Ball Stress, Cover Thickness and Ball Mass

The ball has tensile stress from the like electric charge. We can find the ball stress and the necessary thickness of the ball cover. If the ball is in a vacuum and the ball charge, Q, is constant, the internal force within the ball is

( ) ,2

,,2

,2

,1094

1,,2

,

22

2

2

29

0

2

kaEf

kEaQ

akQf

akQWk

kaC

CQW

aWf bb

b

−==−=

=×====∂

∂=

πε (8)–(9)

where f is the ball’s internal tensile force [N]; Wb is the charge energy [J]; C is the capacity of the ball as a spherical capacitor [F]; E is electric intensity [V/m].

The internal pressure of the ball is then

,8

,4,2

2

kEpaS

Sfp bb π

π === (10)

where p is internal pressure [N/m2], Sb is ball surface area [m2].

The thickness of a ball cover is

σπδ

σδδσππ

kaEapapa

16,

2,2

22 === , (11)

where δ is the cover thickness [m]; σ is the safe cover stress [N/m2].

The ball mass is then

σγπδγ

kEaMaSSM sbbs 4

,4,23

2 === , (12)

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where Ms – ball (sail) mass [kg]; γ – ball cover density [kg/m3]; σ – safe stress level of the ball cover [N/m2].

For our case where a = 1 m, E = 108 V/m, γ = 1800 kg/m3, σ = 109 N/m2, the mass of the ball is Ms = 0.5 kg [equation (12)].

4. Technology of the thin plate-petals

The thin plate-petals can be produced by electrolytic or vapor precipitation.

5. Design of Artificial Moon

The proposed idea may be used to construct on artificial Moon when the light pressure equals the Earth’s gravity and a gigantic electrostatic mirror illuminates the Earth’s surface.

6. Estimation of the Trust

May be computed by [5] or [1] Ch.13. Other electrostatic applications are offered in the References [1–9].

Possible Form of Solar Sail

Figure11. NASA Solar Sail


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Figure 12. Flying away on a wing and a prayer: The Canadian Solar Sail Project for a proposed race to the moon in 1992 in honor of the 500 year anniversary of Columbus coming to America.

References

(Reader can find part of these articles at the author’s website: http://Bolonkin.narod.ru/p65.htm, http://arxiv.org, search term: “Bolonkin”, in the book "Non-Rocket Space Launch and Flight", Elsevier, London, 2006,488 pgs., and book “New Concepts, Ideas, Innovations in Aerospace, Technology and Human Sciences”, NOVA, 2008, 502 pgs.; “Macro-Projects: Environment and Technology”, NOVA, 2009, 536 pgs.)

[1] Bolonkin A.A., “Non-Rocket Space Launch and Flight”, Elsevier, 2006, 488 pgs. [2] Bolonkin A.A., “New Concepts, Ideas, and Innovation in Aerospace, Technology and

Human Science”, NOVA, 2008, 400 pgs. [3] Bolonkin, A.A., Method of Stretching of Thin Film. Russian patent application

#3646689/10 138085. 28 September 1983 (in Russian), Russian PTO. [4] Bolonkin, A.A., “Electrostatic Utilization of Asteroids for Space Flight”, 41 Propulsion

conference, 10–12 July, 2005, Tucson, Arizona, USA, AIAA-2005-3857. [5] Bolonkin, A.A., Electrostatic Solar Wind Propulsion, 41 Propulsion conference, 10–12

July, 2005, Tucson, Arizona, USA, AIAA-2005-3653. [6] Bolonkin, A.A., “Guided Solar Sail and Electric Generator”, 41 Propulsion conference,

10–12 July, 2005, Tucson, Arizona, USA, AIAA-2005-3857. [7] Bolonkin A.A., “Electrostatic Levitation and Artificial Gravity”, 41 Propulsion

conference, 10-12 July, 2005, Tucson, Arizona, USA, AIAA-2005-3365. [8] Bolonkin, A.A., “Radioisotope Space Sail and Electric Generator”, 41 Propulsion

conference, 10-12 July, 2005, Tucson, Arizona, USA, AIAA-2005-3653. [9] Bolonkin A.A., “Macro-Projects: Environment and Technology”, NOVA, 2008, 420

pgs. [10] “Dispersion of light”, Big Soviet Encyclopedia Moscow (in Russian). [11] Kikoin I.K., Tables of physical values (directory). Moscow, 1975 (in Russian).


Short Communication C

SOLAR AND SOLAR WIND AB-SAIL1


Abstract

The Solar and Solar Wind sail is a large thin film used to collect solar light and solar wind pressure for the moving of space apparatus. Any solar sail simultaneously is the solar wind sail because the light and solar wind have a same direction. The light (photons) and solar wind (protons and electrons) are adsorbed by a sail material. Unfortunately, the solar radiation pressure is very small, about 9 μN/m2 at Earth's orbit. The solar wind pressure is much less. However, the light and wind forces significantly increases up to 0.2 - 0.35 N/m2 near the Sun. The author offers his research on a new revolutionary highly reflective solar sail which performs a flyby (after a special maneuver) near Sun and attains a velocity up to 400 km/sec enabling reaching far planets of the Solar system in short time, and enabling escape flights out of the solar system. New, highly reflective sail-mirror allows avoiding overheating of the solar sail. It may be useful for probes close to the Sun as well as probes to Mercury and Venus.

Keywords: AB-solar sail, highly reflective solar sail, high-speed propulsion.

1. Introduction

A solar and solar wind sail is a thin film reflector that uses solar energy for propulsion. The spacecraft deploys a large, lightweight sail which reflects light from the Sun (or some other source). The radiation pressure on the sail provides thrust by reflecting photons and braked solar wind. The solar radiation pressure is very small 6.7 Newtons per gigawatt. That equals 9.12×10-6 N/m2 at Earth's orbit (1 AU - Astronomical Unit = 150 million km) and decreases

1 This work was presented as Bolonkin’s paper AIAA-2006-4806 for 42 Joint Propulsion Conference, Sacramento,

USA, 9-12 July, 2006. 2 Correspondence to: C&R, A.Bolonkin, 1310 Avenue R, #F-6, Brooklyn, NY 11229, USA, T/F 718-339-4563,


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by the square of the distance from the sun. However, the solar light and solar wind pressure significently increases near the sun and not far above it can reach 0.2 - 0.35 (up to 0.4 on Solar surfice) N/m2.

Brief History of Solar Sail

The conventional solar sail concept was first proposed by Friedrich Zander in 1924 [1] and gradually refined over the decades. The author proposed innovations and a new design of Solar sail in 1965 [2, 3], and theory was developed in [3] - [6]. The author offers a new revolutionary solar AB-sail. Its main distinction is very high reflectivity which allows the AB-sail to come very close to the Sun without great heating and to attain high light and wind forces and high speed.

This innovation allows (main advantages only): 1) to achieve very high speed up 400 km/s; 2) an easily controlled amount and direction of thrust without need to turn a gigantic sail; 3) to utilize the solar sail as a power generator (for example, electricity generator); 4) to use the solar sail for long-distance communication systems.

Information about the Sun Radiation

The pressure of light equals P = 2E/c (where E is energy of radiation, c is light speed (c = 3×108 m/s)). The solar light energy at Earth's orbit equals 1.4 kW/m2, but near a solar surface it reaches up to 64×103 kW/m2 (it increases 47 thousand times!). As the result the light pressure jumps up to 0.4 N/m2. The space apparatus can get significant acceleration (up to 80 m/s2) and high speed up to 400 - 500 km/s. Spectrum of Sun is presented in Figure 1. Note, the space mirror (sail) will not heat only if it reflects all solar spectrum (λ = 0.2 ÷ 3μm).

Figure 1. Spectrum of solar radiation. λ is the wavelength [0.25–2.5 μm, 250 – 2500 nm].

AB-Solar and Solar Wind Sail.

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Brief Information about Solar Wind

The Sun emits plasma which is a continuous outward flow (solar Wind) of ionized solar gas through out our solar system. The solar wind contains about 90% protons and electrons and some quantities of ionized α-particles and gases. It attains speeds in the range of 300–750 km/s and has a flow density of 5×107 – 5×108 protons/ electrons/cm2s. The observed speed rises systematically from low values a 300–400 km/s to high values of 650–700 km/s in 1 or 2 days and then returns to low values during the next 3 to 5 days (Figure 1, Ch.9). Each of these high-speed streams tends to appeal at approximately 27-day intervals or to recur with the rotation period of the Sun. On days of high Sun activity the solar wind speed reaches 1000 (and more) km/s and its flow density 109 – 1010 protons/electrons/ cm2s, 8–70 particles in cm3. The Sun has high activity periods some days each year.


10 ÷ 6.3×10–9 N/m2. This value is double when the particles have full reflection. The interstellar medium also has high energy particles. Their density is about 1 particle/cm3.

2. Description and Innovations of Suggested Solar Sail

Description of the offered light-magnetic sail

The suggested AB space sail is presented in Figure 2. It consists of: A thin high reflection film (solar sail) supported by an inflatable ring (or other method), space apparatus connected to solar sail,; a heat screen defends the apparatus from solar radiation.

Figure 2. High reflective space AB-sail. (a) Side view of AB-sail; (b) Front view; (c) cross-section of sail surface; (d) case of non-perpendicular solar beam; (e) triangle reflective sail. Notation: 1 - thin film high reflective AB-mirror, 2 - space apparatus, 3 - high reflective heat screen (shield) of space apparatus, 4- inflatable support thin film ring, 5 - inflatable strain ring, 6 - solar light, 9 - solar beam, 10 - reflective sell, 11 - substrate, 12 - gap.

The thin film includes millions of very small prisms (angle 45o, side 3 - 30 μm). The solar light is totally reflected back into the incident medium. This effect is called total internal reflection. Total internal reflection is used in the proposed reflector. As it is shown in [5]

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Ch.12 the light absorption is very small (10 -5 ÷10 -7) and radiation heating is small (see computation section).

Another possible design for the suggested solar sail is presented in Figure 3a. Here, the solar sail has concave form (or that plate is made like a Fresnel mirror).

The sail concentrates solar light on a small control mirror 4. That mirror allows a re-directed (reflected) solar beam to change value and direction of the sail thrust without turning the large solar sail. Between thin films 1, 8 there is a small gas pressure, which supports the concave form of reflector 1. Concentration of energy can reach 103 ÷ 104 times, temperature greater than 5000 oK. This energy may be very large. For the sail of 200×200 m, at Earth orbit the energy is 5.6×104 kW. This energy may be used for apparatus propulsion or other possibilities (see [5]), for example, to generate electricity, or even to flash a signal to greet amateur astronomers. The concave reflector may be also utilized for long-distance radio communication. The current conventional NASA design of solar sail is shown in Figure 3b.

The trajectory of the high speed solar AB-sail is shown in Figure 4. The sail starts from Earth orbit. Then it is accelerated by solar light to up 11 km/s in opposed direction of Earth moving around Sun and leaves Earth gravitational field. The Earth has a speed about 29 km/s in its around Sun orbit. The sail will be subtracting additional 11 km/s from this to achieve a net velocity of 18 km/s. That braking slows it down and gravity then speeds it up; the sail moves Sunward. (trajectory 4). Near the Sun the reflector is turned for acceleration to get a high speed (up to 400 km/s) from a powerful solar radiation. The solar escape velocity is about 619 km/s. If AB sail makes revolutions around Sun, it can then reach speed of a 1000 km/s and leaves the Solar system with a residual speed of about 400 km/s. The suggested highly reflective screen protects the apparatus from excessive solar heating. Note, the offered AB sail allows us also to brake an apparatus very efficiently from high speed to low speed. If we send an AB sail to another star, it can brake at that star and became a satellite of the star, free to move around the local system on local ‘solar’ power, with no reaction mass required.

Figure 3a. Highly reflective solar AB-sail with concentrator. (a) side view; (b) front view. Notation: 1 - highly reflective AB mirror (it may have a Fresnel form), 2 - space apparatus, 3 - highly reflective heat

screen, 4 - control mirror, 5 - reflected solar beam, 6 - inflatable support thin film ring, 7 - inflatable strain ring, 8 - thin transparent film, 9 - solar beam.


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Figure 3b. NASA solar sail. 94K. Credit NASA.

Figure 4. Maneuvers of AB solar sail for reaching a high speed: braking for flyby near Sun, great acceleration from strong solar radiation and flight away to far planets or out of our Solar system. Notation: 1 - Sun, 2 - Earth, 3 - Solar AB-sail, 4 - trajectory of solar sail to Sun, 5 - other planets, 6, 7 - speed of solar sail.

3. Estimation and Computation

1. Light Pressure Is Calculated by Equation

cEp

cEp 2,1for,)1( ==+= ρρ

(1)

where p is light pressure, N/m2; E is energy, J/m2; c = 3×108 m/s is light speed; ρ is reflective coefficient (ρ = 0 ÷ 1). At solar surface E = 64×103 kW/m2 and p = 0.4 N/m2. At Earth's orbit the E = 1,4 kW/m2 and p = 9 μN/m2.

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2. Temperature of Sail. The temperature of sail equals

4

21 )(100

εεγ

+=

ScET

(2)

where T is temperature, oK; E is heat flow, W/m2; γ is absorption coefficient of light energy, cS = 5.67 is coefficient, 0 < ε <1 is coefficients of blackness (emissivity) of two sail sides.

In [5] Ch. 12, Annt. #3 it is shown the absorption coefficient may reach γ = 10-7 for the suggested mirror. If it is taken that γ =10-4, ε1 = ε2 = 0.9, the sail temperature near the sun will be about 500 oK. That temperature is safe for many dielectric materials. The tangential sail speed in nearest point to Sun reaches 600 km/s and the abiding time of such an AB-sail near the Sun is only some minutes.

3. Trajectory and Speed of the Offered Sail

The apparatus (sail) radial speed and flight time can be estimated by equations [5] p.322.

max0max

0

20

2 ,,,2,112V

stAdMMM

pAaasVss

asV SaS

≈=+

==⎟⎟⎠

⎞⎜⎜⎝

⎛−=

(3)

where: V is radial sail speed, m/s; Vmax is maximum radial sail speed, m/s; a is initial (maximal) sail acceleration, m/s2; s is distance of the sail from a Sun center, m; s0 is minimal distance, m; p = (0.25 ÷ 0.4) is maximal light pressure [Eq.(1)], N/m2; MS is mass of sail; A is sail area, m2; d = (0.001 ÷ 0.005) is specific mass of sail, kg/m2; t is flight time from Sun to far planets, sec.

For example: If A = 200×200 = 4×104 m2, d = 0.005 kg/m2, p = 0.3 N/m2, Ma = 100 kg, that a = 40 m/s2. The period of an elliptic rotation of apparatus around Sun or planet may be computed by the equation:

200

2/311 ,2 sgKa

KT ==

π

(4)

where T1 is period of rotation, in seconds; a1 is semi-axis of big axis of ellipse, m; g0 is planet (star) gravitation at distance s0, m/s2, (for Sun K ≈ 1.33×1020 m3/s2; g0 ≈ 274 m/s2; s0 ≈ 700×106 m; for Earth K ≈ 4×1014 m3/s2, g0 ≈ 9.81 m/s2; s0 ≈ 5.378×106 m).

Computations are presented in Figure 5 - 7. It can be seen that the AB sail can reach a very high additional radius speed (up 400 km/s) at a distance of perhaps 10 millions km (<1 AU) from Sun, affording convenient escape possibilities past any object in the Solar System. The flight time from the immediate region of the Sun to the far planets is short time if we use the AB space sail (to Pluto about 150 days). But we must add in the required time of braking (from 29 km/s to ≈ 1 km/s) and about 65 days moving from Earth orbit to Sun (trajectory 4 in Figure 4) to compute total mission time to flyby.


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4. Trust from Solar Wind

The thrust from solar wind may be estimated by [5] Ch.13.

Figure 5. Approximately additional radius AB-sail speed versus distance from Sun for several initial accelerations a (acceleration at minimum distance from Sun).

Figure 6. Maximal sail radius speed versus initial sail acceleration.

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Figure 7. Trip time from Sun to far planets versus a distance from Sun.

The main particularity of the offered AB-sail-reflector is a special layer with very high reflectivity in the full main range of a solar spectrum (Figure 1) from 0.1 to 5 μm. That means the temperature of the offered sail will be significantly lower than the solar temperature and safe, allowing longer-term endurance for the spacecraft and its payload.

The other remarkable feature is a special selective coating, which has high thermal emissions close to that of an absolute black body in a wide range of the solar spectrum.

7. Solar Magnetic Field

Solar magnetic field is shown in Figure8 below. All matter in the Sun is in the form of gas and plasma because of its high temperatures. This makes it possible for the Sun to rotate faster at its equator (about 25 days) than it does at higher latitudes (about 35 days near its poles). The differential rotation of the Sun's latitudes causes its magnetic field lines to become twisted together over time, causing magnetic field loops to erupt from the Sun's surface and trigger the formation of the Sun's dramatic sunspots and solar prominences (see magnetic reconnection). This twisting action gives rise to the solar dynamo and an 11-year solar cycle of magnetic activity as the Sun's magnetic field reverses itself about every 11 years. The influence of the Sun's rotating magnetic field on the plasma in the interplanetary medium creates the heliospheric current sheet, which separates regions with magnetic fields pointing in different directions. The plasma in the interplanetary medium is also responsible for the strength of the Sun's magnetic field at the orbit of the Earth. If space were a vacuum, then the Sun's 10-4 tesla magnetic dipole field would reduce with the cube of the distance to about 10-11 tesla. But satellite observations show that it is about 100 times greater at around 10-9 tesla. Magnetohydrodynamic (MHD) theory predicts that the motion of a conducting


375

fluid (e.g., the interplanetary medium) in a magnetic field, induces electric currents which in turn generates magnetic fields, and in this respect it behaves like an MHD dynamo [13].

If we charge our space ship, we can receive additional thrust from Sun’s magnetic field.

Figure 8. The Sun’s magnetic field, spinning, warps the Heliospheric Current Sheet, the 10000 km boundary between solar magnetic north and south halves of the solar system as it washes from the Sun to beyond Pluto. Credit: NASA.

Discussion

The conventional mirror or multilayer dielectric mirror [12] is useless in this case. They have a high reflectivity only in narrow range of solar spectrum (Figure 1) and decrease the utilizable solar energy up to 2--5%. The solar surface has a temperature about 5800 oK and will melt any dielectric layer together with the sail-mirror.

Conclusion

The suggested new AB sail can fly very close to the Sun's surface and attain a high speed, which is enough for quick flight to the far planets and out of our Solar System. Advantages allow: 1) to get very high speed up 400 km/s; 2) easy to control an amount and direction of thrust without turning a gigantic sail; 3) to utilize of the solar sail as a power generator (for

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example, electricity generator); 4) to use the solar sail for long-distance communication systems.

The same researches were made by author for solar wind sail and other propulsion [7]-[11].

Possible Solar Light-Wind Sails

Figure 9. 35K.

Figure 10. 20K. Credit NASA.


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Figure 11. 203K.

Figure 12. 40K.

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Acknowledgement

The author wishes to acknowledge R.B. Cathcart (USA) and J. Friedlander (Israel) for helping to correct the author’s English.

References

(The reader can find part of these articles at the author’s website: http://Bolonkin.narod.ru/ p65.htm, http://arxiv.org, search term: “Bolonkin”; in the books "Non-Rocket Space Launch and Flight", Elsevier, London, 2006,488 pgs.; “New Concepts, Ideas, Innovations in Aerospace, Technology and Human Science”, NOVA, 2008, 502 pgs., and book “Macro-Projects: Environment and Technology”, NOVA, 2009. 536 pgs. )

[1] Tsander, K., From a Scientific Heritage, NASATFF-541, 1967 (quoting 1924 report). [2] A.A. Bolonkin, “Theory of Flight Vehicles with Control Radial Force”. Collection

Researches of Flight Dynamics, Mashinostroenie, Moscow, 1965, pp. 79–118 (in Russian).

[3] A.A.Bolonkin, “Solar Sail Engine for Spaceships”. Patent (Author certificate # 1262870), priority since 10 January 1985, USSR Patent Office.

[4] A.A. Bolonkin, “Guided Solar Sail and Electric Generator”, AIAA-2005-3857, 41st Propulsion Conference, 10-12 July, 2005, Tucson, Arizona, USA.

[5] A.A. Bolonkin, Non-Rocket Space Launch and Flight, Elsavier, London, 2006, 488 ps. [6] A.A. Bolonkin, “Method of stretching of thin film”. Russian patent application

#3646689/10 138085, 28 September 1983 (in Russian), Russian PTO. [7] A.A. Bolonkin, Electrostatic AB-Ramjet Space Propulsion, AIAA-2006-6173.

http://arxiv.org. [8] A.A. Bolonkin A.A., Beam Space Propulsion, AIAA-2006-7492. http://arxiv.org. [9] A.A. Bolonkin A.A., Electrostatic Linear Engine, AIAA-2006-4806. AEAT, Vol.78,

No. 6, 2006, pp. 502-508. [10] A.A. Bolonkin A.A., Suspended Air Surveillance System, AIAA-2006-6511.

http://arxiv.org. [11] A.A. Bolonkin A.A., Optimal Solid Space Tower (Mast), http://arxiv.org. [12] G. Landis, "Dielectric Films for Solar- and Laser-pushed Lightsails," AIP Conference

Proceedings Volume 504, pp. 989-992; Space Technology and Applications International Forum (STAIF-2000), Jan. 30 - Feb. 3, Albuquerque NM.

[13] Wikipedia. http://wikipedia.org.


Short Communication D

ELECTROSTATIC MAGSAIL1


Abstract

The first reports on the “Space Magnetic Sail” concept appeared more 30 years ago. During the period since some hundreds of research and scientific works have been published, including hundreds of research report by professors at major research universities. The author herein shows that all these works related to Space Magnetic Sail concept are technically incorrect because their authors did not take into consideration that solar wind impinging a MagSail magnetic field creates a particle magnetic field opposed to the MagSail field. In the incorrect works, the particle magnetic field is hundreds times stronger than a MagSail magnetic field. That means all the laborious and costly computations revealed in such technology discussions are useless: the impractical findings on sail thrust (drag), time of flight within the Solar System and speed of interstellar trips are essentially worthless working data! The author reveals the correct equations for any estimated performance of a Magnetic Sail as well as a new type of Magnetic Sail (without a matter ring).

Keywords: magnetic sail, theory of MagSail, space magnetic sail, Electrostatic MagSail.

Introduction

The idea of utilizing the magnetic field to aggregate matter in space, harness a drag from solar wind or receive a thrust from an Earth-charged particle beam is old. The MagSail is a gigantic (more than 50 -100 km in radius) super-conductive ring located in outer space that produces a

1 Presented as Bolonkin’s paper AIAA-2006-8148 to 14th AIAA/AHI Space Planes and Hypersonic Systems and

Technologies Conference, 6 - 9 Nov 2006 National Convention Centre, Canberra, Australia. See also AIAA-2007-0499.

2 Correspondence to: C&R, A.Bolonkin, 1310 Avenue R, #F-6, Brooklyn, NY 11229, USA, T/F 718-339-4563, [email protected] or [email protected] http://Bolonkin.narod.ru

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magnetic field and reflects the impinging solar wind, or particles beamed from the Earth (Figure1 - 3).

Figure 1. Possible form of a rigid magnetic ring and space ship. Credit NASA.

Figure 2. Possible form of a rigid magnetic ring and space ship. Credit NASA.

Unfortunately, the currently used theory for computation of drag from solar wind or thrust from particle beam is complex. The magnetic field changes in wide dispersion: every particle moves in its own trajectory and it is exquisitely difficult to accurately estimate a summary drag. Over the years, many space researchers have offered many equations for drag estimation that give remarkably different results. However, no known equations take into

Electrostatic MagSail

381

proper consideration the magnetic field of particles moving in a ring-shaped magnetic field. These particles create their own magnetic field that is OPPOSED to the MagSail’s magnetic field. This magnetic field of charged particles can be stronger—by hundreds of times—than a ring field. It can fully deactivate the MagSail magnetic field.

Figure 3. MagSail. 35K.

The simplest computation shows a profound mistake in all known works. Some of them

are presented in [1]-[39]. Take the typical MagSail ring: radius of ring is R = 50 km, electric current I =104 A. The

intensity H1 of magnetic field in center of ring is:

A/m1.01052

102 4

4

1 =⋅⋅

==RIH

(1) This intensity is approximately the same inside of the ring as well as near it. We assume

in our subsequent computation that H1 = constant. Take the typical solar wind flows into the ring at a distance from Sun = 1 AU (the Earth’s

orbit about its primary star) with average wind speed V = 400 km/s, and density N = 107 1/m3. The solar wind contains electrons and protons. Within the ring magnetic field they rotate under Lorentz force and produce their own magnetic field that is OPPOSED to the ring magnetic field, decreases it (diamagnetic property), and pumps the ring magnetic energy into energy of its own magnetic field (the sum of the energy is constant). This magnetic field from the rotated electrons (we here neglect the additional magnetic field from the rotated protons) can be estimated by equations (we consider only electrons into the ring):

( ) 1012

12 ,,

/,

2HBqNVRi

BmqVr

riH

e

μπ ==== (2)

Alexander Bolonkin

382

where H2 is magnetic intensity from rotated solar wind electrons, A/m; r is electron gyro-radius, m; i is electric currency of solar wind electrons, A; V = 400 km/s is average solar wind speed, B1 is magnetic intensity, T; μ0 = 4π10-7 is magnetic constant.

Substituting our values, we received r = 18.2 m; i = 5024 A; H2 = 276 A/m. The last magnitude shows that the magnetic intensity of solar wind electrons is 2760 times greater (H2 >> H1) than the ring magnetic intensity of MagSail! It is correct for any charged beam that interacts with the MagSail. That means all research and computation (without taking into account the influence the solar wind or charged beam into MagSail) is wrong and basically worthless for all practical space exploration and exploitation applications.

How can it happen that hundreds of researchers, professors at famous universities, audiences of specialists, members of scientific Conferences and Congresses, editors of scientific journals: "Journal of Propulsion and Power", (Editor V. Yang); Journal "Spacecraft and Rockets", (Editor V. Zoby), paid so little attention to student-level mistakes in many scientific publications and public presentations to scientific conferences? More over, the director NASA Institute for Advanced Concepts (NIAC) Mr. R. Cassanova awarded (totaling more than $1 million dollars!) to his close associate, professor R.M. Winglee (University of Washington) for pseudo-scientific work about MagSail.[1] #

It is still happening because popular textbook authors continue to use as a reference frame the interaction between the strong magnetic field of particle accelerators and small amount of charged particles where we can neglect the influence of charged particles in the magnetic field of the accelerator. With MagSails, we have the opposite situation: The weak ring magnetic field and strong magnetic field of solar wind or charged beam. The influence of charged particles on the magnetic field is then paramount and can hardly be ignored!

Figure 4a. Sun magnetic field. 48K.

# Mr. Cassanova invented a new method of legal larceny of government money. He personally awarded taxpayer-funded money grants to his friends, protégés and other useful persons for mere promises of great discoveries and revolutionary developments in future in space sciences. In eight years of NIAC’s existence under him, Mr. Cassanova spent in excess of fifty millions dollars of taxpayer money in pseudo-scientific works, but has not presented to the public even one new researched scientific concept. The Scientific Committee of a famous organization, the CAGW (Citizen against Government Waste), awarded NIAC and Mr. Cassanova pseudo-Nobel prize-2005 and 2006[42]-[47].


383

Theory of MagSail

Below, the author suggests the correct theory of MagSail operation, which takes into consideration the influence of the solar wind flow into the ring magnetic field and allows an estimation of the drag of a MagSail like device (Figure 4).

Let us to take the equations (2) in form:

( ) ( ) )(,,/

,/

,2

, 2102322

11 HHBVqNRi

BmqVR

BmqVr

riH

RIH

pe

−====== μπ (3)

where mp is mass of positive particle, for proton mp=1.67×10-27, kg; R2 is rotate radius of positive particles (protons for Solar Wind), m; R3 is capture radius of positive particles, m.

Figure 4b. Magnetic field of ring. 9K.

Notice particularly the last equation (3). In this equation, the active term is summary magnetic intensity B!

For getting the maximum solar wind drag the turn radius of heavy particles must be 90 degrees. Assume R = R1 = R2 = R3. We have 6 equations (3) and 6 unknown values. From set equations (3) we receive the estimation of the radius efficiency R:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

02

2 2μπ Vm

qINq

mRp

e (4)

From (4) we get minimal ring electric currency

qVm

I p

0

2μ

≥ (5)

Alexander Bolonkin

384

For average solar wind speed V = 400 km/s the minimal ring electric currency is I = 6.65×103 A.

The solar wing drag, D, equals approximately

22 VNmRD pπ= (6)

Results of computation are presented in figures 5 - 6. Look you attention: for receiving

good drag we need in high electric current. For typical current I = 104 A (I = 10 kA) the efficiency radius R and drag D are small.

Figure 5. Radius efficiency of MagSail via ring electric current.

Figure 6. Drag of MagSail via ring electric current at distance from Sun equals 1 Astronomical Unit.


385

Offered Electrostatic MagSail (EMS)

The conventional MagSail with super-conductive ring has big drawbacks: 1. It is currently difficult to place or build a gigantic (tens of km radius) ring in outer

space. 2. It is difficult to insert and, maintain, unquenched, large amounts of energy into a

superconductive ring. 3. A super-conductive ring needs a low temperature to function at all. The Sun heats all

bodies in the Solar System to a temperature higher than the transition temperature of super-conductive materials.

4. The super-conductive ring explodes if the temperature is increased over critical value.

5. It is difficult to control the value of MagSail thrust and the thrust direction. The author offers new Electrostatic MagSail (EMS). The innovation includes the central

positive charged small ball and a negative electronic equal density ring rotated around the ball (Figure 7).

Figure 7. Electrostatic MagSail. Notations: 1-Spaceship; 2-Positive charged ball; 3–electrical ring; 4-solar wind; 5-EMS drag.

The suggested EMS has the following significant advantages in comparison with conventional MagSail:

(1) No heavy super-conductive large ring. (2) No cooling system for ring is required. (3) Electronic ring is safe. (4) The thrust (ring radius) easily changes by varying of the ball charge.

Alexander Bolonkin

386

Electrostatic Offered MagSail Theory

Let us consider a method of estimation of electronic ring magnetic intensity in the electronic ring’s center [2]. We will take into consideration a repulsion of electrons from the electron ring (blocking the ball charge by the electronic ring) and relativistic speed of electrons. We will not take into consideration the diamagnetic property of the solar wind or charged beam because our purpose here is only to find the magnetic intensity from the electronic ring. The blocking the MagSail magnetic field by the particles flow the reader find in previous section (above). We also neglect the radiation of the rotary electronic ring because the ring is a symmetrical circle, has constant density and that does not emit synchronous radiation (this assumption needs further research. Synchronous radiation appears when electrons rotate in an outer magnetic field, the electron ring is unclosed or has non-constant density. In our case, the ring electric and magnetic fields are constant and do not emit energy in outer space).

From equilibrium of the centrifugal and attraction forces we have

,,,)(21

22

2212

QQq

QmMR

QQQkR

MVe

e >=−

= (7)

where M is mass of electron ring, kg; Ve is speed of electrons, m/s; R is ring radius, m; k = 9×109 is electrostatic constant; Q1 is positive charge of the central ball, C; Q2 is negative charge of the electron ring, C; me is mass of electron, kg; q = 1.6×10-19 is electron charge, C.

The best relation between Q1 and Q2 is Q1 = 2Q2. Substituting this value into (7) we receive

( ) HBR

VQIRIH

mqkRVQ

RQ

mqkV e

e

e

ee 0

22

222 ,

2,

2,

/, μ

π====⎟⎟

⎠

⎞⎜⎜⎝

⎛= (8)

where I is ring electric currency, A; H is magnetic intensity, A/m; B is magnetic intensity, T; μ0 = 4π10-7 is magnetic constant.

Substitute the previous Eqs. (8) in the last equation (8) for B and use the formula for relativistic electron mass

( )( )

2

30

30

20

30

14/,

1,,

/4 ββ

πμ

ββ

πμ

−=

−===

kRqmcBmm

cV

mqkV

RB ee

ee

e

e (9)

where c = 3×108 m/s is light speed; me0 = 9.11×10-31 kg is electron mass at Ve = 0.

Let us to add formula for estimation charge and radius of ball and substitute the known values into last equation (9). We received the final equations for estimation of MagSail size:

( ) 0

22

2

2

0

2

22

33

02

33 2,

1/,

111036.1,

11107.1

EkQa

mqkRcQ

RBH

RB

e

=−

=−

⋅==−

⋅= −

ββ

ββ

μββ (10)

where a is radius of ball, m; E0 is safety electric intensity at ball surface, V/m.


387

If the magnetic intensity into ring is constant, we can estimate the energy needed for starting of ring:

2,

22,

2Φ,

2

2

000ILWR

RSLILS

RI

RIH ======

πμμμ (11)

where Φ is magnetic flux, Wb: L is ring inductance, Henry; S is ring area, m2; final equation in (11) W is energy, J. For conventional ring of MagSail having R = 50 km and I = 104 A the W = 5×106 J. The Eqs. (7) - (11) allow us to find the magnetic intensity of a MagSail for a given ring radius and electron speed (without the presence of solar wind or plasma beam), charge and radius of ball for a given electrostatic ball intensity, energy of a rotating ring, but they do not permit us to estimate a MagSail’s drag. We can estimate the drag of a conventional MagSail (see section above), to compute the drag of the electrostatic sail offered by author in [3] Chapter 18, but unfortunately we cannot do an estimate for the drag EMS at the present time. The trajectory of charged particles into both fields (magnetic and electric) are very complex.

Possible forms of MagSail, Space Ships and apparatus. (Credit NASA)

Alexander Bolonkin

388

References

(Reader can find part of these articles at the web pages: http://Bolonkin.narod.ru/p65.htm, http://arxiv.org, search term: "Bolonkin", in the book "Non-Rocket Space Launch and Flight", Elsevier, London, 2006, 488 pgs., book “New Concepts, Ideas, Innovations in Aerospace, Technology and Human Science”, NOVA, 2008, 502 pgs., and book “Macro Projects: Environment and Technology”, NOVA, 2009, 536 pgs.)


389

[1-39] (Respectively). Some Manuscripts about MagSail published or presented to AIAA Conferences: (1) Winglee R.,M., at al. (4 co-authors), "Mini-Magnetospheric Plasma Propulsion. Tapping the Energy of the Solar Wing for Spacecraft Propulsion", Journal of Geophysical Reserach. Vol. 105, No. 6., 2000. (2) AIAA-2006-5257, (3) AIAA-2006-769 (4 coauthors). (4) JSP 2006, Vol. 43, no. 3, (667-672). (5) AIC-05-C4.6.07. (6) AIAA-2005-4463 (6 coauthors). (7) AIAA-2005-4791. (8) AIAA-2005-4461. (9) AIAA-2004-3502 (7 co-authors). (10) AIAA-2003-4292 (8 co-authors). (11) IAC-03-5.6.06. (12) AIAA-2003-4886. (13) AIAA-2003-4292. (14) AIAA-2003-6201. (15) AIAA-2003-5226. (16) AIAA-2003-5227. (17) "Journal Propulsion and Power (JPP)" 2003, Vol.19, no 6 (1129-1134). (18) JPP, vol.20, No 4 (763-764). (19) JPP, vol.21, No. 5, 2005 (853-861)(4 co-authors). (20) AIAA-2004-3706. (21) AIAA-2001-840. (22) AIAA-2001-3517. (23) AIAA-1998-3403. (24) AIAA-1997-3072. (25) AIAA-1997-3208. (26) AIAA-1997-2792 (3 co-authors). (27) Journal "Spacecraft and Rockets". 1994, Vol. 31, No. 2 (342 - 344). (28) AiAA-1992-3862. (29) AIAA-1991-2538. (30) AIAA-1991-3352. (31) AIAA-1990-2367. (32) AIAA-1990-1997 (6 co-authors). (33) AIAA-1990-3799. (34) AIAA-1989-2861, (35) JSR 1991, Vol. 28, no.2, (197-203). (36) AIAA-1990-1997. (37) AIAA-1990-2367. (39) AIAA-1990-3799. (39) AIAA-1989-2941.

[40] Bolonkin A.A., "A Space Motor Using Solar Wind Energy (Magnetic Particle Sail)", IAF-0615. The World Space Congress, 28 August - 5 September 1992, Washington DC, USA.

[41] Bolonkin A.A., Non-Rocket Space Launch and Flight, Elsevier, London, 2006, 488 pgs. [42] GO TO: http://auditing-science.narod.ru or http://www.geocities.com/auditing.science/ [43] GO TO: http://NASA-NIAC.narod.ru. [44] Johnson A., Space Research: Organizing for Economical Efficiency. Presented as paper

AIAA-2006-7224 in Conference "Space-2006", 19-21 September 2006, San Diego, California, USA.

[45] Johnson A., Space research: problems of efficiency. Journal "Actual Problems of Aviation and Aerospace System", No.1, 2007. http://www.kcn.ru/tat_en/science/ans/journals/rasj_cnt/07_1_10.html

[46] Bolonkin A.A., “New Concepts, Ideas, Innovations in Aerospace, Technology and Human Science”, NOVA, 2008, 502 pgs., Appendix 1, pp. 445 – 458.

[47] Bolonkin A.A., Cathcart R.B., “Macro Projects: Environment and Technology”, NOVA, 2009, 536 pgs.). Part III, pp. 465 - 479.


Short Communication E

THE 27-DAY PERIODICITY IN GEOMAGNETIC ACTIVITY AND SOLAR WIND PARAMETERS

OVER SOLAR CYCLE 23

Ana G. Elias1,2, Virginia M. Silbergleit1,3, Ana Curcio3 and Patricia A. Larocca3

1Consejo Nacional de Investigaciones Cientificas y Tecnicas, CONICET, Argentina 2Universidad Nacional de Tucuman, Facultad de Ciencias Exactas y Tecnologia,

Departamento de Fisica, Tucuman, Argentina 3Universidad Nacional de Buenos Aires, Facultad de Ingenieria,

FIUBA, Buenos Aires, Argentina

Abstract

Geomagnetic activity and solar wind parameters are analyzed in terms of the periodicity linked to solar rotation that is the 27-day cycle. Its fluctuation in frequency and time is studied using the wavelet power spectrum. For this purpose we used the geomagnetic activity aa index and three solar wind parameters: magnetic field magnitude (B), density (d) and velocity (v). The sunspot number, Rz, is also analyzed to have a solar activity reference. The study was carried out for the period July 1996 – December 2005, which corresponds to solar cycle 23, except for the last years corresponding to its final minimum level. For the time period and parameters here analyzed, the 27-day periodicity is observed to have enhanced power during maximum and falling phase of the solar activity cycle, with no significant power during the ascending phase, not even in solar activity. Besides the time evolution, a periodicity variation is also noticed along the solar cycle. In some cases the period decreases as the solar cycle approaches minimum levels, as expected from the meridional movement of active regions towards lower solar latitudes during this time. However, periodicites lower than 27.27 days (synodic period at the solar equator ) are also observed, pointing out inner regions of the sun as possible sources of the active regions, or a surface phenomenon arising because of solar activity shifts during solar rotation.

Ana G. Elias, Virginia M. Silbergleit, Ana Curcio, et al.

392

Introduction

Magnetic active regions’ distribution at the solar surface is not homogeneous, but tend to form regions of activity at preferred longitudes. This tendency for active regions to cluster in active longitudes has long been recognized (Warwick, 1964). The lifetime of these activity bands were found to be of several solar rotations (Bogart, 1982; Bai, 1987). A 27-day period is therefore reflected in solar and geomagnetic activity parameters as seen from Earth. Observations of different structures, however, give slightly different synodic periods of rotation (Ruzmaikin et al., 2001).

Near the solar surface, the synodic rotation rate at the equator corresponds to 27.27 days (sidereal rotation period 25.38 days), increasing gradually to 35 days as one moves toward the poles in the sun. This pattern extends through the convection zone. After the tachocline, the angular velocity adjusts to apparent solid-body with a period of around 26.8 days (Howe et al., 2000). For a thorough analysis of the internal rotation of the sun see Thompson et al. (2003).

The rotation rate changes through the solar cycle and also from one solar cycle to another (Gilman and Howard, 1984; Astafyeva and Bazilevskaya, 2000; Kane, 2002; Rybak et al., 2005; Balthasar, 2007; to mention a few). Many studies exist on this subject, some dating back to the XVIII century. Following, some works are mentioned as examples of the diversity of this theme.

Pap et al. (1990) observed that the 27-day periodicty is more pronounced in the descending phase of the solar cycle than in the ascending phase, explaining that during maximum and falling phases of solar cycle, the magentic field is much more organized and long-lived. Temmer et al. (2004, 2005), analyzing solar cycles 19 to 22, reported a 24-day period in solar flare occurrence which is observed mainly around the solar maximum. An explanation refers to the rotation of the solar interior: deeper zones of activity rotate faster than the solar photosphere. Bai (1987) finds that active zones rotate with a period of 26.75 days. He also finds superactive regions which have similar longitudes in a frame rotating at a constant rate of 23.7 days. This could be due to activity sources in the deep layer rotating at that rate. Bai and Sturrock (1993), from an analysis of solar flares, proposed a fundamental period of 25.5 days as a result of two activity centers that rotate about an axis tilted by 40º, which gives rise to the well known 154-day period.

In the present work, the fluctuation in frequency and time of 27-day periodicity is studied using the wavelet power spectrum. The aa index, three solar wind parameters (magnetic field magnitude, B, density, d, and velocity, v) and the sunspot number, Rz, are analyzed along solar cycle 23. With this study we attempt to find some additional results on a subject that already has many contributions.

Data Analysis

Daily solar wind parameters, the aa index and Rz where analyzed for the period July 1, 1996 to December 31, 2005 (solar cycle 23). Magnetic field magnitude (B), density (d) and velocity (v) of the solar wind are OMNI data obtained from the GSFC/SPDF OMNIWeb interface at http://omniweb.gsfc.nasa.gov (King and Papitashvili, 2004). The aa index and Rz are available at the National Geophysical Data Center (http://www.ngdc.noaa.gov/).

The 27-Day Periodicity in Geomagnetic Activity and Solar Wind Parameters

393

The few data missing in the OMNI records for the period we choose to analyze, where linearly interpolated in order to obtain the complete daily data sets required by the statiscal method we applied.

The wavelet power spectrum of the five data series was assessed using the wavelet software provided by C. Torrence and G. Compo (available at http://atoc.colorado.edu/research/wavelets/). The Morlet wavelet is used with the parameter ω = 40, which, in our case, shows a reasonable resolution in both frequency and time. The power spectra, shown in Figure 1, was assessed for the period range 24-30 days in order to determine frequency and time variation of periodicities linked to the solar rotation period. Zones in the figures with colors from yellow to red are significant at a 95% level.

Beginning with the solar wind, in the case of B, enhanced power of the solar rotation period is obtained during solar maximum (around year 2000) and during almost the complete declining phase of the solar cycle. When a global power spectrum is calculated, the most prominent period is 27.5 days, however, it appears as a 28.6-day periodicity around solar maximum, decreasing towards the synodic period 27.25-days through the declining phase of the solar cycle. In the case of d, significant power is noticed at 27.0 days only at the maximum of the solar cycle. For V, enhanced power is obtained at the synodic rotation rate during solar maximum and during the declining phase, being the latter more prominent, as opposed to what happens with d.

(a)



394

(b)

(c)



395

(d)

(e)

Figure 1. Wavelet power spectrum using the Morlet wavelet with the parameter ω = 40, for the period range 24-30 days assessed for the time series: (a) solar wind magnetic field intensity, B, (b) solar wind density, d, (c) solar wind velocity, v, (d) aa inex, (e) sunspot number Rz, during the period period July 1, 1996 to December 31, 2005 (solar cycle 23). Zones in the figures with colors from yellow to red are significant at a 95% level.


396

In the case of aa, the frequency and time behaviour of the spectrum is much more complex than in the case of the solar wind parameters just described. Again, enhanced power is oberved at the maximum and towards the declining phase of the solar cycle. The most important periodicity observed corresponds to 27.5 days during the maximum and falling phase. However, and with much less power, significant peaks are noticed at lower (∼26 days) and higher periods (∼30 days) towards the solar cycle minimum. During the falling phase, it also appears a significant peak at a 24-day period, as that already noticed by Temmer et al. (2004, 2005).

For Rz, power peaks appear at 27.0-days at solar maximum, around year 2000, and then this peak period decreases to 26.3-days. This period variation is highly consistent with the fact that at the start of a cycle, sunspots tend to appear at mid-latitudes and then move toward the equator as each cycle progresses. Both values, lower than the synodic period, may be due to these magnetic features are anchored at levels below the photosphere moving faster (Gilman, 1974; Bai, 1987).

Comparison of the Solar-Rotation Related Cycle with Variations at Higher Frequencies

The wavelet power spectrum was also assessed for the period range 11-30 days in order to determine the relative importance of the solar rotation related cycles with lower periodicities, as it is the well-known 13.5-day period. Figure 2 presents the results obtained for the five parameters here analyzed.

(a)



397

(b)

(c)



398

(d)

(e)

Figure 2. Wavelet power spectrum using the Morlet wavelet with the parameter ω = 40, for the period range 11-30 days assessed for the time series: (a) solar wind magnetic field intensity, B, (b) solar wind density, d, (c) solar wind velocity, v, (d) aa inex, (e) sunspot number Rz, during the period July 1, 1996 to December 31, 2005 (solar cycle 23). Zones in the figures with colors from light-blue to red are significant at a 95% level.


399

In the case of B, the 13.5 day cycle has more power than the solar-rotation cycle. It appears with the same structure and time variation as the 27-day period, presenting half-period length and suggesting that the solar active structures are 180º appart over the solar surface. This is why, prominent half-rotation cycles are observed. During a short interval of time, between 2003 and 2004, a 22.5-day peak is also observed with similar power to that of the solar rotation period.

In the case of V, the 13.5-day period presents again the same structure and variability as the solar rotation period, but with less power. For d, it has increased power during the declining phase of the solar cycle, although the rotation period is important during the maximum and almost absent during the phalling phase.

The aa power spectrum, presents a prominent peak at 21.9 days with more than twice the power of the solar rotation cycle. However, when one looks at the global power spectrum during the whole solar cycle, it appears with half the power due to its short time interval appearance. The 13.5-day periodicity, which is significant only during the falling phase, is also more prominent than the solar rotation period.

The Rz power spectrum, do not present a significant peak at the 13.5 days during solar cycle 23, being the solar rotation period the most important at the low frequency range here analyzed.

Conclusion

As already mentioned and observed by several authors, the periodicity linked to solar rotation presents a time varying power and a fluctuating periodicity value.

For the parameters here analyzed, and taking into account that only one solar cycle was studied, this periodicity is enhanced during maximum and falling phase of the solar activity cycle. During the ascending phase, there is no significant power at this period. One may think that its importance during maximum and falling phase may mask its presence during rising phase. However, Ozguc et al. (2002) analyzing only the ascending branch of the solar cycle of cycle 23, do not detect this periodicity, being a 35-day cycle the lowest significant periodicity they obtain.

The frequency variation of the solar rotation period may be probably due, not only to meridional movements of active regions over the solar surface, but also to radial movements where a gradient of angular velocity exists.

The 27.0 value observed in d and Rz coincides with the 27.03-day periodicity observed by Neugebauer et al. (2000), which they explain by a depth increase of the corresponding solar source. Ruzmaikin et al. (2001) further explains this fact by the presence of a robust magnetic structure on the sun which rotates more rapid than the solar equatorial rotation. Henney and Harvey (2002), who showed later that the coherency of this periodicity is significant for the past two decades, found that its origin are long-lived complexes of active regions in the norhtern hemisphere..

In the case of aa, a very strong 21.9-day period appear over a short time interval (2003- 2004), which, although stronger than any other cycle in the 11-30 days range, due to its short duration, it does not appear as a significant peak in the global spectrum. Its time appearance coincides with the 22.5-day peak observed in B.


400

Regarding the 13.5-day period, although absent in Rz, it appears as the strongest cycle in most of the cases here analyzed: in the case of B, over the whole period when the solar rotation related period is significant, and in the cases of d and aa, during the solar cycle falling phase. For V, although not the strongest, the 13.5-day period is a very important cycle. This means, that the 180º separation in active longitudes is a strong determinant of time variation in active regions and solar wind characteristics.

The study and understanding of periodic variations in solar and geomagnetic activity (including solar wind parameters) is essential for predicting future activity levels and for characterizing the sources in the sun that generates them. To understand solar influences on global climate change and space weather we need to comprehend solar variations. For this, we require models and analysis based on observation results. Our results, intend to contribute to this subject through the latter option.

Acknowledgements

We acknowledge the National Space Science Data Center for providing the OMNI data, and C. Torrence and G. Compo for the wavelet software.

References

Astafyeva, N.M., Bazilevskaya, G.A., Long term changes of cosmic ray intensity: spectral behaviour and 27-day variations. Phys. Cham. Eartc (C) 2000, 25, 129-132.

Bai, T., Distribution of flares on the sun: Superactive regions and active zones of 1980-1985. Ao. J. 1987, 314, 795-807.

Balthasar, H., Rotational periodicities in sunspot relative numbers. Astron. Astrophys. 2007, 471, 281-287.

Bogart, R.S., Recurrence of solar activity: Evidence for active longitudes. Sol. Phys. 1982, 76, 155-165.

Gilman, P.A., Solar rotation. Annu. Rev. Astron. Astrophys 1974, 12, 47-70. Gilman, P.A., Howard, R., Variations in solar rotation with the sunspot cycle. Ap.J. 1984,

283, 385-391. Henney, C.J., Harvey, J.W., Phase coherence analysis of solar magnetic activity. Solar

Physics, 2002, 207, 199-218. Howe, R., Christensen-Dalsgaard, J., Hill, F., Komm, R.W., Larsen, R.M., Schou, J.,

Thompson, M.J., Toomre, J., Dynamic variations at the base of the solar convection zone. Science 2000, 287, 2456-2460.

Kane, R.P., Variability in the periodicity of 27 days in solar indices. Solar Physics, 2002, 209, 207-216.

King, J.H., Papitashvili, N.E., Solar wind spatial scales in and comparisons of hourly Wind and ACE plasma and magnetic field data. J. Geophys. Res. 2004, 110, doi 10.1029/2004JA010804.

Neugebauer, M., Smith, E.J., Ruzmaikin, A., Feynman, J., Vaughan, A.H., The solar magnetic field and the solar wind: Existence of preferred longitudes. J. Geophys. Res. 2000, 105, 2315-2324.


401

Ozguc, A., Atac, T., Rybak, J., Flare index variability in the ascending branch of solar cycle 23. J. Geophys. Res. 2002, 107, doi 10.1029/2001JA009080.

Pap, J., Tobiska, W.K., Bouwer, S.D., Periodicities of solar irradiance and solar activity indices, I. Solar Physics 1990, 129, 165-189.

Ruzmaikin, A., Feynman, J., Neugebauer, M., Smith, E.J., Preferred solar longitudes with signatures in the solar wind. J. Geophys. Res. 2001, 106, 8363-8370.

Rybak, J., Ozguc, A., Atac, T., Sozen, E., Intermittence of the short-term periodicities of the flare index. Adv. Space Res. 2005, 35, 406-409.

Temmer, M., Veronig, A., Rybak, J., Brajsa, R., Hanslmeier, A., On the 24-day period observed in solar flare occurrence. Solar Physics 2004, 221, 325-335.

Temmer, M., Rybak, J., Veronig, A., Hanslmeier, What causes the 24-day period observed in solar flares?. Astron. Astrophys 2005, 433, 707-712.

Thompson, M.J., Christensen-Dalsgaard, J., Miesch, M.S., Toomre, J., The internal rotation of the sun. Annu. Rev. Astron. Astrophys 2003, 41, 599-643.

Warwick, C.S., Longitude distribution of solar flares. Ap. J. 1965, 141, 500-504.

In: Handbook on Solar Wind: Effect, Dynamics … ISBN: 978-1-60692-572-0 Editor: Hans E. Johannson © 2009 Nova Science Publishers, Inc.

Short Communication F

WEIBULL PARAMETERS FOR WIND SPEED DISTRIBUTION AT FIFTEEN LOCATIONS IN ALGERIA

Y. Himri1,1, S. Himri2,2 and A. Boudghene Stambouli3,3 1Electricity & Gas National Enterprise (SONELGAZ) Béchar, Algeria 2University of Béchar, Department of fundamental Sciences, Algeria

3University of Sciences and Technology of Oran, Department of Electronics, Algeria

Abstract

In the present study the Weibull parameters distribution function were computed for 15 locations in Algeria. The wind data which covers a period of almost 10 years between 1977 and 1988 was adopted. The average wind speed at a height of 10 m above ground level was found to range from 2.3 to 5.9 m/s. The Weibull distributions parameters (c & k) were found to vary between 3.1 and 7.2 m/s and 1.19 to 2.15 respectively. Higher wind speeds were observed in the day time between 09:00 and 18:00 h and relatively smaller during rest of the period. Generally the long-term seasonal wind speeds were found to be relatively higher during spring to the autumn month of September compared to other months. The two parameters of a Weibull density distribution function for the three areas namely (Littoral, Highlands and Sahara) were compared and wider distributions were observed in the Sahara. It is also noticed from this work that the Weibull distribution give a good fit to experimental data. The aim of this work is to provide information about the distribution of wind in different regions of Algeria (Littoral, Highlands and Sahara) and give useful insights to engineers and experts dealing with wind energy.

1 Correspondence to: Electricity & Gas National Enterprise (SONELGAZ) Béchar, Algeria, 05 rue Mokadem

Ahmed, Béchar 08000, Algeria, E-mail: [email protected], Tel.: +213 774 757714; fax: +213 49 801674. 2 E-mail: [email protected] 3 E-mail: [email protected]

Y. Himri, S. Himri and A. Boudghene Stambouli

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1. Introduction

The Swedish physicist W. Weibull is among the first founders of Probabilistic Mechanics of Structures and Materials. His probability laws have been also used in many other applications, such as aerospace, electric power, medical, electronics and every industry. In recent years most attention has been focused on this method for wind energy applications, the many publications for different locations of the world have demonstrated that the Weibull two parameters distributions, is the most widely used to fit the wind speed data. Justus et al. [1] applied the Weibull and Log-normal distribution to wind speed data from more than a hundred stations of the USA National Climatic Centre and concluded that the Weibull Distribution rendered the best fit.

Gupta [2] performed work on estimating the annual and monthly Weibull parameters for five locations in India and these revealed two parameters which varied over a wide range. Lun and Lam [3] computed the two parameters of the Weibull density distribution function for three different locations in Hong Kong, using a long-term data source, consisting of 30 years of hourly mean wind speed data. Hennessey [4] found that the energy output calculated using wind speeds derived from the Rayleigh distribution was within 10% of those derived from the Weibull distribution. Garcia et al. [5] solved the estimation of the annual Weibull and Log-normal parameters from 20 locations in Navarre, Spain. Akpinar et al. [6] carried out a study using Weibull density function to demonstrate wind energy potential of Maden-Elazıg in eastern Turkey.

Results reveal that the mean speed for investigated site varies between 5 and 6 m/s and yearly average power density is 244.65W/m2. Ulgen et al. studied the wind variation for a typical site using Weibull distribution and Rayleigh distribution was found to be suitable to represent the actual probability of wind speed data for the site studied [7].

Sahin et al. [8] determined the wind energy potential of the east Mediterranean region of Turkey and identified the best wind source locations using a computer package program called the Wind Atlas Analysis and Application Program (WAsP). Youcef Ettoumi et al. used first-order Markov chain and Weibull distribution methods for statistical bivariate modeling of wind using the data wind speed and wind direction measurements collected every 3 h at the meteorological station of Essenia. Also, a detailed study has been made on the statistical features of the wind at Oran, in Algeria [9].

Himri et al [10] presented the wind characteristic at three locations in Algeria. They concluded that the energy could be harnessed for almost 64% the time using wind machines with cut-in –speed of 3 m/s or more. In the present study the Weibull parameters namely, scale parameter c and shape parameter k were used for describing the wind speed frequency distribution. These two parameters were computed using WAsP.

The aim of this work is to provide information about the distribution of wind in different regions of Algeria (Littoral, Highlands and Sahara) and give useful insights to engineers and experts dealing with wind energy.

Weibull Parameters for Wind Speed Distribution at Fifteen Locations in Algeria

405

2. Wind Data and Sites Description

In this study, the wind speed data which cover a period of 07 to 12 years (between1976 – 1988) are used at 15 sites in Algeria. Table 1 shows names, latitude, longitude, altitude, measurement duration and the measurement years of the locations.

Table 1. Geographical coordinates of the data collection stations used in the study.

Location Latitude (deg)

Longitude (deg)

Altitude (m)

Duration (years)

Measurement Years

Adrar 27° 49’ N 00° 17’ E 263 11 1977 - 1988

Tindouf 27° 40’ N 08° 06’ W 401 8 1976 - 1984

Béchar 31° 37’ N 02° 14’ W 811 12 1976 - 1988

Tamanrasset 22° 47’ N 05° 31’ E 1377 12 1976 - 1988

In Amenas 28° 03’ N 09° 38’ E 561 11 1977 - 1988

Ghardaia 32° 24’ N 03° 48’ E 468 9 1978 - 1987

El Oued 33° 30’ N 06° 47’ E 62 12 1976 - 1988

M’sila 35° 40’ N 04° 30’ E 441 11 1977 - 1988

Setif 36° 11’ N 05° 15’E 1033 7 1981 - 1988

Tlemcen 34° 57’ N 01° 17’ W 592 7 1980 - 1987

Oran 35° 38’ N 00° 37’ W 90 9 1979 - 1988

Chlef 36° 12’ N 01° 20’ E 143 8 1977 - 1985

Algiers 36° 43’ N 03° 15’ E 24 9 1979 - 1988

Skikda 36° 53’ N 06° 54’ E 1 9 1979 - 1988

Annaba 36° 49’ N 07° 49’ E 5 9 1979 - 1988

The wind speed measurements were made 10 meters above ground level and recorded

every three hour interval (viz, 0, 3, 6, 9, 12, 15, 18 and 21 hours) at all the stations. These stations cover Algeria from north to south and from east to west, including the

highland region. The geographical locations of these stations are also shown in Figure 1. Figure 2 provides the variation of long-term mean wind speed during entire data

collection period at 15 stations under consideration in this study. It is seen from Figure 2 that Adrar has the maximum mean wind speed of 5.9 m/s while

Tlemcen has the minimum wind speed of 2.3 m/s. It is also noticed that both the southern and highland regions have higher mean wind speeds compared to the northern regions like Oran, Chlef, Algiers, etc. it is also observed that towns in the south western area such as Tindouf and Adrar has higher mean wind speeds. The seasonal variation of mean wind speed for all the locations are depicted in Figure 3.


406

Figure 1. Map showing the locations of the wind measurement stations.

Figure 2. Variation of long-term mean wind speed at all sites.


407

Figure 3. Seasonal variation of long-term mean wind speed

As seen from Figure 3, higher wind speeds were found during spring to the autumn month of September compared to other months. This trend is true for all locations. The diurnal change in long-term mean wind speed at all stations is shown in Figure 4.


408

Figure 4. Diurnal variation of long-term mean wind speed


409

In general the higher wind speeds were observed in the day time between 09:00 and 18:00 h and relatively smaller during rest of the period. This indicates that higher electricity could be produced during 09:00–18:00 h, which also coincide with higher electricity demand time. It is also evident from this Figure that wind speed was highest at Adrar while lowest at Tlemcen during the entire day.

3. The Weibull Distribution Function

The wind speed data is obtained from the Algerian Wind Energy Atlas (1990). As noticed from the Weibull parameters, namely, shape parameter k and scale parameter c are computed for all 15 locations in Algeria based on annual average wind speed. As shown from Figure 5.

Figure 5. Weibull distribution parameters in all 15 stations

The value of the shape parameter is found to be around 1.63 in the highland part of the country whereas at coastal sites this value ranges from 1.19 to 1.76. A higher value of k, i.e. 2.15, is obtained in the south western of Algeria. For the scale parameter c, highest values, i.e. greater than 5.5 were found at Adrar, Tindouf, In Amenas and Ghardaia (Sahara sites) whiles the lowest (lower than 5.5) at the rest areas of the country.

Figure 6 shows the wind speed histograms of the percent frequency distribution for all 15 locations.

These curves were obtained by superimposition of the values of k and c for different locations on the wind speed histograms the wind speed data for almost locations are good fit represented by the Weibull distribution.


410

Figure 6. Wind frequency histograms for all 15 stations

4. Conclusion

We can conclude from this work the following results: 1. Using wind data, consisting of hourly wind speed records over almost 10 year period,

1977–1988, wind data at 15 locations, Algeria were investigated. 2. The average wind speeds were found to range between 2.3 – 5.9 m/s. The maximum

mean wind speed was observed in Adrar while the minimum value was noticed in Tlemcen.


411

3. The shape parameter varies between 1.19 and 2.15. The higher values of the parameters k were found in the southwest region of Algeria (Adrar and Tindouf) while the minimum values in the northern region (Tlemcen, and Chlef).

4. The scale parameter varies between 3.1 and 7.2. The values of c have maximum at Adrar and Tindouf but their minimum values is found in Tlemcen.

5. Generally the long-term seasonal wind speeds were found to be relatively higher during spring to the autumn month of September compared to other months.

6. The higher wind speeds were observed in the day time between 09:00 and 18:00 h and relatively smaller during rest of the period.

7. The aim of this work is to provide information about the distribution of wind in different regions of Algeria (Littoral, Highlands and Sahara) and give useful insights to engineers and experts dealing with wind energy.

Acknowledgements

The authors would like to thank Mr A. Slimani Rector of University of Béchar. Further thanks are due respectively to Mrs R. Aissaoui and Mr S. Guezzane Director of CREDEG (Centre Recherche Et Développement Electricité Gaz); Sonelgaz R&D Office for their cooperation.

References

[1] Justus, C. G; Hargraves, W.R.; Yalcin, A. Nation wide assessment of potential output from wind powered generators. Journal of Applied Meteorology. 1976,15(7),673-8.

[2] Gupta, B.K. Weibull parameters for annual and monthly wind speed distributions for five locations in India. Solar Energy. 1986, 37(6), 469–71.

[3] Lun, I.Y.F.; Lam, J. C.A study of Weibull parameters using long- term wind observations. Renewable Energy. 2000, 20, 145-153.

[4] Hennessey, J. J. A comparison of the Weibull and Rayleigh distributions for estimating wind power potential. Wind Engineering, 1978, 2(3),156-64.

[5] Garcia, A.; Torres, J.L.; Prieto, E.; De Francisco, A. Fitting wind speed distribution: a case study. Solar Energy. 1998, 62 (2), 139–144.

[6] Akpinar, E.K.; Akpinar, S. Determination of the wind energy potential for Maden-Elazig Turkey. Energy Convers Manage. 2004, 45,2901–14.

[7] Ulgen, K.; Genc, A. ; Hepbasli, A.; Oturanc, G. Assessment of wind characteristics for energy generation. Energy Sources. 2004,26(13),1227–37.

[8] Sahin, B.; Bilgili, M.; Akilli, H. The wind power potential of the eastern Mediterranean region of Turkey. J Wind Eng Ind Aerodynam. 2005,93,171–83.

[9] Youcef Ettoumi, F.; Sauvageot, H., Adane AEH. Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribution. Renewable Energy. 2003,28,1787–802.

[10] Himri, Y.; Draoui, B.; Himri, S. Wind characteristics of Algeria. Nanotechnology Conference and Trade Show June 1-5 Boston Massachusetts U.S.A. 2008.


Short Communication G

ON THE LIMITS OF APPLICABILITY OF THE RAY INTERFERENCE INTEGRAL METHOD FOR

CALCULATIONS OF THE TEMPORAL STRUCTURE OF SOLAR RADIO BURSTS

A.N. Afanasiev1 and N.T. Afanasiev2 1Institute of Solar-Terrestrial Physics, Irkutsk, Russian Federation

2Irkutsk State University, Irkutsk, Russian Federation

Abstract

We discuss the possibility of using the ray interference integral method to carry out calculations of scattering of radio emission from sources embedded in the corona and solar wind. We point out that preliminary analysis of the topology of caustics produced by geometrical optics rays and by partial waves forming the interference integral enables correct calculations of the solar radio burst structure.

Introduction

The interpretation of the temporal structure of solar radio bursts is one of the most difficult issues in solar physics. This structure in general is determined both by processes occurring within the source itself and by propagation effects in the corona and solar wind. The near-solar plasma represents an extremely inhomogeneous and nonstationary medium. It is natural, therefore, that the universal analytical method to describe radio emission propagation in such a medium does not exist. That is why it is necessary to use various approximate approaches.

Based on the ray interference integral (RII) approximation, Afanasiev and Altyntsev (2006) and Afanasiev (2006) analysed the observed temporal structure of the solar radio spikes and of the type IIId decameter bursts. However, the limits of applicability of the RII method for taking into account strong regular refraction of radio emission in the solar corona require additional discussion. Therefore, we shall consider here a question concerning the

A.N. Afanasiev and N.T. Afanasiev

414

fundamental possibility of calculating the structure of solar radio emission propagated through the corona and solar wind by the RII method.

Theoretical Relations and Discussion

According to Orlov (1972, 1974), the ray interference integral represents the solution of the wave equation, written as a superposition of infinitely many partial waves (WKB modes):

( ) ( )∫= αα dUU s ,rr , (1)

where

( ) ( ) ( )[ ]αψαα ,exp,, rrr sss ikAU = , (2)

cfk π2= is the wave number, f is the radiation frequency, c is the velocity of light in a

vacuum, and α is the spectral parameter. The phase of a WKB mode ( )αψ ,rs is the solution of the eikonal equation

( )[ ] ( )rr εαψ =∇ 2, , (3)

where ( )rε is the dielectric permittivity of medium. The amplitude of a WKB mode is determined from solving the transport equation

02 2 =∇+∇∇ ssss AA ψψ (4)

and have the form:

( )( )

( )rr

s

ss J

AA0

= , (5)

where sJ is the ray divergence of the partial wave, and ( )0

sA is determined by the initial conditions.

The calculation of Equation (1) by the stationary phase method results in the geometrical optics (GO) approximation for the field (Orlov, 1972). In this case, the equation, from which the stationary points are determined, coincides with the geometrical optics ray equation. If the observer is at the caustic formed by the geometrical optics rays, then the GO approximation gives an infinite increase in the field amplitude (Kravtsov and Orlov, 1990).

Earlier publications repeatedly discussed the question of applicability of the RII method for studying radio emission propagation in both stratified and horizontally inhomogeneous media (Avdeev and Yarygin, 1978; Avdeev, Shilov, and Yarygin, 1981; Orlov and Demin,

On the Limits of Applicability of the Ray Interference Integral Method

415

1983; Avdeev et al., 1988; Krestjaninov and Permjakov, 1993). It is well known (Orlov, 1974; Avdeev et al., 1988) that the partial waves constituting the ray interference integral can produce caustics as well. At these caustics, the amplitudes of the WKB modes tend to infinity (the denominator in Equation (5) turns to zero). However, the partial wave singularities are usually integrated (Orlov and Demin, 1980, 1981a, 1981b, 1983; Avdeev et al., 1988; Krestjaninov and Permjakov, 1993). If the observer is far from the caustic of partial waves (but, maybe, close to the caustic of geometrical optics rays), then the RII method provides good coincidence with the exact solution. If the observer is at the point where these caustics coincide, then the RII method gives albeit a finite but overestimated value for the field amplitude (Orlov and Demin, 1983). In this case it is better to use a more general uniform (caustic) interference integral (a superposition of the Airy asymptotics, etc.) (Orlov, 1974; Avdeev et al., 1988).

When solving the statistical problems of scattering by the RII method, in view of strong regular refraction of radio waves in randomly inhomogeneous media, the following integral representation is usually used (Afanasiev and Tinin, 1982; Tinin, 1983):

( ) ( ) ( ) ( )[ ] ,,~,exp,~100 ααψαψα dikAU sss rrrr += ∫ (6)

where 0sA and 0sψ are the amplitude and the eikonal of the partial wave in a regular

medium, and 1~

sψ describes the eikonal fluctuations related to the influence of random fluctuations of dielectric permittivity of medium. The latter function is calculated to a first approximation of the perturbation theory. Representation (6) takes into account only phase fluctuations of partial waves.

Representation (6) has been successfully used in solving problems of radio wave scattering not only in the randomly inhomogeneous media that are stratified on average, but also in the media, the average dielectric permittivity of which is specified by a two-dimensional function (Afanasiev et al., 1983; Az'muko et al., 1988, 1991; Afanasiev et al., 1997, 1998a, 1998b, 2001; Tinin et al., 1992; Zheonykh et al., 1999). In particular, Tinin (1989) has derived, based on the RII method in the form of Expression (6), an expression for the mean intensity of radio waves for any given horizontally inhomogeneous model for the ionosphere. Tinin et al. (1992), in addition to the plane-stratified model for a regular ionosphere, considered a more complex horizontally inhomogeneous model. The numerical calculations in the mentioned paper were carried out using the RII method in the form of Expression (6).

When solving the statistical problems by the RII method, in view of strong regular refraction, the problem of calculating the moments of the field in the presence of caustics of partial waves remains to exist. Therefore, in order to apply the RII method in a correct way, it is necessary to analyse preliminarily the geometrical optics structure of the field and to reveal the presence of the caustics near the observer. Such an approach was applied by Az'muko et al. (1991), who performed calculations of the mean intensity of monochromatic radio waves propagating in an ionosphere containing periodic regular inhomogeneities. Using the same approach, Afanasiev et al. (1997) carried out a numerical modeling of the mean intensity of monochromatic radio waves for the case where a cloud-like sporadic layer sE presents in the ionosphere. Furthermore, Az'muko et al. (1988) calculated the mean profile of a radio pulse


416

propagated through an ionosphere with localized electron density inhomogeneities. In all the cases, there arise the caustics of geometrical optics rays and of partial waves.

To apply the RII method in a correct way, Afanasiev and Altyntsev (2006) and Afanasiev (2006) carried out first the geometrical optics analysis of the field structure. This allowed the authors to draw conclusions that refraction of radio waves on large-scale regular inhomogeneities of the solar corona is responsible for the multi-component temporal profiles of the investigated radio bursts. Then, calculations of the mean temporal pulse profiles were carried out using the ray interference integral. When performing the calculations, true geometrical optics trajectories of radio emission, connecting the source and the receiver, were determined first, and then, in the vicinities of these trajectories, fluctuations of trajectory characteristics of partial waves were calculated. Under the condition of strong scattering (under which the expression for the frequency coherence function was derived by Afanasiev and Altyntsev, 2006), this way of calculating the interference integral is right because these vicinities are small. The burst profiles presented in the papers by Afanasiev and Altyntsev (2006) and by Afanasiev (2006) correspond to the observer's position in the area of geometrical optics multipathing, but not at caustics of geometrical optics rays. Therefore, the results of these calculations are correct.

It is important to note that if the observer is at the caustic produced by geometrical optics rays, then the RII method-based calculations of pulse profiles are also correct, provided that the caustic of partial waves is far from the observer. Otherwise, such calculations give a finite but overestimated result. In this case, in order to fit experimental data better, it is necessary to calculate the moments of the field on the basis of the caustic interference integral.

As concerns the amplitude fluctuations of partial waves, they are mainly caused by radio emission diffraction on plasma inhomogeneities with scales less than the size of the Fresnel zone. Therefore, strictly speaking, the amplitude fluctuations of partial waves cannot be neglected in the case of the horizontally inhomogeneous medium with small-scale random inhomogeneities. This limitation is indicated in the papers by Afanasiev and Altyntsev (2006) and by Afanasiev (2006). Note that this limitation refers to a plane-stratified background medium as well. At the same time, it is possible to develop the technique applied by Afanasiev and Altyntsev (2006) for taking into account inhomogeneities of smaller scales, using the method of smooth perturbations for calculating the amplitudes of the partial waves (see Zernov, 1994).

Conclusion

Overall, the RII method correctly describes the refractive mechanism of formation of the multi-component temporal profiles of the solar radio spikes and of the type IIId decameter bursts, which was proposed by Afanasiev and Altyntsev (2006) and by Afanasiev (2006). Our calculations (Afanasiev, 2005, 2006, 2007; Afanasiev and Altyntsev, 2006; Afanasiev and Afanasiev, 2007, 2008) have revealed that the RII method represents in a number of cases a powerful tool to carry out mathematical modeling of scattering of radio emission in the corona and solar wind.

On the Limits of Applicability of the Ray Interference Integral Method

417

References

Afanasiev, A. N. J. Atmos. Sol. Terr. Phys. 2005, 67, 1002-1013. Afanasiev, A. N. Solar Phys. 2006, 238, 87-104. Afanasiev, A.N. Astron. and Astrophys. Trans. 2007, 26, 647-653. Afanasiev, A. N.; Afanasiev, N. T. Solar Phys. 2007, 245, 355-367. Afanasiev, A. N.; Afanasiev, N. T. In Solar Physics Research Trends; Wang, P.; Ed.; Nova

Science Publishers: Hauppauge, NY, 2008; pp 17-27. Afanasiev, A. N.; Altyntsev, A. T. Solar Phys. 2006, 234, 151-167. Afanasiev, N. T.; Tinin, M. V. Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa

1982, 61, 236-241. Afanasiev, N. T.; Grozov, V. P.; Krasikov, A. A.; Nosov, V. E.; Tinin, M. V. Issledovaniya

po geomagnetizmu, aeronomii i fizike Solntsa 1983, 63, 180-196. Afanasiev, N. T.; Zheonykh, A. A.; Ivelskaya, M. K.; Sazhin, V. I.; Tinin, M. V.

Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa 1997, 107, 327-332. Afanasiev, N. T.; Zheonykh, A. A.; Sazhin, V. I.; Tinin, M. V.; Ivelskaya, M. K. J. Atmos.

Sol. Terr. Phys. 1998a, 60, 1687-1694. Afanasiev, N. T.; Zheonykh, A. A.; Ivelskaya, M. K.; Polyakov, V.M.; Sazhin, V. I.; Tinin,

M. V. In Proc. URSI Symposium on Electromagnetic Theory; Thessaloniki, Greece, 1998b; Vol. 2, pp 328-332.

Afanasiev, N. T.; Zheonykh, A. A.; Ivelskaya, M. K.; Sazhin, V. I.; Tinin, M. V.; Unuchkov, V. E. J. Atmos. Sol. Terr. Phys. 2001, 63, 1967-1972.

Avdeev, V. B.; Yarygin, A. P. In Abstracts of the XII All-Union Conference on Radio Wave Propagation; Nauka: Moscow, USSR, 1978; Vol. 2, p 294.

Avdeev, V.B.; Shilov, N.V.; Yarygin, A.P. In Abstracts of the XIII All-Union Conference on Radio Wave Propagation; Nauka: Moscow, USSR, 1981; Vol. 1, pp 302-303.

Avdeev, V. B.; Demin, A. V.; Kravtsov, Yu. A.; Tinin, M. V.; Yarygin, A. P. Izv. VUZov Radiofiz. 1988, 31, 1279-1294.

Az'muko, N. A.; Afanasiev, N. T.; Pobedina, A. P.; Tinin, M. V. Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa 1988, 81, 257-265.

Az'muko, N. A.; Afanasiev, N. T.; Pobedina A. P.; Tinin, M. V. In Ionosphere Dynamics; Drobzhev, V. I.; Ed.;Gylym: Alma-Ata, USSR, 1991; Vol. 3, pp 69-74.

Kravtsov, Yu. A.; Orlov, Yu. I. Geometrical Optics of Inhomogeneous Media; ISBN 3-540-51944-0; Springer-Verlag: Berlin Heidelberg New York, 1990; 312 pp.

Krestjaninov, S. V.; Permjakov, V. A. In Abstracts of the XVII Conference on Radio Wave Propagation; Nauka: Ulyanovsk, USSR, 1993; Vol. 6, pp 46.

Orlov, Yu. I. Trans. Moscow Institute for Energy 1972, 119, 82-91. Orlov, Yu. I. Izv. VUZov Radiofiz. 1974, 17, 1035-1041. Orlov, Yu. I.; Demin, A. V. Trans. Moscow Institute for Energy 1980, 497, 10-15. Orlov, Yu. I.; Demin, A. V. Trans. Moscow Institute for Energy 1981a, 553, 5-9. Orlov, Yu. I.; Demin, A. V. In Abstracts of the XVII Conference on Radio Wave Propagation;

Nauka: Moscow, USSR, 1981b; Vol. 1, pp 304-306. Orlov, Yu. I.; Demin, A. V. In Issledovanie uslovii rasprostraneniya radiovoln; IZMIRAN:

Moscow, USSR, 1983; pp 48-57. Tinin, M. V. Izv. VUZov Radiofiz. 1983, 26, 36-43.


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Tinin, M. V. Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa 1989, 88, 145-155. Tinin, M. V.; Afanasiev, N. T.; Mikheev, S. M.; Pobedina, A. P.; Fridman, O. V. Radio Sci.

1992, 27, 245-255. Zernov, N. N. Radiotekhnika i elektronika 1994, 39, 241-252. Zheonykh, A. A.; Afanasiev, N. T.; Ivelskaya, M. K.; Sazhin, V. I.; Tinin, M. V.; Unuchkov,

V. E. In Proc. URSI XXVI General Assembly; Toronto, Canada, 1999, 519.

Reviewed by Dr. A. A. Stanislavsky, Institute of Radio Astronomy, NAS Ukraine

INDEX

A

AAS, 317 abiotic, 74 absorption, 216, 234, 272, 289, 351, 359, 370, 372 absorption coefficient, 359, 372 academic, 9 acceleration, x, xii, 185, 212, 213, 214, 219, 220, 232,

233, 238, 239, 244, 245, 248, 259, 260, 264, 277, 281, 284, 291, 292, 310, 311, 312, 315, 353, 354, 355, 357, 360, 361, 368, 370, 371, 372, 373

accelerator, 202, 203, 218, 382 accommodation, 26 accounting, 111, 127, 158, 332, 336 accuracy, 82, 91, 112, 229, 237, 268, 283, 345 ACE, 20, 30, 82, 87, 99, 127, 139, 141, 142, 400 achievement, 90, 354 acid, 163 acoustic, 331, 335, 336 activity level, 178, 187, 400 ADA, 318 aerosols, 16, 40, 187 aerospace, 222, 404 Africa, 11, 33, 48, 67, 168 age, 68, 272, 289, 345 ageing, 127 agents, 2, 20, 157, 175 aggregates, 282, 289 agricultural, 154, 165, 169, 342, 343 agriculture, 155, 163, 169 aid, 167 AIP, 337, 376 air, xi, 2, 6, 7, 9, 11, 12, 15, 18, 19, 21, 23, 26, 42, 45,

47, 48, 49, 51, 53, 55, 58, 59, 69, 70, 77, 153, 155, 160, 167, 168, 170, 172, 173, 174, 191, 192, 198, 221, 341, 342, 345, 347

Air Force, 318

air quality, 168, 170, 173 Aircraft, 221, 222 Alabama, 223 Alaska, 75, 192 Alberta, 27, 72 alcohol, 154 aldehydes, 167 Algeria, xiii, 403, 404, 405, 409, 410, 411 algorithm, 191, 321, 324, 325 alloys, 359 alpha, 64, 217 alternative, 11, 148, 157, 162 alternatives, 146, 158, 283 aluminium, 172, 357 aluminum, xii, 62, 353, 355, 357, 359, 360, 362 ambiguity, 18 amplitude, 14, 66, 74, 84, 88, 104, 113, 131, 315,

414, 415, 416 anaerobic, 148, 149, 152 anaerobic digesters, 152 angular momentum, 277 angular velocity, 392, 399 animals, 149 anisotropy, 100 annihilation, 295 annuals, 171 anomalous, 187 Antarctic, 8, 55, 79, 177, 193 antenna, 357 anthropogenic, 2, 4, 5, 15, 17, 158 application, viii, 26, 30, 68, 78, 145, 146, 166, 173,

222, 223, 244, 251, 287, 348, 351, 364, 376 appraisals, 167 appropriate technology, 175 Archimedes, 65 Arctic, viii, 7, 9, 67, 77, 177, 179, 191, 192 Argentina, 13, 391

Index 420

argument, 169, 239, 240, 248, 249, 250, 251, 252, 253, 259, 261, 264, 267

Arizona, 28, 74, 197, 222, 224, 289, 364, 376 Armenia, 23, 25 ash, 151, 167 Asia, 3, 11, 168, 175 Asian, 17 aspect ratio, 284, 286 asphalt, 151 assessment, 164, 336, 411 assumptions, 42, 157, 335, 344 asymmetry, 116, 132, 140, 329, 330 asymptotic, 257, 259, 261 asymptotically, 249, 252, 256, 257, 260, 261 asymptotics, 415 Athens, 57 Atlantic, 7, 9, 21, 41, 47, 55, 59, 67, 70, 79 Atlantic Ocean, 41 Atlas, 144, 351, 404, 409 atmosphere, vii, viii, 3, 4, 9, 12, 15, 18, 19, 20, 27,

35, 39, 41, 44, 45, 46, 47, 51, 53, 55, 58, 59, 60, 62, 63, 68, 69, 70, 73, 75, 137, 145, 158, 161, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 193, 195, 196, 198, 218, 292, 313, 320, 344

atmospheric pressure, 45, 73 atoms, 45, 58, 156, 263, 264, 321, 326 Aurora, 54 Australia, 34, 55, 79, 379 authenticity, 68 automobiles, 147 availability, 2, 148, 149, 158, 160, 169, 342, 343 averaging, 112, 189, 237, 240, 247, 324 aviation, 198, 222

B

balance of payments, 146 Balkans, 24, 58, 61 batteries, 147 battery, 171 behavior, viii, x, 21, 27, 67, 69, 81, 83, 109, 122, 126,

131, 137, 179, 227, 228, 251, 253, 257, 259, 261, 266, 269, 273, 286, 292, 321, 327, 329, 333, 334, 335, 336

Belarus, 22, 23 Belgium, 23, 25 benefits, 157, 163 biodiversity, 170 biofuels, 174 biogas, 152 Biogas, 152, 175 biomass, 69, 154, 157, 165, 166 biosphere, 62

biotechnology, 169 birds, 167 black body, 374 black hole, 62 blowing agent, 157 boats, 148 boiling, 160 Boltzmann constant, 184, 264 bonding, 156 booms, 355 boreal forest, 73, 74, 75 Boston, 291, 411 boundary conditions, 190, 325 Brazil, 33 Britain, 67, 163 British Columbia, 5, 74, 78 Brooklyn, 197, 353, 367, 379 Brussels, 175 bubble, vii, 320 Buenos Aires, 391 building code, 158 buildings, 146, 160, 173 Bulgaria, 23, 25, 67, 78 burn, 35, 50, 60, 72, 76, 151 burning, viii, 27, 28, 30, 34, 35, 39, 50, 59, 68, 69,

70, 145, 163

C

cables, 202 campaigns, 165 Canada, 55, 73, 74, 78, 182, 418 capacitance, 217, 363 capacity building, 167 capital cost, 147, 160 carbon, 4, 72, 152, 158, 160, 163, 166, 167 carbon dioxide, 4, 152, 158, 163, 167 carbon monoxide, 4, 167 cardboard, 151 carrier, 147 case study, 73, 411 Caspian, 29, 30, 32 cast, 67, 172 catalyst, 3 catastrophes, 26 Caucasus, 30 causality, vii, 1, 30, 68 cavities, x, 291, 294, 295, 296, 297, 298, 299, 301,

302, 303, 306, 308, 310, 311, 313, 314, 315 CDC, 296, 299, 311 cell, 147, 321, 324, 325, 327, 333 cement, 151 Central America, 168 Central Europe, 59

Index 421

CERN, 20 certificate, 376 CH4, 148, 152 changing environment, 58 channels, 153, 308 charcoal, 156 charge density, 206, 209, 329, 330 charged particle, vii, x, 20, 41, 53, 63, 69, 70, 182,

183, 184, 185, 186, 187, 188, 195, 200, 201, 204, 205, 206, 219, 228, 291, 292, 294, 295, 298, 301, 304, 306, 307, 308, 310, 311, 313, 314, 315, 320, 330, 335, 356, 358, 379, 381, 382, 387

chemicals, 157 China, 351 chlorofluorocarbons (CFCs), 156, 157 CHP, 149, 157, 158, 159, 164, 175 chromosphere, 96 circulation, 9, 15, 21, 26, 39, 44, 46, 47, 51, 59, 60,

67, 160, 190, 280 classes, 354 classical, 172, 347 clay, 151 climate change, 2, 3, 4, 5, 8, 9, 10, 11, 13, 15, 20, 26,

51, 52, 71, 78, 79, 163, 175 climate warming, 14, 24 climatology, 2 clouds, 15, 16, 18, 19, 39, 51, 59, 69, 74, 77, 139,

326, 343, 348 clusters, 181, 182, 183, 187 CME, 42 CO2, 2, 3, 4, 5, 9, 149, 152, 163, 175 coal, viii, 145, 147, 154, 163, 167 codes, 320 coding, 282 coherence, 21, 55, 69, 400, 416 coil, 161 collaboration, 289 collisions, 55, 62, 183, 184, 185, 188, 189 colors, 330, 393, 395, 398 Columbia, 5, 74, 78 combustion, vii, 1, 39, 149 commodity, 169 communication, xi, 288, 341, 368, 370, 376 communication systems, 368, 376 community, 174 competitiveness, 147 complexity, 133, 137 components, 100, 102, 103, 104, 106, 117, 119, 121,

132, 150, 152, 164, 173, 174, 183, 184, 188, 229, 233, 239, 264, 281, 285, 297, 350

composition, 2, 100, 142, 181, 278, 282 computation, 200, 209, 210, 213, 217, 219, 220, 342,

351, 359, 361, 370, 380, 381, 382, 384

computing, 251, 320, 325, 351 concentrates, 20, 228, 370 concentration, 3, 5, 11, 40, 58, 98, 108, 152, 160,

163, 182, 183, 185, 186, 187, 189, 190, 191, 195, 217, 229, 263, 286

concrete, 1, 24, 60, 70, 151 condensation, 160 conditioning, 160 conduction, 160 conductive, 199, 379, 385 conductivity, ix, 161, 162, 178, 181, 185, 191, 192,

195, 292, 293 confidence, 6, 11, 18, 28, 180 confidence interval, 6, 180 configuration, ix, 14, 136, 161, 177, 308, 313, 330,

331, 336 confrontation, 9 confusion, 4, 12, 55, 60 Congress, 73, 198, 221, 222, 223, 387 connectivity, 55 conservation, 163, 170, 172, 343 constant rate, 392 constraints, 170 construction, viii, 145, 151, 162, 163, 168, 175, 355 Construction and demolition, 151 consumption, 147, 148, 150, 162, 163, 168, 174, 219 continuity, 322 control, 26, 51, 75, 106, 143, 171, 173, 174, 178, 190,

202, 358, 370, 375, 385 convection, 38, 69, 75, 300, 392, 400 convective, 25 conversion, 97, 148, 149, 150, 157, 342, 343 conviction, 51 cooking, 147, 148, 151, 167 cooling, 8, 19, 69, 149, 157, 165, 167, 191, 192, 385 corona, vii, xiii, 63, 82, 83, 195, 289, 292, 413, 416 coronal mass ejection, 16, 19, 20, 42, 55, 62, 139,

142 correlation, xi, 14, 16, 18, 28, 66, 109, 131, 132, 135,

180, 181, 186, 192, 195, 299, 311, 341, 343, 345, 347, 349, 350

correlation coefficient, 28, 66, 186, 192 correlations, xi, 18, 77, 100, 191, 341, 345, 347, 350,

351 corridors, 125, 130, 134 corrosive, 160 cosmic ray flux, 17, 78, 182, 183 cosmic rays, 17, 19, 20, 51, 58, 62, 73, 74, 78, 142,

182, 187, 316 cost-effective, 163, 164 costs, 148, 154, 160, 161, 163, 170 Coulomb, 107, 184, 205 coupling, ix, 75, 177, 179, 181, 220

Index 422

covering, xi, 153, 319, 320 CPU, 283 crack, 53 creativity, 62 credit, 170 critical value, 385 criticism, 5 Croatia, 23, 25 crop residues, 147, 151 crops, 156, 157, 171, 172 cross-sectional, 20 CRS, 73 crust, 11 cryogenic, 151 cultivation, 168 cultural heritage, 163 culture, 169 currency, 382, 383, 384, 386 customers, 162 cycles, vii, 12, 13, 66, 67, 81, 82, 83, 84, 92, 113,

114, 117, 122, 123, 126, 127, 128, 135, 137, 141, 142, 144, 181, 193, 194, 195, 292, 392, 396, 399

cyclone, 9, 51, 59, 79 cyclones, 14, 21, 59, 63 cyclotron, x, 108, 291, 299, 300, 311, 315, 324 Cyprus, 23, 25

D

danger, 24, 35, 39, 74 data collection, 343, 405 data processing, 24, 28, 112 data set, vii, 11, 81, 82, 87, 88, 112, 114, 116, 135,

140, 180, 194, 393 database, 68, 127, 138, 283, 342 dating, 392 decay, 313, 331, 336 decision makers, 166 decomposition, 152, 233, 238 decompression, 137 deficiency, 96, 97 definition, 292 deforestation, 148 degradation, 155 delivery, 198, 222 Denmark, 23 depressed, 294, 295 depression, 295 derivatives, 246, 248, 249, 255 designers, 170 destruction, 39, 165, 228, 231 detection, 55 developed countries, 150, 151, 167, 169

developing countries, 147, 150, 151, 156, 167, 170, 342, 351

deviation, 40, 57, 88, 89, 90, 91, 93, 96, 102, 122, 123, 125, 126, 127, 130, 134, 200, 217, 334, 335

diamonds, 304, 313, 314 dielectric constant, 184 dielectric materials, 372 dielectric permittivity, 414, 415 differential equations, 241, 243 diffraction, 416 diffusion, 167, 314 diffusivity, 161 digestion, 148, 149 dipole, xi, 106, 136, 282, 287, 306, 319, 320, 321,

326, 331, 332, 333, 334, 335, 336, 374 direct measure, 82, 333 directives, 63 disaster, 36, 38 discharges, 9, 27, 68 Discovery, 287 discretization, 325 dispersion, 46, 70, 88, 89, 90, 91, 104, 122, 123, 125,

126, 127, 130, 131, 132, 133, 134, 135, 136, 308, 380

displacement, 21, 322, 323 distribution function, xiii, 84, 95, 322, 403, 404 district heating, 149 divergence, 13, 414 diversity, 79, 170, 392 division, 106 dollar costs, 163 drainage, 151 drought, 4, 14, 15, 26, 67, 69, 74, 75 droughts, 14, 50, 163 dry ice, 191 dung, 147, 151 duration, xi, 82, 83, 87, 88, 96, 104, 112, 117, 123,

143, 179, 341, 342, 344, 346, 347, 348, 399, 405 dust, x, 174, 227, 228, 229, 230, 231, 234, 238, 241,

243, 244, 245, 247, 248, 250, 251, 252, 253, 254, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289

E

earth, 33, 42, 65, 67, 87, 116, 160, 161, 163, 174, 298, 342, 343, 344, 354

Eastern Europe, 168 ecological, vii, 1, 73, 163, 166, 170, 171 economics, 71, 163 ecosystem, 26 ecosystems, 170 electric charge, 58, 60, 63, 210, 218, 284, 285, 363

Index 423

electric circuit, ix, 177, 179, 180, 181, 184, 190, 191, 192, 195

electric conductivity, ix, 178, 191, 192, 293 electric current, 181, 184, 185, 186, 188, 190, 191,

192, 375, 381, 384 electric energy, 181, 198, 206 electric field, x, 40, 56, 83, 105, 106, 119, 121, 130,

132, 143, 181, 184, 185, 186, 187, 190, 195, 202, 205, 206, 217, 219, 293, 299, 300, 301, 310, 311, 312, 315, 322, 323, 325, 326, 327, 329, 330, 333, 336

electric power, 69, 404 electrical power, 354 electrical resistance, 185 electricity, 149, 150, 152, 154, 157, 160, 162, 163,

199, 342, 351, 368, 370, 376, 409 electricity system, 149 electrodes, 204 electromagnetic, viii, x, 1, 19, 20, 30, 33, 35, 36, 39,

43, 54, 63, 64, 70, 77, 78, 108, 137, 177, 178, 190, 195, 227, 228, 234, 237, 238, 239, 243, 244, 246, 259, 261, 268, 269, 271, 275, 276, 277, 278, 279, 280, 281, 282, 284, 286, 288, 291, 300, 306, 315, 322, 330

electromagnetic wave, 19, 30, 33, 35, 36, 39, 54, 63, 70, 322

electromagnetic waves, 19, 30, 33, 35, 36, 39, 54, 63, 70, 322

electromotive force (EMF), ix, 177, 179, 190 electron, 13, 19, 20, 39, 55, 63, 108, 109, 111, 143,

182, 183, 184, 186, 188, 206, 207, 217, 218, 294, 295, 299, 300, 302, 303, 308, 310, 311, 312, 321, 322, 323, 326, 331, 382, 386, 387, 416

electron charge, 322, 386 electron density, 13, 143, 322, 416 electrons, vii, xii, 33, 42, 46, 58, 107, 183, 184, 186,

198, 200, 201, 206, 216, 218, 292, 294, 301, 302, 304, 305, 307, 308, 309, 310, 312, 314, 320, 322, 323, 356, 367, 369, 381, 382, 386

electrostatic force, 362 emission, vii, xiii, 1, 2, 5, 15, 20, 55, 70, 75, 122,

158, 160, 235, 272, 281, 413, 414, 416 emission source, 158 employees, 10 employment, 147, 169, 175 encouragement, viii, 145, 146, 147, 149 endurance, 374 energy audit, 164 energy channels, 308 energy consumption, 147, 150, 163, 168, 174 energy density, 360 energy efficiency, 145, 146, 149, 157, 158, 163, 167,

172

energy recovery, 150, 163 energy supply, 147, 148, 156, 157 energy transfer, 178 engines, viii, 145, 149, 162 England, 21 enterprise, 169 Enthalpy, 98 entropy, 112, 114 environment, 19, 40, 54, 68, 73, 76, 145, 146, 148,

149, 152, 155, 163, 167, 168, 170, 172, 306, 336, 343

environmental control, 174 environmental impact, 148, 149, 155 environmental issues, 165 environmental protection, 163 environmentalists, 163 equality, 88 equilibrium, 137, 182, 186, 190, 235, 386 equilibrium state, 235 erosion, 171, 231 estimating, 352, 404, 411 Estonia, 23, 25 ethanol, 154 Ethanol, 154 Europe, vii, 1, 2, 3, 21, 22, 23, 24, 28, 29, 30, 31, 32,

41, 49, 53, 58, 60, 62, 67, 70, 72, 149, 160 European Community, 351 European Space Agency, 74 European Union, 149 evaporation, 279, 280, 281, 286 evolution, x, xiii, 26, 74, 138, 227, 228, 239, 240,

241, 242, 243, 244, 246, 247, 249, 250, 251, 252, 253, 254, 256, 257, 258, 259, 260, 261, 264, 265, 269, 272, 276, 277, 278, 279, 286, 287, 329, 333, 391

exclusion, 171 exploitation, 154, 160, 382 explosions, 54 exposure, 56 extinction, 234 extraction, 160, 168 extrapolation, 15 Extraterrestrial, 341

F

fabric, 148 failure, 5, 356 FAO, 22, 23, 25, 28, 68, 73 farmers, 154, 169, 170 farming, 147, 174 fear, 10 feedback, 11, 20 feet, 201

Index 424

ferrous metal, 151 fertiliser, 170 Feynman, 76, 100, 104, 140, 142, 400, 401 FFT, 112 film, ix, xi, xii, 197, 198, 199, 201, 202, 204, 223,

353, 354, 355, 356, 357, 359, 360, 361, 367, 369, 370, 376

film thickness, 359, 360 films, 370 filtration, 270 finance, 163 financial resources, 167 financing, 167 finite differences, 324 fire, 2, 4, 5, 14, 16, 22, 24, 25, 26, 27, 28, 30, 33, 34,

35, 38, 39, 41, 47, 60, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 157

fire event, 69 fire suppression, 27 fires, vii, 1, 2, 3, 4, 9, 13, 14, 21, 22, 23, 24, 25, 26,

27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 47, 48, 50, 51, 52, 58, 59, 60, 61, 62, 63, 65, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 147

firewood, 156, 165 fish, 167 fission, 150 flame, 35, 48 flank, 26 flare, 19, 32, 33, 39, 56, 67, 76, 114, 392, 401 flatness, 89 flexibility, 171 flight, xii, 197, 198, 205, 212, 220, 371, 372, 375,

379 flow, xi, 16, 19, 39, 41, 46, 48, 51, 53, 69, 96, 98,

109, 136, 143, 161, 167, 192, 198, 200, 204, 217, 229, 234, 289, 292, 319, 320, 321, 329, 331, 332, 334, 335, 336, 356, 369, 372, 383, 386

fluctuations, x, 75, 104, 139, 140, 154, 291, 298, 299, 300, 302, 303, 306, 310, 311, 312, 315, 415, 416

flue gas, 149 fluid, 160, 161, 320, 321, 322, 323, 324, 326, 328,

329, 332, 333, 335, 375 foams, 157 focusing, 167 food, 147, 150, 154, 156, 163, 167, 169, 170 football, 354 forecasting, 4, 10, 19, 70, 78, 144, 343 forest fire, vii, 1, 2, 4, 9, 13, 14, 16, 21, 22, 23, 24,

26, 27, 28, 29, 30, 35, 38, 50, 58, 63, 65, 68, 70, 71, 73, 74, 75, 78, 79

forest fires, vii, 1, 2, 4, 9, 13, 14, 21, 22, 23, 24, 26, 27, 28, 29, 30, 35, 38, 50, 58, 63, 65, 68, 70, 71, 73, 74, 78

forestry, 24, 73, 74, 76 forests, vii, 1, 5, 24, 50 fossil, 146, 148, 151, 154, 157, 163, 167 fossil fuel, 146, 148, 151, 154, 157, 163, 167 fossil fuels, 146, 148, 151, 154, 157, 163 Fourier, 82, 83, 112, 139 Fourier analysis, 139 fragmentation, 114 France, 13, 23, 25, 29, 38 frequency distribution, 404, 409 friction, 45 fuel, viii, 2, 26, 27, 69, 145, 148, 149, 152, 154, 162,

163, 164, 168, 197, 355 fuel type, 27 funds, 146 furniture, 151

G

galactic, 16, 20, 51, 70, 142, 187, 195 Galileo, x, 275, 276, 278, 287 Gamma, 29 gas, x, 4, 10, 16, 41, 97, 99, 107, 108, 109, 111, 149,

152, 154, 157, 158, 162, 163, 167, 175, 183, 198, 227, 228, 263, 264, 265, 266, 267, 268, 269, 270, 272, 321, 326, 356, 369, 370, 374

gas turbine, 152 gases, 3, 152, 157, 185, 198, 356, 369 gasification, 151, 157 Gaussian, 88 generalization, 242, 244, 284, 322 generation, 82, 109, 148, 149, 151, 161, 163, 351,

411 generators, ix, 153, 177, 181, 198, 203, 219, 411 geomagnetic field, 41, 44, 55, 75, 183, 293, 297, 298,

304, 305, 306, 314 geometrical optics, xiii, 413, 414, 415, 416 geophysical, 32, 75, 78 geothermal, 160, 161, 162 geothermal field, 160 Germany, 23, 25, 143 glaciers, 7 glass, 151, 164, 171, 172, 173 glasses, 287 global climate change, 5, 400 global warming, 3, 4, 5, 6, 9, 10, 13, 14, 15, 26, 27,

69, 73, 75, 76, 78, 148 goodness of fit, 348 government, 10, 51, 149, 158, 170, 382 grains, x, 12, 227, 228, 238, 243, 244, 258, 259, 261,

263, 265, 266, 272, 273, 275, 276, 277, 283, 286, 287, 288, 289

grants, 138, 337, 382 graphite, 287

Index 425

grass, 75 gravitation, 238, 262, 372 gravitational constant, 238, 276 gravitational effect, x, 245, 275 gravitational field, 370 gravitational force, 43, 45, 50, 228, 243, 244, 276,

277 gravity, vii, x, 227, 262, 263, 265, 266, 267, 268, 269,

275, 276, 277, 279, 281, 284, 364, 370 Greece, 23, 25, 29, 58, 417 Green Revolution, 170, 175 greenhouse, 3, 4, 5, 9, 10, 11, 16, 27, 72, 148, 155,

158, 163, 164, 168, 171, 172, 173, 174, 175 greenhouse gas, 3, 4, 10, 11, 158, 163 greenhouse gas (GHG), 158 greenhouse gases, 3, 4, 11 Greenland, 6 grid services, 147 grids, vii, 324, 354 grouping, 84 groups, 39, 164, 310 growth, 7, 8, 27, 128, 131, 144, 149, 157, 169, 329 GSM, 106, 304, 305 guilt, 68 guilty, 69 Guinea, 33

H

H1, 347, 348, 381, 382 H2, 347, 348, 382 handling, 162 harmonics, 112, 114, 117, 119, 121 hazards, 3, 61, 74, 150, 356 health, 15, 24, 163 heart, 343 heat, 3, 25, 72, 77, 147, 149, 151, 152, 157, 160, 161,

168, 170, 171, 172, 173, 190, 368, 369, 370, 372 heat loss, 173 heat transfer, 25 heaths, 104 heating, ix, 21, 62, 66, 82, 146, 147, 148, 149, 151,

165, 167, 172, 174, 178, 181, 184, 186, 188, 189, 190, 191, 342, 368, 370

heating rate, 66, 188, 189 heavy particle, 53, 383 height, xiii, 14, 70, 88, 90, 180, 182, 183, 403 heliosphere, 82, 100, 116, 137, 139, 140, 142, 144,

263, 264, 269, 270, 276, 288 helium, 86, 98, 99, 108, 127, 273, 299, 301, 302, 303,

308, 311 helix, 44 helplessness, 15

hemisphere, 7, 12, 18, 44, 70, 76, 182, 189, 297, 298, 302, 307, 309, 399

heuristic, 16 high pressure, 99, 218 high temperature, vii, 1, 14, 96, 97, 126, 135, 374 high-speed, 19, 41, 65, 72, 104, 144, 198, 356, 367,

369 histogram, viii, 81, 83, 103, 122, 123, 125, 126, 127,

128, 130, 131, 132, 133, 134, 135, 243, 409, 410 Hm, 45, 345 Holland, 318 Holocene, 74, 75 Hong Kong, 404 hospitals, 148 hot water, 160, 161, 165, 167 household, 165 households, 163, 169, 342 housing, vii, 1, 149, 170 human, 2, 53, 148, 149, 163, 167, 174, 195 human activity, 195 humans, 2, 15 humidity, 2, 26, 51, 59, 168, 172, 173, 174, 192 Hungary, 61 hurricanes, 163 hybrid, xi, 108, 167, 319, 320, 321, 322, 323, 325,

331 hydro, 4, 174 hydrocarbons, 4 hydrodynamic, 19, 45, 48, 55 hydrogen, 154, 160, 263, 264, 266, 267, 269 hydrogen atoms, 263, 264 hydrogen gas, 266, 267, 269 hydropower, 146, 167 hyperbolic, 200, 201, 202, 277, 278 hypothesis, 18, 19, 30, 39, 41, 47, 51, 55, 60, 63, 66,

68, 69, 191 hysteresis, 83, 122, 131, 140

I

IAC, 221, 222, 387 Iberian Peninsula, 51 ice, 6, 7, 8, 11, 12, 79, 191, 192, 193, 195, 196, 262 ICE, 143 identity, 170, 322 IDP, 231, 232, 233, 234, 238, 239, 243 images, 64 IMF, vii, xi, 17, 21, 55, 63, 75, 81, 82, 83, 85, 86, 87,

88, 100, 101, 102, 103, 104, 105, 106, 108, 111, 112, 117, 119, 121, 122, 128, 130, 131, 132, 133, 135, 136, 137, 141, 142, 187, 189, 297, 298, 313, 319, 326, 329, 330, 336

implementation, 157, 167, 321, 325 imports, 146, 147

Index 426

impurities, 160 in situ, x, 55, 82, 143, 291, 295, 304 incentives, 154, 165, 170 incidence, 4, 20, 27, 234, 282, 284 incineration, 163 inclusion, 191, 280 income, 167, 169 India, 33, 404, 411 Indian, 18, 41, 72 Indian Ocean, 41 indication, 51, 112, 179, 182 indices, 12, 14, 27, 114, 178, 400, 401 induction, 43, 44, 45, 46, 47, 60 industrial, 6, 7, 15, 147, 149, 150, 159, 162, 169, 175,

342 industry, viii, 145, 147, 149, 152, 155, 163, 404 inefficiency, 154 inequality, 256, 257 inertia, 323, 343 infinite, 217, 218, 220, 277, 414 infrared, 284 infrastructure, 147, 167, 170 inherited, 117, 133 inhomogeneities, 83, 137, 415, 416 initiation, 2, 27, 74 injections, 195, 306, 336 innovation, 156, 198, 218, 220, 224, 364, 368, 385 inspection, 38, 39, 329 instabilities, 289 institutions, 13, 342 instruments, 10, 30, 34, 35, 38, 39, 51, 54, 60, 63, 71,

82, 342 insulation, 150, 151, 164, 167, 168, 174, 201 insurance, 163 integration, 148, 200, 243 integrity, 169 interaction, ix, 13, 18, 53, 58, 96, 97, 100, 104, 117,

137, 178, 182, 183, 184, 187, 199, 200, 203, 232, 235, 236, 237, 244, 281, 283, 294, 311, 313, 320, 321, 335, 336, 382

interdisciplinary, 69 interface, 336, 392 interference, xiii, 112, 114, 116, 117, 121, 413, 414,

415, 416 Intergovernmental Panel on Climate Change (IPCC),

2, 5, 6, 26, 163, 175 International Energy Agency (IEA), 175 interplanetary medium, 42, 62, 85, 104, 106, 143,

374 interstellar dust, x, 275, 276, 277, 278, 279, 280, 283,

285, 287, 288, 289 interval, 83, 85, 88, 93, 95, 96, 101, 102, 104, 105,

106, 110, 111, 113, 115, 119, 120, 122, 123, 132,

178, 198, 242, 261, 265, 278, 280, 311, 326, 344, 356, 369, 399, 405

intrinsic, 27 investment, 157, 164 ion-clusters, 181, 187 ionic, 186 ionization, 79, 182, 183, 187, 189 ionosphere, 19, 20, 53, 55, 178, 181, 190, 195, 196,

415 ions, ix, xi, 45, 53, 98, 177, 182, 183, 184, 185, 186,

187, 188, 195, 217, 218, 292, 294, 295, 296, 301, 303, 304, 306, 308, 311, 313, 314, 315, 319, 320, 321, 322, 323, 324, 327, 329, 330, 331, 336

IOP, 333, 334, 335 irradiation, 341, 343, 344, 346, 347, 348, 349 irrigation, 170 Israel, 22, 223, 376 Italy, 29, 58, 61, 345, 351

J

Japan, 54 Japanese, 356 Jerusalem, 223 jobs, 163 joints, 164 Jordan, xi, 289, 341, 345, 347, 350, 351 Joule heating, ix, 178, 181, 184, 186, 188, 189, 190,

191 judge, 114 justification, 18, 30

K

Kazakhstan, 23, 25 kinetic energy, vii, 42, 43, 50, 55, 65, 70, 95, 97, 99,

184, 202, 215, 292, 311, 312, 313 kinetics, 321 King, 82, 92, 100, 102, 138, 139, 141, 143, 196, 392,

400 Kosovo, 35 Kyoto protocol, 3, 166

L

land, 2, 7, 8, 9, 13, 15, 28, 36, 76, 149, 154, 160, 168, 169, 170

land use, 169 landfill, 151, 152, 157, 158, 159, 175 landfill gas, 152, 158, 175 landfills, 158, 162 large-scale, 15, 78, 82, 100, 137, 169, 416 lasers, 355, 356 lattice, 287 Latvia, 23, 25

Index 427

law, 46, 73, 178, 205, 245, 292, 293, 303, 304, 323, 329, 336

laws, 50, 70, 240, 404 legislation, 162 lettuce, 171 lifetime, 392 light scattering, 283 light transmission, 172 limitation, 416 limitations, 112 linear, 6, 7, 45, 47, 84, 85, 90, 91, 96, 97, 112, 117,

206, 218, 347, 348, 359 linear model, 347 linear regression, 348 linkage, 51 links, 5, 11, 52, 137, 167, 170, 202 liquid water, 18 liquids, 154 Lithium, xi, 319, 321, 326, 327, 329, 330, 333 Lithuania, 23, 25 Little Ice Age, 75 livestock, 169 living standards, 167 loading, 26 lobby, 163 location, 14, 19, 26, 27, 29, 343, 344, 348 lognormal, 85, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99,

100, 101, 102, 106, 109, 110, 111, 113, 123, 126, 127, 131, 133, 135, 136, 137

London, 71, 221, 271, 272, 289, 364, 376, 387 long distance, 219 long period, 21, 53, 182, 320, 342 long-distance, 368, 370, 376 longevity, 165 losses, 39, 44, 216 low temperatures, 126 low-density, 99 low-income, 167 low-temperature, 97 luminosity, 17, 238

M

Macedonia, 23, 25 machinery, 148 machines, viii, 145, 147, 149, 404 magnesium, 277, 278, 284, 286 magnet, 321, 331, 332, 333, 334 magnetic moment, 295, 313, 314, 315, 332, 336 magnetic structure, 29, 399 magnetism, 65 magnetosphere, ix, x, 12, 18, 20, 21, 39, 40, 41, 42,

43, 53, 54, 55, 56, 62, 63, 64, 65, 69, 70, 87, 106, 109, 143, 178, 179, 190, 199, 291, 292, 293, 297,

298, 306, 309, 313, 314, 315, 316, 320, 321, 331, 336

maintenance, viii, 145, 147, 148, 164, 170, 174, 343, 355

management, 26, 157, 158, 162, 163, 169, 175 man-made, 10, 26 manpower, 342 mantle, 63 market, 158, 160, 163, 166, 169, 170 marketing, 166 markets, 169, 343 Markov, 404, 411 Markov chain, 404, 411 Mars, ix, 6, 114, 197, 198, 215, 221, 225, 355 Martian, 320 mask, 399 Massachusetts, 71, 411 mathematics, 68 matrix, 282, 283 meanings, 348 measurement, 10, 55, 333, 342, 343, 405, 406 measures, 24, 68, 69, 70, 158, 162, 164, 166, 170,

173, 174 media, 9, 33, 414, 415 median, 88, 90, 91, 92, 97, 99, 104 Mediterranean, 24, 38, 73, 404, 411 megawatt, 53 melon, 172 melt, 375 melting, 7, 8 melts, 8 memory, 41, 137 men, 27, 69, 201 Mercury, xii, 114, 367 meridian, 96, 97 messages, 16 metals, 159 meteor, 35, 273 meteorological, 11, 13, 16, 30, 51, 59, 62, 63, 70,

342, 343, 344, 404 methane, 4, 149, 152, 158, 159, 160 methanol, 154 metric, 168 Mexico, 28, 74 MHD, 137, 289, 320, 321, 322, 331, 336, 374 micrometer, 356 microorganisms, 157 micro-turbine, 162 microwave, 151 military, 354 mineralogy, 287 mining, 163 Minnesota, 151

Index 428

mirror, xii, 200, 202, 203, 204, 354, 355, 358, 359, 364, 367, 368, 369, 370, 372, 375

misconception, 157 misleading, 43, 67 missions, 4, 71, 116, 145, 149, 158, 159, 163, 168,

175, 320, 354 MIT, 71, 141, 338 mites, 174 MLT, 294, 296, 300, 302, 307, 311 mobility, 185 modeling, 27, 55, 75, 137, 179, 244, 283, 321, 336,

404, 411, 415, 416 models, ix, 2, 4, 5, 11, 14, 26, 44, 56, 63, 65, 67, 69,

140, 142, 172, 178, 191, 196, 203, 312, 322, 343, 351, 400

modulation, 139, 316 modules, 171, 343 moisture, 14, 19, 51, 69, 79, 174 molecules, 51, 183, 185, 187, 188 momentum, x, 108, 111, 137, 229, 231, 232, 234,

235, 236, 237, 277, 291, 355 money, 168, 382 monsoon, 17, 72 Montana, 141 Moon, xii, 221, 222, 270, 271, 353, 364 Moscow, 76, 81, 143, 144, 196, 221, 223, 365, 376,

417 moulding, 151 mountains, 34, 167, 343 movement, ix, xiii, 13, 60, 70, 178, 183, 391 MPI, 325, 338 multifractal, 131, 138 multiplication, 106, 132, 136 municipal solid waste (MSW), 162

N

NAS, 418 NASA, 3, 6, 19, 54, 77, 138, 139, 187, 189, 196, 201,

225, 284, 287, 289, 315, 317, 318, 354, 362, 365, 370, 371, 375, 377, 380, 382, 388

National Oceanic and Atmospheric Administration (NOAA), 9, 354

NATO, 316 natural, viii, 3, 5, 6, 9, 15, 41, 61, 73, 88, 97, 113,

145, 154, 158, 160, 163, 165, 167, 168, 170, 174, 192, 205, 243, 245, 413

natural capital, 73 natural gas, 154, 158 natural resource management, 163 natural resources, viii, 145, 165, 170, 174 NEA, 342, 351 negativity, 358 neglect, 108, 109, 234, 381, 382, 386

negligence, vii, 1 neighbourhoods, 170 Netherlands, 73, 316 network, 10, 342 neutrons, 60, 313 Nevada, 5 New Mexico, 28, 74 New York, 77, 138, 175, 269, 270, 287, 289, 317,

318, 351, 417 NGOs, 158, 162 Ni, 182, 183, 184 Nielsen, 338 nitrogen, 152, 160, 167 nitrogen oxides, 167 NOAA, 9, 19, 76, 77, 140, 141, 143, 144, 354 nodes, 325 noise, 91, 143, 163, 167, 170 nonlinearities, 137 normal, viii, 40, 52, 60, 69, 81, 88, 89, 90, 91, 92, 97,

99, 100, 104, 105, 106, 137, 161, 233, 277, 404 normal distribution, 88, 89, 100, 137, 404 normalization, 9 North America, 21, 28, 77, 160, 168 North Atlantic, 9, 59, 67, 79 Northern Hemisphere, 13, 76 Norway, 23 nuclear, 146, 148, 150, 163, 167, 204, 216, 217, 219 nuclear charge, 216 nuclear power, 146, 148, 163, 167 nucleation, 18, 40 nucleons, 20

O

obligation, 160 observations, xi, 6, 10, 11, 16, 17, 30, 32, 41, 53, 54,

55, 58, 62, 67, 68, 75, 99, 137, 139, 140, 178, 244, 291, 292, 297, 299, 302, 304, 305, 306, 310, 313, 314, 321, 334, 374, 411

Oceania, 168 oceans, viii, 11, 145 oil, viii, 145, 146, 147, 154, 163, 167 oil spill, 163 opposition, 5, 9 optical, 238, 241, 245, 266, 267, 282, 283 optical properties, 238, 241, 245, 266, 267, 282, 283 optics, xiii, 413, 414, 415, 416 optimization, 325 Oregon, 71 organic, 152 organic compounds, 152 orientation, 102, 103, 104, 106, 132, 171, 187, 234,

237, 264, 282, 283, 284 orthodox, viii, 145

Index 429

oscillation, 141, 253 oscillations, 15, 67, 112, 114, 143, 261 oxides, 167 oxygen, 142, 152, 156 ozone, ix, 9, 16, 44, 53, 58, 156, 157, 178, 181, 182,

188, 189, 190, 191

P

Pacific, 7, 14, 41, 55, 67, 69, 76 packets, 154 Pap, 392, 401 parabolic, 204 parameter, 83, 88, 89, 90, 91, 92, 99, 117, 121, 122,

135, 136, 137, 144, 178, 186, 187, 188, 189, 192, 238, 245, 246, 252, 254, 255, 259, 260, 263, 277, 278, 279, 283, 321, 332, 333, 335, 342, 345, 393, 395, 398, 404, 409, 411, 414

particle density, 32, 70, 208, 209 particle shape, 282 particulate matter, 4 passive, ix, 175, 177, 181 pathways, 154 Pb, 45 PCA, 9 per capita, 150 perception, 10 periodic, 11, 14, 83, 187, 326, 400, 415 periodicity, xii, 71, 82, 113, 114, 116, 117, 121, 127,

131, 135, 139, 141, 142, 195, 391, 392, 393, 396, 399, 400

peri-urban, 169 permafrost, 191, 192 permeability, 323 permit, 219, 310, 387 permittivity, 285 Perth, 34 perturbation, 239, 259, 260, 264, 268, 415 perturbation theory, 415 perturbations, 62, 69, 246, 416 pesticide, 170 phase shifts, 131 phase space, 313, 314, 315, 326 Philadelphia, 338 photochemical, 184 photon, 62, 204, 231 photons, xii, 204, 234, 235, 236, 355, 367 photovoltaic, 343 photovoltaics, 342 physical properties, 106 physicists, 20, 21 physics, 5, 10, 15, 54, 66, 68, 71, 78, 82, 88, 178,

220, 228, 243, 288, 292, 306, 321, 322, 413 pilot studies, 167

pitch, 305, 313 PL, 225, 362 plague, 354 planar, 244, 250, 277 Planck constant, 231 planetary, 18, 67, 72, 99, 113, 114, 197, 218, 246,

251, 252, 253, 260, 261, 320, 336 planets, x, xii, 113, 114, 116, 139, 219, 220, 227, 228,

243, 271, 272, 367, 371, 372, 374, 375 planning, 149, 157, 166, 343 plants, 152, 157, 160, 165, 167, 168, 171, 172, 173 plasma physics, 322 plastic, xi, xii, 62, 151, 353 play, 15, 16, 19, 51, 102, 106, 146, 149, 156, 168,

173 Pliocene, 74 Poland, 23, 24, 58, 59, 61, 78 polarity, 100, 117, 121, 122, 131, 132, 219, 285 polarization, 70, 234, 283, 311, 312 policy makers, 343 pollutants, 152, 174 polluters, 15 pollution, viii, 3, 145, 148, 150, 154, 155 polynomial, 4 polynomials, 112 poor, 14, 62, 85, 91, 95, 99, 131, 161, 169, 172 population, 30, 99, 163, 165, 166, 169, 305, 306, 312 population growth, 169 porosity, 45, 62 porous, 282 Portugal, vii, 1, 2, 13, 23, 24, 25, 29, 30, 41, 47, 48,

50, 51, 55, 73, 75, 76, 337 positive correlation, 191 positive feedback, 20 potential output, 411 poverty, 169 powder, 151 power plant, 146, 148, 149, 157, 168, 173 powers, 342 precipitation, 2, 9, 10, 14, 18, 19, 27, 28, 44, 51, 55,

59, 73, 181, 364 prediction, xi, 4, 26, 39, 66, 68, 333, 334, 335, 341,

343, 345, 350 predictive models, 69 press, 78, 271, 337, 338 prevention, 69 prices, viii, 145, 158, 168, 169, 171, 174 private, 168, 288, 356 probability, 27, 73, 88, 102, 137, 278, 279, 280, 281,

283, 285, 404 probability distribution, 88, 102, 137 probe, ix, 197, 202, 210, 212, 213, 214, 215, 220 producers, 150

Index 430

production, 149, 151, 152, 154, 155, 156, 161, 162, 169, 171, 174, 182, 343

productivity, 169, 175, 343 professionalism, 14 profit, 282 profitability, 169 profits, 163 prognosis, 5, 67, 68 program, 9, 54, 354, 404 propagation, 234, 322, 331, 413, 414 propane, 154 property, 88, 89, 91, 113, 162, 245, 249, 381, 386 propulsion, ix, xi, xii, 197, 198, 199, 200, 202, 203,

204, 218, 219, 220, 319, 320, 353, 354, 355, 356, 367, 370, 376

protection, 24, 26, 151, 163, 171, 201, 320, 321, 335 protocol, 3 protons, vii, ix, xii, 20, 29, 40, 42, 50, 60, 62, 63, 70,

98, 107, 108, 197, 198, 199, 200, 201, 204, 206, 208, 210, 215, 216, 218, 220, 292, 294, 304, 308, 309, 310, 311, 313, 320, 332, 336, 355, 356, 357, 359, 367, 369, 381, 383

prototype, 356 proxy, 10, 72 PSD, 313, 314 pseudo, 382 PTO, 222, 223, 364, 376 public, 4, 5, 27, 35, 149, 154, 170, 382 public health, 170 pulse, 167, 415, 416 pumping, 148 pumps, 381 purification, 148 pyrolysis, 151 pyromania, vii, 1

Q

quality of life, 150, 165 quantitative estimation, 83 quasi-periodic, 14

R

Radiation, 173, 229, 234, 236, 238, 269, 271, 272, 288, 289, 301, 312, 318, 341, 343, 347, 348, 368

radiation damage, 88 radio, xiii, 122, 357, 370, 413, 414, 415, 416 rain, 2, 15, 18, 148, 163 rainfall, 15, 18, 72, 160 rainwater, 166, 167 random, 88, 90, 106, 112, 137, 344, 350, 415, 416 range, xiii, 11, 38, 75, 84, 87, 96, 97, 100, 104, 109,

111, 113, 114, 116, 122, 132, 133, 135, 148, 150,

152, 155, 161, 165, 171, 185, 186, 198, 219, 276, 303, 311, 312, 313, 334, 355, 356, 369, 374, 375, 393, 395, 396, 398, 399, 403, 404, 410

Rayleigh, 282, 404, 411 reality, ix, 67, 177, 179, 181, 182, 184, 191, 228, 246,

262 recognition, 306 recombination, 55, 182, 183, 187 recovery, 135 recreation, 170 rectum, 241, 242, 243 recyclables, 150 recycling, 148, 150, 151, 157, 163, 175 redistribution, 192 reference frame, 229, 230, 231, 232, 233, 244, 264,

282, 382 reflection, 173, 198, 332, 336, 356, 361, 369 reflectivity, 355, 357, 368, 374, 375 regenerate, 170 regeneration, 59, 151 regional, 5, 7, 9, 10, 13, 16, 18, 21, 24, 51, 69, 147,

155 regression, 342, 344, 346, 347, 348, 350 regression analysis, 344 regression line, 344, 348 regression method, 350 regular, 82, 83, 99, 127, 131, 135, 137, 178, 324, 413,

415, 416 regulation, 74 rejection, 21 relationship, vii, 1, 14, 16, 20, 27, 42, 52, 76, 96, 97,

132, 135, 139, 141, 142, 161, 162, 348 relationships, 20, 25, 26, 69, 78 relevance, xi, 320, 326 reliability, 112, 137, 165 renewable energy, viii, 145, 146, 147, 149, 157, 165,

166, 167, 174, 175, 342 representative samples, 30 research and development (R&D), 342, 351, 411 residues, 147, 151, 156 resistance, 171, 185, 186 resistivity, 40, 322 resolution, 71, 112, 114, 320, 333, 334, 335, 393 resources, viii, 76, 145, 146, 147, 148, 150, 153, 155,

156, 158, 163, 165, 167, 170, 174, 351 retention, 158 returns, 198, 356, 369 revenue, 166 Rhode Island, 222 ring magnet, 381, 382, 383, 386 rings, 10, 73, 265 risk, 25, 79, 158 risks, 158, 163

Index 431

roadmap, 354 robustness, 174 Romania, 23, 25, 61 Rome, 73, 76 rotation axis, 283, 284 rotations, 100, 392 routines, 325 Royal Society, 272, 289 runoff, 170 rural, viii, 145, 146, 147, 148, 150, 151, 160, 165,

167, 169, 342 rural areas, viii, 145, 147, 148, 150, 151, 165, 342 rural development, 165 Russia, 22, 24, 29, 168, 177, 196 Russian, viii, 6, 21, 23, 76, 81, 138, 140, 143, 144,

177, 195, 196, 221, 222, 223, 288, 356, 364, 365, 376, 413

Russian Academy of Sciences, 6, 81, 138

S

SAE, 222, 223 safety, 73, 146, 150, 386 sales, 163, 165 salinity, 160 sample, 326, 330 sampling, 112, 122 sand, 12 satellite, 3, 12, 29, 30, 32, 33, 38, 39, 41, 51, 53, 60,

63, 68, 77, 85, 92, 178, 189, 201, 272, 292, 295, 297, 298, 299, 300, 302, 303, 307, 308, 309, 314, 370, 374

satisfaction, 282 saturation, 19, 172 savings, 149, 150 scalability, 325 scalar, 236 scaling, 334 scatter, 344 scattering, xiii, 234, 272, 282, 283, 289, 314, 413,

415, 416 sea ice, 192 sea level, 79, 163, 347 search, 178, 221, 364, 376, 387 searching, 30 seasonal variations, 192 seasonality, 2 seawater, 191, 192 secular, x, 11, 113, 227, 228, 239, 240, 241, 242, 243,

246, 247, 248, 249, 250, 251, 252, 253, 256, 257, 258, 259, 260, 261, 264, 265, 266, 268, 269, 286

secular trend, 11 security, 163, 169 sediments, 10

seed, 171, 306, 307, 310, 312 selecting, 148 sensitivity, 11, 71 sensors, 144, 304 separation, 162, 198, 219, 308, 400 Serbia, 1, 23, 25, 28, 35, 36, 37, 38, 77 Serbia & Montenegro, 23, 25 series, 6, 11, 13, 18, 21, 28, 33, 35, 56, 65, 67, 189,

194, 198, 219, 393, 395, 398 services, 147, 169 settlements, 167 severity, 4, 10, 158 shade, 172 Shanghai, 351 shape, 16, 35, 72, 91, 92, 99, 102, 108, 122, 136, 170,

182, 268, 282, 284, 333, 404, 409, 411 shock, xi, 19, 20, 75, 96, 109, 137, 140, 270, 319,

320, 321, 326, 329, 330, 333, 334, 335, 336 shock waves, 19, 20 shocks, xi, 71, 96, 97, 319, 320 shortage, 168 short-term, 157, 165, 178, 193, 344, 401 Siberia, 21, 55, 72 sign, 11, 14, 20, 21, 33, 55, 192, 218 signals, 44, 63, 112 signs, 10, 13, 33 silicate, 277, 278, 284, 286, 287 similarity, 83, 91, 126, 194, 306 simulation, 14, 25, 70, 320, 321, 324, 325, 326, 327,

331, 332, 333, 334, 335, 336, 343 simulations, ix, 25, 72, 75, 178, 190, 260, 285, 312,

320, 321, 331, 332, 333, 336, 337 Singapore, 141 singular, 112 singularities, 415 sites, 5, 152, 170, 342, 405, 406, 409 skeptics, 3 skewness, 88, 89, 91, 93, 97, 99, 100, 102, 104, 106,

111, 126, 133 Slovakia, 23, 61 Slovenia, 23, 25 sludge, 149 smoke, 47 smoothing, 112 snaps, 43 social benefits, 157 social development, 165 software, 393, 400 SOHO, 141 soil, 70, 151, 156, 161, 170, 191 soil erosion, 156, 170 solar cells, 198, 355 solar collectors, 146

Index 432

solar energy, xi, 20, 167, 178, 341, 342, 343, 367, 375

solar plasma, 306, 413 solar prominences, 374 solar system, vii, xii, 20, 51, 62, 68, 198, 263, 288,

342, 343, 354, 355, 356, 367, 369, 375 solid waste, 162, 163 South America, 8, 11, 168 Southeast Asia, 3 Southern Hemisphere, 9 Soviet Union, 223 space environment, x, 42, 197, 320, 337 space exploration, 220, 354, 382 space-time, x space-time, 227, 228, 268 Spain, vii, 1, 13, 23, 24, 25, 29, 48, 73, 404 spatial, 24, 28, 77, 137, 141, 293, 320, 324, 325, 326,

329, 332, 400 species, 7, 170, 181, 313, 323, 324, 325 specific heat, 161 spectral analysis, 121, 311 spectrum, xiii, 82, 112, 116, 140, 237, 276, 277, 278,

303, 304, 359, 368, 374, 375, 391, 392, 393, 395, 396, 398, 399

speculation, 220 speed of light, 63, 208, 217, 229, 276, 309, 322, 355 spheres, 319, 320 spills, 163 spin, 141 sporadic, 4, 69, 415 sputtering, 228 stability, 355 stages, 333, 342 standard deviation, 85, 88, 89, 90, 91, 92, 96, 102,

104, 111 standards, 167 stars, 62, 63, 138 statistical analysis, 88 statistics, 63, 88, 92, 93, 97, 99, 100, 102, 103, 104,

106, 111, 112, 136, 137, 141, 348 steady state, 161, 293 steel, 151, 172 stimulus, 3 stochastic, 26, 51, 62, 75, 273 stochastic processes, 51 storage, 148, 154, 158, 168, 198 storms, vii, viii, 14, 19, 40, 43, 67, 76, 106, 138, 177,

178, 320, 354 strain, 369, 370 strategies, 157, 320 stratosphere, ix, 44, 53, 58, 76, 77, 178, 179, 180,

181, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 193, 195

streams, 18, 65, 96, 97, 99, 104, 106, 111, 122, 123, 126, 127, 131, 132, 136, 144, 198, 287, 356, 369

strength, 16, 33, 41, 53, 63, 67, 86, 87, 101, 119, 131, 132, 135, 136, 139, 140, 185, 186, 187, 294, 295, 296, 297, 299, 300, 301, 302, 303, 307, 308, 309, 310, 311, 374

stress, 112, 210, 212, 213, 214, 215, 216, 237, 246, 363, 364

stress level, 364 stretching, 104, 223, 376 strikes, 26, 27, 28, 171 subjective, 9 subsidies, 171 substitution, 277 Sudan, v, xi, 341, 342, 343, 347, 348, 350, 351 suffering, 170 summer, 5, 8, 13, 67, 69, 77, 171, 172, 173, 186, 189,

192 sunlight, xi, 171, 173, 174, 353, 355 sunspot, xiii, 5, 13, 17, 20, 42, 66, 67, 69, 74, 83, 84,

91, 112, 113, 114, 116, 117, 121, 122, 123, 127, 131, 133, 135, 178, 194, 292, 391, 392, 395, 398, 400

superimposition, 409 superposition, 113, 117, 135, 414, 415 supply, 146, 147, 148, 149, 158, 165, 169 suppression, 27, 96, 132 surface area, 19, 24, 171, 211, 363 surface water, 170 surpluses, 154, 156 surprise, 16, 26, 65, 292 surveillance, 62 survival, 174 surviving, 285 sustainability, 165 sustainable development, 145, 147, 158, 163, 174 Sweden, 23, 25 Switzerland, 3, 23, 25, 72 symmetry, 40, 89 synchronous, 9, 386 synchrotron, 218 synergistic effect, 169 systems, xi, 27, 39, 69, 149, 153, 160, 164, 203, 219,

222, 227, 228, 321, 336, 342, 343, 346, 356

T

Taiwan, 81, 138 tariff, 164, 171 technical assistance, 167, 169 technical change, 170 technology, xii, 27, 62, 151, 153, 157, 165, 166, 169,

219, 220, 353, 354, 355, 356, 379

Index 433

temporal, 6, 11, 15, 24, 28, 69, 77, 135, 136, 137, 194, 298, 320, 413, 416

tensile, 210, 211, 363 tensile stress, 210, 363 terrorist, 30 Texas, 56, 198, 221, 222 thermal energy, 97, 111, 292, 342 thermal properties, 161 thermodynamic, 97 thermodynamic properties, 97 thermonuclear, 203, 204, 217, 219, 220 Thessaloniki, 417 thin film, ix, xii, 197, 198, 201, 204, 223, 354, 355,

357, 367, 369, 370, 376 thin films, 370 Thomson, 76, 112, 143 threat, 26, 169 threatening, 169 three-dimensional, 25, 141 tides, 161 timber, 151 time resolution, 71, 112, 114 time series, 6, 13, 18, 189, 194, 395, 398 tissue, 169 topographic, vii, 1, 39, 70 topology, xiii, 136, 413 torque, 69 total energy, 12, 108, 147, 150, 158, 172, 179 total internal reflection, 369 tourist, 28, 198 toxic, 15, 166 tracking, 79, 321, 326 traffic, 163 training, 157, 164, 166 trajectory, 43, 44, 45, 50, 183, 200, 201, 202, 206,

221, 281, 370, 371, 372, 380, 387, 416 transcripts, 71 transfer, 25, 70, 137, 355 transformation, 137, 158, 229, 230, 231, 232 transformations, 91, 236 transition, 136, 385 transition temperature, 385 transmission, 87, 106, 149, 172, 342, 345 transparency, 346 transparent, 370 transport, 14, 55, 150, 155, 163, 308, 313, 314, 315,

321, 414 transportation, 147, 307 travel, 202, 234 troposphere, 9, 12, 19, 43, 44, 48, 51, 55, 56, 77 trust, 358, 359 tsunamis, 41 tunneling, 19

turbulence, 71, 140, 296, 306, 316, 330 turbulent, 137, 306, 334 Turkey, 22, 23, 25, 404, 411 two-dimensional, 102, 103, 104, 415

U

UAE, 175 Ukraine, 22, 23, 61, 418 ultraviolet, 53, 62, 321, 351, 355 Ultraviolet, 53 ultraviolet light, 53 umbra, 20, 63 uncertainty, 11, 67, 158, 333 unfolded, 357 uniform, 329, 415 United Kingdom (UK), 76, 79, 145, 154, 160, 175,

196, 272, 341 United Nations (UN), 28, 68, 71, 76, 175, 351 United Nations Environment Program (UNEP), 71,

75 United States, 14, 72, 73, 74, 78 universities, xii, 379, 382 uranium, viii, 145, 163 urban areas, 7, 15, 165, 169, 170 urban population, 169 urbanisation, 154, 156 USSR, 196, 376, 417 UV, ix, xi, 178, 188, 189, 193, 271, 319, 326 UV radiation, ix, xi, 178, 188, 189, 193, 319, 326

V

vacuum, 45, 205, 206, 210, 218, 285, 331, 363, 374, 414

valence, 19 validity, 18 vapor, 39, 364 variability, viii, 3, 4, 5, 10, 12, 15, 16, 44, 51, 70, 71,

73, 77, 78, 79, 81, 82, 83, 88, 100, 102, 114, 121, 122, 127, 135, 137, 138, 142, 179, 191, 292, 399, 401

variables, 106, 137, 344 variance, 100 variation, xi, xiii, 14, 17, 82, 89, 102, 104, 116, 117,

122, 127, 128, 131, 132, 133, 135, 140, 144, 161, 195, 293, 294, 295, 296, 303, 307, 308, 313, 329, 341, 391, 393, 396, 399, 400, 404, 405, 407, 408

vector, vii, x, 21, 39, 43, 44, 46, 81, 101, 102, 103, 205, 227, 229, 230, 231, 233, 234, 237, 238, 244, 245, 262, 264, 276, 277, 278, 322, 332

vegetables, 157, 168 vegetation, 7, 14, 15, 27, 30, 39, 68, 70 vehicles, 148, 162, 198, 221, 354

Index 434

ventilation, 167, 171, 174 Venus, xii, 114, 367 village, 35, 51 violence, 62 violent, 63 visible, 53, 63, 292, 330, 334 vision, 69, 157 visualization, 137, 321 vortex, 48, 53, 189 vulnerability, 169

W

waking, 163 waste management, 162, 163, 175 wastes, 149, 157, 163, 168 wastewater, 152 wastewater treatment, 152 water, 5, 11, 15, 18, 146, 149, 151, 152, 153, 160,

161, 163, 165, 166, 167, 170, 172, 174, 342, 351 water quality, 163 water vapour, 152, 172 wave number, 414 wave power, viii, 145, 153, 175 wave propagation, 287 wavelengths, 63 wavelet, xiii, 18, 82, 112, 114, 116, 138, 391, 392,

393, 395, 396, 398, 400 wavelet analysis, 82, 138 wavelets, 393 wealth, 169

web, 82, 387 web pages, 387 Weibull, vi, xiii, 403, 404, 409, 411 Weibull Distribution, xiii, 403, 404, 409, 411 West Africa, 33 Western Europe, 168 wholesale, 165 wildfire, 28, 34, 58, 69, 71, 72, 73, 75 wildfires, 4, 28, 69, 74 wildland, 73 wildlife, 169, 170 wind speeds, xiii, 142, 403, 404, 405, 407, 409, 410,

411 windows, 64 winning, viii, 145 winter, 2, 9, 15, 25, 67, 171, 172, 173, 179, 189, 192,

193 wood, 147, 151, 157, 167, 172 Wyoming, 182

X

X-axis, 102, 103, 104 X-rays, 62, 187

Y

Y-axis, 102 Yemen, 175 yield, 67, 172, 232, 236, 247, 259, 262, 324

Handbook on Solar Wind - Effects, Dynamics, Interactions - H. Johannson (Nova, 2009)BBS

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