26 September 2003 1 Waves and turbulence in the solar wind The solar wind as a turbulence laboratory Global structure of the heliosphere Key results: –Alfvén.

26 September 2003

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Waves and turbulence in the solar wind

• The solar wind as a turbulence laboratory• Global structure of the heliosphere• Key results:

– Alfvén waves– Active turbulent cascade– Intermittency– Anisotropy

• Open questions• Future opportunities• Useful references

Tim Horbury

Imperial College London

26 September 2003

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Notes on this file

• This talk was presented at the Summer School at Chalkidiki, in September 2003, organised by Loukas Vlahos.

• I generated this version of the presentation after the meeting and there are some changes to the original:– I have added a short list of good review articles at the end– I have attributed a few of the more important figures, with their full

reference– Some of the material, particularly that on anisotropy, is unpublished– The file does not contain movies, to save space

• If anyone has any comments or questions, they are welcome to contact me at [email protected]

Tim Horbury, London, 7th October 2003

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What is the solar wind?

• Collisionless, magnetised plasma• Continual, but variable, outflow from Sun’s corona• Blows a cavity in interstellar medium: heliosphere• At edge of heliosphere, merges with interstellar medium• Interacts with planets and other bodies

• Supersonic (super-Alfvénic, …)• Hot: >105 K• Rarefied: few per cm3 at Earth• Complex due to solar variability, solar rotation, and in situ processes• Variable on all measured scales, from sub-second centuries

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What does the solar wind look like?

• Very rarefied• Can’t usually see it• Near-Sun solar wind is visible during eclipses

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Origin of the solar wind

• Sun’s upper corona expands into space

• Accelerates and forms the solar wind

• Variable speed, density, temperature

• Carries magnetic field from corona

• Also carries waves and turbulence…

SoHO coronagraph (LASCO)Artificial eclipseSee http://sohowww.nascom.nasa.gov for movies

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Solar wind as a turbulence laboratory

• Characteristics– Collisionless plasma– Variety of parameters in different locations– Contains turbulence, waves, energetic particles

• Measurements– In situ spacecraft data– Magnetic and electric fields– Bulk plasma: density, velocity, temperature, …– Full distribution functions– Energetic particles

• The only collisionless plasma we can sample directly

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Importance of waves and turbulence

Energetic particle transport• Controls cosmic rays throughout the

solar system

Effect on the Earth• Can trigger reconnection, substorms,

aurorae, …

Understanding solar processes• Signature of coronal heating, etc.

Application to astrophysical plasmas• Turbulence is pervasive

Turbulence as a universal phenomenon• Comparison with hydrodynamics

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Global structure of the solar wind

• Source in the corona• Relation to coronal structure• Effect of solar rotation• Solar cycle dependence• Transient events• Interaction with the interstellar

medium

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The solar corona

• Hot rarefied atmosphere above visible surface

• Plasma beta <<1 in corona magnetic field dominates

• Closed magnetic field: plasma trapped

• Open magnetic field: plasma can expand into interplanetary space

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Skylab: the first movies of the corona

• First US space station

• Launched 1973

• Converted Saturn upper stage

• Carried early X ray solar camera

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Skylab movie of the corona

• First movies of the Sun’s corona in X-rays

• Coronal holes– dark regions, often near

poles• Active regions

– bright regions, associated with sunspots

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The solar corona: modern instruments

• Movie from the SoHO spacecraft

• In orbit since 1996

• Several coronal holes

• Very active corona• Lots of structure

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Expansion of the upper corona

• Corona is very hot• Pressure is higher than ambient

interstellar medium• Expands into interplanetary space

(Parker, 1958): solar wind

• Carves a cavity in interstellar medium: heliosphere

• Nearly radial flow• Accelerates to full speed by ~20

solar radii

SoHO coronagraph (LASCO)Artificial eclipse

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The heliosphere

• Solar wind blows bubble in interstellar medium

• Probably around 100 AU from Sun at the nose

• Cosmic rays enter heliosphere: motion controlled by turbulent magnetic field

Interstellarmedium

Heliopause

Terminationshock

Solarwind

Cosmicrays

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Interstellar bowshocks

• Shocks also form between stellar winds and interstellar medium

• General shape is probably similar to the Sun’s bowshock

NASA and The Hubble Heritage Team (STScI/AURA)

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Three months of solar wind data

• Field and particle measurements

• MHD on these scales

• Variable speed, density, magnetic field, …

• Not random: presence of large scale structures

• 30-day repeats

• We can explain this structure

Ulysses: 4.5 AU

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Solar wind: relation to coronal structure

• Fast and slow

High latitudes: fast, from coronal hole Low latitudes: slow, variable

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Latitude variation in solar wind speed

• Solar minimum: dipolar solar magnetic field

• Ulysses measurements

• High latitudes dominated by high speed wind from polar coronal holes

• Low latitudes: fast and slow streams, very variable

• Different magnetic polarity in each hemisphere: solar dipole

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The corona and the solar cycle

Solar minimum

Dipolar magnetic field

Open fields over poles

Solar maximum

Complex magnetic field

No latitude dependence

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Large scale structure of the heliosphere

• Fast and slow solar wind streams• Sun’s rotation winds structures into

spirals: compressions and rarefactions

• Just like a lawn sprinkler…

• These data derived from ground-based interplanetary scintillation measurements (Bernie Jackson: see http://cassfos02.ucsd.edu/solar/tomography/ for more info)

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Magnetic field: the Parker spiral

• Solar rotation drags out solar wind magnetic field into Archimedian spiral

• Predicted by Gene Parker Parker spiral

• Winding angle depends on wind speed, but:

• ~45º at Earth• ~90º by 10 AU

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Typical conditions at 0.3 AU

• Closest measurements to date• Before stream-stream interactions are

important• Highest density in slow wind

Density and temperature anticorrelated

Magnetic field ~0º from radial

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Typical conditions at 1.0 AU

• Stream-stream interactions more important

• Shocks beginning to form

Density and temperature correlated: compression at velocity increase

Magnetic field ~45º from radial: Parker spiral

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Coronal mass ejections

• Sun can eject discrete structures into space

• Coronal mass ejections (CMEs)

• Around 1 per day (varies with the solar cycle)

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Flares, CMEs and energetic particles

• Fast-moving particles produced by flare and associated shocks

• Particles can sometimes reach Earth

• Propagation of particles controlled by magnetic field

• Scattered by waves and turbulence

• Aside: is the slow wind formed of many small ejecta?

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The magnetosphere

• Interaction of solar wind with Earth’s magnetic field

• Bowshock: high Mach number shock

• Magnetosheath: shocked solar wind plasma

• Magnetosphere: very low beta plasma

Good:Different conditionsMany spacecraftHigh data rate

Bad:Taylor’s hypothesis not satisfied (more later)Very complicated

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Significant spacecraft

Wind, ACE (present)• Near-Earth (L1). Good,

modern instrumentation

Helios (1975-1984?)• Closest approach to the Sun

(0.29 AU, 63 solar radii)

Ulysses (1990-2006)• Only measurements at high

latitudes

Voyager 1 &2 , Pioneer 10 & 11 (mid-1970’s, some still operating)

• Only outer heliosphere measurements (80+AU) You are here

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Ulysses

• Launch 1990, still operating

• First spacecraft to explore high latitudes: up to 80º

• Eccentric orbit: 1.3 - 5.4 AU

• Orbit has provided long intervals of near-stationary data

See http://sci.esa.int/ulysses/

for more info

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Helios

• Closest approach to Sun: 0.29 AU

• Two spacecraft, launch 1974 & 1976

• Provide measurements of very “young” solar wind

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Cluster

• Launch 2000• Four spacecraft in formation in

Earth orbit• Separations vary: ~100 km, ~600

km, ~5000km• Measures magnetosphere,

magnetosheath, solar wind

• Combine four spacecraft data to determine information about the 3D structure of the plasma

• http://sci.esa.int/cluster

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Spacecraft particle measurements

Measure:• Bulk distribution function, for ions

and electrons

Calculate:• Moments of distribution function:

velocity, temperature, density, etc.

• Particle composition (protons, helium, oxygen, etc.)

• Ion charge states• Time variations at sub-

gyroperiod scales

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Spacecraft magnetic and electric field measurements

• Measure magnetic and electric field from DC up to ~Hz, as time series• Measure higher frequencies (can be up to MHz) using spectra

Spacecraft measurements are difficult:• Very low fluxes and fields• Spacecraft contamination• Instrument effects• Low power and mass• Telemetry constraints

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Why we need to understand the data

• No instrument provides an exact measurement of any physical quantity• We must know how a measurement is made, and its limitations, before

we can use it with confidence

Example 1: SoHO EIT (ultraviolet) image of the Sun

Flare (bottom right) is overexposed, and light “bleeds” into neighbouring pixels to left and right

These pixels do not accurately represent the real intensity

We are familiar with such effects - but other artefacts are much more subtle…

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Why we need to understand the data

Example 2: Cluster magnetic field data

Wave-like variation visible, particularly in second field component (BY)

Period of wave is ~4s

This is spin period of spacecraft - a big hint!

In fact, this signal is an artefact of the instrument calibration process, and can be removed with better calibration

-6

-4

-22001 day 44 Cluster FGM 5/s GSE

BX (

nT)

2.5

3

3.5

BY (

nT)

-2

0

2

BZ (

nT)

00:23:00 00:23:30 00:24:000

5

|B| (

nT)

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Why we need to understand the data

Example 3: The Earth’s radiation belts (“Van Allen” belts)

The radiation belts around the Earth (composed of trapped cosmic rays) were discovered in 1958 by James Van Allen using Explorers 1 and 3.

Both spacecraft carried a single Geiger counter to measure fluxes of energetic particles

In parts of the orbit, the rate was zero

Van Allen correctly interpreted a zero rate as saturation of the detector, and hence high fluxes of particles - radiation belts!

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The turbulent solar wind

• Fluctuations on all measured scales

f -1

f -5/3waves

turbulence

Power spectrum• Broadband• Low frequencies: f -1

• High frequencies: f -5/3

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Fundamental observations of waves and turbulence

Alfvén waves• Waves of solar origin

Active turbulent cascade• Not just remnant fluctuations from corona

Intermittency• Similar high order statistics to hydrodynamics

Field-aligned anisotropy• Fundamental difference to hydrodynamics

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Interpreting spacecraft measurements

• In the solar wind (usually),

VA ~50 km/s, VSW >~300 km/s

• Therefore,

VSW>>VA

• Taylor’s hypothesis: time series can be considered a spatial sample• We can convert spacecraft frequency f into a plasma frame

wavenumber k:

k = 2f / VSW

• Almost always valid in the solar wind• Makes analysis much easier• Not valid in, e.g. magnetosheath, upper corona

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Interpreting spacecraft measurements

• Solar wind flows radially away from Sun, over spacecraft• Time series is a one dimensional spatial sample through the plasma• Measure variations along one flow line

Flow

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Alfvén wavesField-parallel Alfvén

wave:• B and V variations

anti-correlated

Field-anti-parallel Alfvén wave:

• B and V variations correlated

• See this very clearly in the solar wind

• Most common in high speed wind

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Average magnetic field sunwardPositive correlationPropagating anti-parallel to fieldPropagating away from Sun in plasma frame

Propagation direction of Alfvén waves

• Waves are usually propagating away from the Sun

Average magnetic field anti-sunwardNegative correlationPropagating parallel to fieldPropagating away from Sun in plasma frame

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Spectral analysis of Alfvén waves

• For an Alfvén wave:

b = v,

• Where

b = B /(0)1/2

• Calculate Elsässer variables:

e = b v

• Convention: e+ corresponds to anti-sunward (so flip e+ and e- if B away from Sun)

• Also power spectrum

Z (f) = PSD (e )

• If pure, outward Alfvén waves,

e+ >> e-

Z+ >> Z-

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Inward and outward spectrum

Fast wind Slow wind

Note:• When e+>>e-,

magnetic field spectrum ~ e+ spectrum

Define: Normalised cross helicity

C = (e+-e-)/(e++e-)

C = 1 for pure, outward waves

C = 0 for mixed waves

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Speed dependence of turbulence

Slow: coronal hole boundarye+ ~ e-

Fast: within coronal holee+ >> e-

• Character of fluctuations varies with wind speed

Tu et al, Geophys. Res. Lett., 17, 283, 1990

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Stream dependence: cross helicity

• Wavelets: measure time and frequency dependence of waves

Fast windPositive cross helicity: anti-sunward Alfvén waves

Sharp transitionTo mixed sense waves

Slow windMixed sense, but very variable

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Dominance of outward-propagating waves

• Solar wind accelerates as it leaves the corona

• Alfvén speed decreases as field magnitude drops

• Alfvén critical point: equal speed (~10-20 solar radii)

• Above critical point, all waves carried outward

Therefore,

• Outward-propagating low frequency waves generated in corona!

Distance from Sun

SpeedSolar wind speed

Alfvén speed

Critical point

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Active turbulent cascade in fast wind

• Bavassano et al (1982)• Fast wind: “knee” in

spectrum• Spectrum steepens

further from the Sun• Evidence of energy

transfer between scales: turbulent cascade

Energytransfer

Po

wer

(lo

g s

cal

e)

after Bavassano et al, J. Geophys. Res., v87, 3617, 1982

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Interpretation

• Initial broadband 1/f spectrum close to Sun

• High frequencies decay, transfer energy

• Spectrum steepens• Progressively lower frequencies

decay with time (distance)• Breakpoint in spectrum moves

to lower frequencies

• Breakpoint is the highest frequency unevolved Alfvén wave

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Summary: spectral index in fast wind• Ulysses polar measurements• Magnetic field component

• Inertial range• Development of cascade• 1/f Alfvén waves at low frequencies

Not shown or considered here:• Dissipation at higher frequencies• Structures at lower frequencies

Alfvén waves Inertial range

Structures

Dissipation

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Large scale variations in power levels

• Power in high speed wind, low and high latitudes

• Ulysses agrees well with Helios

• Data taken 25+ years apart

• Increasing scatter in Helios reflects stream-stream interactions

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High and low latitudes: power levels

• Low latitudes: fast and slow streams

• Stream-stream interactions

• Big variations in power levels

• Cross helicity often low, highly variable

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High and low latitudes: power levels

• High latitudes at solar minimum

• Dominated by high speed wind form coronal hole

• Power levels very steady• Cross helicity steady and

high

Therefore,• Ulysses polar data are

ideal for detailed analysis of turbulence and waves

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Power dependence on distance

• WKB (Wentzel-Kramer-Brillouin)• Assume propagation of waves through a slowly changing medium• Solar wind density scales as r -2

power scales with distance as r -3

• We expect this for low frequency Alfvén waves:– Non-interacting– No driver or dissipation, especially in high latitude polar flows

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Large scale power dependence

• Ulysses: measure large scale trends in power levels

Radial power trend

Low frequency Alfvén waves

r -3 radial scaling (WKB): non-interacting

P f -1

High frequency Alfvén waves

Faster than r -3 radial scaling: energy transfer

P f -5/3

Note: latitudinal power scaling!

Lower power at higher latitudes

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Latitude dependence?

• Horbury: latitude dependence, due to coronal overexpansion

• Bavassano: non-power law scaling, due to nonlinear effects

• Answer is unclear

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Intermittency

• Distributions of increments are not Gaussian

• Well known in hydrodynamics, also present in solar wind MHD

• More ‘big jumps’ than expected

• Is this a signature of the turbulence, or solar wind structure?

Sorriso-Valvo et al., 2001

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Identifying intermittent events

• What causes these large jumps?

• Identify individual events, study in detail• Discontinuities?• Are large jumps part of the turbulent cascade, or are they

structures?

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Intermittency and structure functions

• Structure functions:

• S(,m)=<|b(t+)-b(t)|m >• Moments of the distribution

of differences at different lags

• We are interested in how these scale with time lag:

• S(,m)= (m)

• How do the wings of the distribution change with scale?

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Structure function scaling

• Data not consistent with Kolmogorov (K41) or Kraichnan (K65)

• Intermittency: not a straight line

• Good agreement with hydrodynamic model, with K41 cascade

• Is the model good, or is this analysis just a poor discriminator? • Dots: data

• Square: ‘p model’ fit

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Kolmogorov vs Kraichnan

• Carbone (1992): g(4)==1 for Kraichnan

• Use g(3) and g(4) to distinguish Kraichnan from Kolmogorov

• Answer: Kolmogorov

• Why is it not a Kraichnan cascade?

• Answer (probably) lies with anisotropy….

Inertial range

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Field-aligned anisotropy

• Power levels tend to be perpendicular to local magnetic field direction

anisotropy

• Dots: local minimum variance direction

• Track large scale changes in field direction

• Small scale turbulence “rides” on the back of large scale waves

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Anisotropy and 3D field structure

• Wavevectors parallel to the field: long correlation lengths perpendicular to field (“slab”)

• Wavevectors perpendicular to the field: short correlation lengths perpendicular to field (“2D”)

• Mixture of slab and 2D results in shredded flux tubes

• Consequences for field structure and energetic particle propagation

100% slab0% 2D

20% slab80% 2D

Matthaeus et al 1995

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Turbulence and energetic particles

• Energetic particles follow and scatter from magnetic field

• Ulysses: particles at high latitudes

• Unexplained “latitudinal transport”

• Must be related to 3D structure of magnetic field

• This is poorly understood at present

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Limitations of a single spacecraft

• Solar wind flows radially away from Sun, over spacecraft• Time series is a one dimensional spatial sample through the plasma• Can’t measure variations perpendicular to the flow• How can we measure the 3D structure of the turbulence?

Flow

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How do we measure the 3D structure?

• Assume turbulence is symmetric around magnetic field

• Small scale turbulence rides on top of large scale waves

• When field changes direction relative to flow, we are cutting through it in a different direction

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Anisotropy: “slab” vs “2D” turbulence

• Wavevectors parallel to the field: long correlation lengths perpendicular to field (“slab”)

• Wavevectors perpendicular to the field: short correlation lengths perpendicular to field (“2D”)

• Bieber et al, 1996: look at power levels at different directions of the magnetic field to the flow

• ~20% slab, 80% 2D

Bieber et al, J. Geophys. Res., 101, 2511, 1996

k||B: slab

kB: 2DB

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Measuring anisotropy with Ulysses

• Use 3 years of magnetic field data - only possible with Ulysses high latitude data

• Largely consistent with slab/2D model: 25% slab

• Significantly different spectral index parallel to magnetic field - effect of discontinuities

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Anisotropy and intermittency

• Can measure intermittency in different directions

Along field: steep spectrum (discontinuities)

Kolmogorov-like spectrum in all other measured directions

Level of intermittency comparable to previous, isotropic, measurements, and hydrodynamics

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Anisotropy and Kolmogorov turbulence

• Why is the MHD cascade Kolmogorov-like, not Kraichnan-like?

Kraichnan: • Equal populations of oppositely-propagating Alfvén waves• Decorrelation slows cascade

Solar wind: • Dominated by one propagation direction• Anisotropy: wavevectors usually perpendicular to field

• Wave speed: V = VAcos()

• Perpendicular wavevectors, not propagating: no decorrelation Kolmogorov cascade

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Combining data from two spacecraft

• Compare between spacecraft

• Provides information about variations across flow

• Varying time lag corresponds to varying scale and direction of separation vector

• Limitations on scales and directions

Flow

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Using multiple spacecraft

• Each pair of spacecraft gives a plane on which we can measure the correlation

• Four spacecraft give six planes:

• We have a large range of angles and scales over which we can measure the turbulence structure

Future: Use with Cluster, ACE/Wind/IMP 8, etc

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Summary: unanswered questions

3D structure• What is the 3D form of the turbulence, particularly the magnetic field?• How does this control energetic particle transport?

Intermittency• Is solar wind intermittency “the same” as in hydrodynamics?

Turbulent cascade• How does it occur? Parametric decay?

Coronal heating• What can we learn about coronal conditions from the solar wind?

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Summary: useful data sets

High time resolution and precision data: ACE, Wind

Long duration stationary data: Ulysses

Turbulent evolution: Helios/Ulysses

Dynamically young waves and turbulence: Helios (+Ulysses)

3D structure: L1 constellation (ACE, Wind, IMP 8, Geotail, Cluster, …)

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Future missions

STEREO• Launch 2006: twin LASCO-like imagers, also in

situ. Will help with 3D structure

Solar Orbiter• Launch ~2011: will travel to 0.21 AU, ~40º.

Imaging and in situ: linking solar and solar wind features

Bepi-Colombo• Mercury mission, but also in situ

Sentinels• NASA, multiple spacecraft in inner heliosphere

L1 constellation• Partially present, more to come? Earthshine?

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Useful references

Solar wind waves and turbulence• Tu and Marsch, Space Sci. Rev.,73, 1-210, 1995 • Matthaeus et al., Rev. Geophys. Suppl., 609-614, 1995• Marsch, MHD turbulence in the solar wind, in Physics of the Inner

Heliosphere II, ed. R. Schwenn and E. Marsch, Springer-Verlag, Berlin, 1991

Ulysses polar results• The heliosphere near solar minimum: the Ulysses perspective, ed. A.

Balogh, R. G. Marsden and E. J. Smith, Springer-Verlag, Berlin, 2001