NONLINEAR INTERACTIONS OF ELECTROMAGNETIC WAVES WITH PLASMAS AND SEMICONDUCTORS BY Md. Salimullah ThesiS submitted to the Indian Institute of Technology„Delhi for the award of the Degree of DOCTOR OF PHILOSOPHY Department of Physics Indian Institute of Technology,Delhi October, 1979
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NONLINEAR INTERACTIONS OF ELECTROMAGNETIC WAVES
WITH PLASMAS AND SEMICONDUCTORS
BY
Md. Salimullah
ThesiS submitted to the Indian Institute of Technology„Delhi
for the award of the Degree of
DOCTOR OF PHILOSOPHY
Department of Physics
Indian Institute of Technology,Delhi
October, 1979
DEDICATED TO THE MEMORY OF
MY GRANDFATHER
LATE YAD ALI SARKAR
ACKNOWLEDGEMENT
During my years at the Indian Institute Of
Technology Delhi, I have come into contact with a large
number of individuals whom I want to appreciate for their
support and assistance.
First of all, I am happy to acknowledge that I will
remain ever grateful to Professor N.S.Sodha whose sincere,
skilful and kind guidance helped me to complete the
challenging work of my thesis. What attracted me very much
and induced a great confidence in me is his courageous and
dynamic personality. I find my language very poor to express
my gratitude to him for his sincere and impartial help. I am
grateful to Dr. R.P.Sharma for valuable guidance and many other
valuable friendly cooperation. I am also thankful to Dr. S.D.
Sharma and Dr. V.K.Aggrawal for their help and cooperation
during my stay in India.
It is extremely difficul4:, to express how I am grateful
to pr. V,K.Tripathi whose geniusness and love for research work
inspired me to work in Plasma Physics. I am impressed by his
magnetic character. I am also thankful to the members of his
family who helped me in various forms.
It is an opportunity to thank Professor 0.P.Jain,
Director of this Institution, who supported my cause and
wished me best of luck.
I am thankful to Professor P.K.C.Pillai, Head of
Physics Department, for his sincere wish and official help
during the tenure of my work.
Thanks are also due to Dr. O.P.Agnihotri who inspired
and appreciated me all the time.
Before acknowledging many other individuals, I would
like to express my gratitude to Dr. R.R.Sharma who helped me
at many stages at the time of need.
To express my gratitude and thanks I would like to
mention the names of Dr. L.A.Patel, Dr. N.C.Srivastava,
Dr. J.K.Sharma, Dr. R.C.Sharma, Dr. D.P.Singh, Dr. Govind
Dr. G.Umesh, Dr. G.N.Tiwari Mr. D.Subbarao, Mr. S.K.Sinha,
Mr. S.S.Gupta, Mr. S.N.Bajpai, Mr. A.Raza, Mr. R.Thangraj,
Dr. N,K.Sharma„ Dr. B.K.Gupta and Mr. Tarsem Singh Gill.
My grateful thanks are due to Mr. T.N.Gupta for his
efficient typing and many other cooperation.
I an thankful to the governments of India and
Bangladesh for providing me with the cultural exchange scheme
scholarship.
I express my deep sense of oratitude to my parents,
especially to my elder brother, Mr. M.Habibullah for his
constant encouragement.
Finally, I am happy to thank my wife, Mrs. LI.N.Mily
for her right understanding and ample patience during the
course of the work. Pict - -04
(Md. Salimullah)
ABSTRACT
In the present thesis the author has investigated
some of the nonlinear phenomena in gaseous and solid state
plasmas. The nonlinear phenomena, which result on account
of the interaction of high power EM waves with plasmas, like
stimulated scatterings, filamentation and modulation instability,
harmonic generations, beat heating, nonlinear excitation of
electrostatic waves in a plasma, self focusing, nonlinear
Landau damping and other parametric instabilities play the
important role in coupling the energy of the EM waves with
the plasmas,
The stimulated Brillouin scattering of EM waves of ion
cyclotron range of frequencies is one of the prominent channels
of decay in magnetically confined plasmas. It is found that
the growth rate for backscattering is one order higher than
that for the forward scattering. The effect of self—generated
magnetic field on nonlinear scattering by electron Bernstein
modes in laser produced plasmas is quite significant. Typically
12 0 w/cm2), 1 for Nd:elass laser (.;! ,;3.5x1013
rad.sec-1,
KeV, the growth rate for first electron Bernstein
mode Cr 6x1011 rad.sec-1 The effect of external static
magnetic fields on stimulated Brillouin scattering of laser
radiation in a Piezoelectric semiconductor (n—In5b) has been
examined for both longitudinal and transverse propagation.
It is seen that the growth rate for transverse propagation
is one order higher than that for longitudinal propagation.
A high power laser beam propagating through a dc biased
n--GaAs sample is strongly unstable for filamentation
instability. The instability causes space charge
perturbations in the microwave range of frequencies and the
growth rate attains very large values in the negative
differential resistivity region. This hdr region is seen
to be responsible for the nonlinear absorption and over-
modulation of an amplitude modulated EM beam.
The effect of uniform static magnetic field on the
conversion efficiencies of microwave harmonic generations in
rectangular waveguide when a high power microwave propagates
along the direction of an external static magnetic field.
For second harmonic generation, the nonlinearity arises from
the ponderomotive force on electrons, while the nonlinearity
in the third harmonic is assumed to be through the modula-
tion of collision frequency of electron's. The power Conver-
sion efficiencies show resonance enhancement for some
particular values of plasma density, dimensions of the
waveguide and applied magnetic field. For a microwave of
power 10 MW, too-2:1010
rad. sec-1 1 GOI: OCA.,0 and
dimension of the waveguide being of the order of
wavelength of the fundamental wave, the powers of the
generated second and third harmonic turn out to be 1 MU
and Of 10 kw, respectively.
16
Chapter-VI: Excitation of a Plasma Wave b two_p-Polarized Waves at the Difference Frectuency. in a Plasma
In the present chapter we have set up the general
equations for the excitation of an electron plasma wave at
the difference frequency of two p-polarized waves, propaga-
ting obliquely in a collisionless, hot, unmagnetized and
inhomogeneous plasma. The incident waves are assumed to be
propagating parallel to each other and containing both the
electrostatic and EN components. To keep the mathematics
manageable, we have derived the field components of the
excited electron plasma wave when the scale length of
inhomogeneity of the plasma is much greater than the wave-
lengths of the waves involved. It is observed that the
generated electron plasma wave at the difference frequency
has four components, in addition to a usual natural mode
at the difference frequency, having different Landau damping
rates. The strengths of the generated waves depend on the
electron density, electron temperature and the angle of
incidence of the pump waves at the vacuum-plasma interface.
chapt.e,r7VII: Plasma Wave_arO_Thkr.0)),armop.ic Vnvatioji, Ta_.s p m a plasma s
In this chapter we have set up the equations for
the excitation of an electron plasma wave at twice the
pump wave frequency and third harmonic generation by a p-
polarized EN wave in a collisionless, hot, unmagnetized
and inhomogeneous plasma. The expressions for the field
17
components of the generated Wakes are derived when the
scale length of inhomogeneity is taken much greater than
the wav„-lengths of the waves involved. An expression for
the third harmonic power conversion efficiency has also
been derived in the cold plasma approximation. It is seen
that by changing the angle of incidence of the pump wave
at the vacuum-plasma interface and electron density of
the plasma the third harmonic power conversion efficiency
exhibits maxima and minima,
Chayter-VIII: Generation of an Ion Acoustic Pulse by Two EM Pulses at Difference Freiviency in a ffUnieion ess Plasma
This chapter presents an investigation of the
generation of an ion acoustic pulse by two EM pulses in a
collisicnless hot unmagnetized plasma at the difference
frequency of the two EM pulses. On account of the inter-
action of the two EM pulses, a ponderomotive force at the
difference frequency becomes finite and leads to the
generation of an ion acousti ulse. the two EM pulses
are having Gaussian intensity distriLJtion in time and
uniform intensity distribution in space, the generated ion
acoustic pulse is also Gaussian in time with a pulse width
`.2 t / , ) --rk2 cot .0 where t10 and t20 are the
initial pulse widths of the incident EM pulses. Moreover,
if the incident EM pulses are having Gaussian intensity
distribution in space and time, the nonuniform intensity
distribution of the EM pulses in a plane transverse to the
18
direction of propagation leads to the redistribution of
electrons and ions, and the transient cross focusing of
the pulses may occur for appropriate initial powers of the
EN pulses, The ion acoustic pulse generation is seen to
be drastically modified by cross focusing of the two EM
pulses.
The work presented in the thesis has resulted in
the following publications/communications:—
1. Filamentation of laser radiation in d.c. biased GaAst Md. Salimullah and V.K.Tripathi, Applied Physics (Accepted).
2. Nonlinear absorption and overmodulation of a high power electromagnetic wave in GaAs, Md. Salimullah and %K.Tripathi (Accepted).
3. Stimulated Brillouin scattering of laser radiation in a piezoelectric semiconductor in the presence of a magnetic field, Md,Salimullah, R.R.Sharma and V.K.Tripathi, J.Phys.D: Appl.Phys.
. (In Press, 1979).
4. Microwave third harmonic generation in a plasma filled baveguide in the presence of a magnetic field, R.R.Sharma'and hd.Salimullah (Communicated).
5. Stimulated Raman scattering of laser radiation in semiconductors, Md.Salimullah, R.R.Sharma and V.K.Tripathi (Communicated),
6, Nonlinear microwave second harmonic generation in a plasma filled waveguide in the presence of a static magnetic field, R.R.Sharma and Md, Salimullah (Communicated).
7. Stinulated•8rillouin scattering of electromagnetic ion cyclotron waves in a plasma, Md.Salimullah, R.R.Sharma and V.K.Tripathi, ("Communicated).
19
S. Nonlinear scattering of upper hybrid laser radiation by electron Bernstein modes in a plasma, R.R.Sharma, Md.Salimullah and U.K.Tripathi:P '`R A (In Prtess, 197ai.
9. Excitation of a plasma wave by two p-polarized waves at the difference frequency in a plasma, M.S.Sodha, Md.Salimullah and R.P.Sharma (Communicated).
10. Plasma wave and third harmonic generation by a p-polarized laser beam in a plasma, M.S.Sodhat Md. Salimullah and R.P.Sharma (Communicated).
11. Generation of an ion acoustic pulse by two EM pulses at difference frequency in a collisionless plasma, M.S.ScOha9 Md.Salimullah and R.P.Sharma,
(T n Pices, 1979). In addition to the above mentioned publications
the author has also been associated with the following
communication which has not been included in the thesis:
1. Nonlinear, self distortion of ion acoustic waves in a plasma, J.K.Sharma, Md.Salimullah and V.K.Tripathi Applied Physics (In Press, 1979).
CONTENTS
Acknowledgement
Abstract
Preface
CHAPTER I
Stimulated Brillouin Scattering of EN Ion Cyclotron Waves in a Plasma
1.1 Introduction 20
1.2 Nonlinear dispersion relation 21
1.3 Discussion
34
CHAPJER_II
Nonlinear Scattering of Upper Hybrid Laser Radiation by Electron Bernstein Modes in a Plasma
2.1 Introduction 35
2.2 Coupling coefficient 38
2.3 Growth rate 48
2.4 Discussion 52
CHAPTER III
PART A
Stimulated Orillouin Scattering of a Laser Radiation in a Piezoelectric Semiconductor the Presence of a Magnetic Field