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

longitudinally magnetized plasma filled rectangular waveguide

has been examined in detail and compared with the results of

unmagnetized case.

The beat heating of plasmas by tuo obliquely

propagating p-polarized waves and excitation of plasma wave

and third harmonic wave by a single p--polarized pump wave

have been investigated in considerable detail. In addition to

these, the author has also studied the transient setting of

ponderomotive nonlinearity in a plasma ? transient cross

focusing of two En pulses and the excitation of an ion

acoustic pulse at the difference- frequency of the two EM

pulse's.

PREFACE

There are two schemes to achieve controlled thermo-

nuclear fusionl.

1) Inertial confinement (e.g., laser driven fusion)

2) Magnetic confinement,

In the inertial confinement scheme, the most accepted

idea is that a D—T pellet is irradiated symmetrically by a

number of high power laser pulses and a high temperature

high density nonequilibrium plasma is formed. The high

pressure gradient produces a self—generated shockwave which

compresses the core plasma. Depending upon the confinement

time (r,,10"9 sec) and plasma density (102-103 times the

solid D-T density) one can have significant release of

energy before the plasma diffuses.

In the magnetic fusion scheme, the plasma is confined

by a network of static magnetic fields. Out of the various

configurations of confinement, the tokamak has attained the

highest importance. The confinement time is of the order

of a second and one deals with relatively much lower

electron densities (p./013-1015 cm

-3). In this case one

needs to provide supplementary heating of the plasma by rf

fields, e.g., lower hybrid heating, electron and ion

cyclotron heating etc.

The knowledge of nonlinear interaction of high power.

EN waves with plasmas is the primary need not only for the

above mentioned schemes of controlled thermonuclear

fusion but also for numerous applications in many other

fields of science and technology. The purpose of the present

thesis is to explore basic aspects of some important (yet

incomplete) phenomena of nonlinear interaction of high

power EM waves with gaseous and solid state plasmas.

For a collisional plasma the interaction becomes

nonlinear when the electric field of the En wave is greater

or equal to the characteristic field2 E

EF, — 4.2x 10 [(wc4T+-ii .-10 )T-.5 a

where '9 is the effective collision frequency of electrons

in an equilibrium plasma at temperature-T, GO0 is the

wave frequency and (73 is the mean effective relative

fraction of energy transferred'by an electron of mass m in

a collision with a heavy particle of mass M ( 2m/M).

However, for a collisionless plasma54

L4 where 7:-;e2/6 6 ' T7ri 0'

k8 is the Boltzmann constant

and is the electronic charge.

The consequences of the nonlinear interaction of

intense EN waves with plasmas are a large number of

phenomena3-6, viz., 1) stimulated scatterings, 2, self—

focusing, 3) Parametric instabilities-, 4; harmonic generations,

5) modulation and filamentation instabilities, 6) anomalous

heating, 7) nonlinear Landau damping, 8) profile modifica-

tion, etc. Following are the brief descriptions of the

nonlinear phenomena studied in the present thesis:,,

1. Parametric Instabilities

The phenomena of parametric excitation are known

for over a century and recently it has been recognized as

a widely prevailing nonlinear phenomena in plasmas. Lord

Rayleigh7 first explained Melde's experiments and introduced

the name parametric excitation. This experiment consists

of a stretched string attached to a prong of a tuning fork

vibrating in the direction of the string. It is observed

that transverse oscillation's of the string build up and

get amplified if the frequency of the tuning fork is twice

the natural frequency of the transverse vibration of the

string, The amplification of the transverse oscillations

is caused by a periodic variation of a parameter (the

frequency in this case). Another familiar example is a

child's swing: A child moves his body up and down every

time the swing passes through the bottom and this results

in a periodic modulation of the effective length of the

swine, and hence its frequency, at twice the natural value.

Thus the parametric excitation may be defined as an ampli-

fication of an oscillation due to periodic modulation of a

parameter that characterizes the oscillation.

In plasma physics, parametric instability accounts

for many significant plasma phenomena. It is an important

mechanism of nonlinear mode-conversion from electromagnetic

to electrostatic and from high frequency to low frequency

waves. Physically, it may be looked upon as a nonlinear

instability of two waves (an idler and a signal) by a

modulating wave (a pump) due to a mode-coupling interaction.

The simplest example is the three-wave interaction subject

to the frequency and wave number matching conditions viz.,

Cki = C.0 • z, 4- CO

14;

where the subscripts o, i and s, respectively denote the pump, idler and signal. In such three-wave interaction,

parametric instability is characterized by the fact that

the idler and signal are excited as an instability. This

occurs only when the pump intensity exceeds a threshold

value. Above the threshold, the pump wave can be

efficiently converted to the idler and signal waves. If

these waves are plasma waves, the mode-conversion results

in a deposition of the external pump energy into the plasma.

In this way, parametric excitation can act as an efficient

mechanism to heat the plasmas.

In the presence of a high power EM pump wave ( 640 ,

), the electrons of a plasma acquire an oscillatory

drift velocity. A low frequency density perturbation

( ) interacts with the oscillatory drift velocity of

electrons and the magnetic field of the pump to produce

two high frequency sidebands (CU+ (,) ± ). The side- a9=

bands in turn interact with the pump wave to produce a low

frequency ponderomotive force which then amplifies the

original density perturbation. When this positive feedback

process is strong enough to overcome the natural damping

of these modes, the instability results and both the low

frequency mode and the sideband modes grow (of course at

the expense of the pump energy). The decay modes are

eventually absorbed by electrons or ions through Landau

damping and/or cyclotron damping giving rise to enhanced

heating of the plasma.

When the low frequency perturbation (63 1 k) is an

eleotrostatic mode, the high frequency lower sideband

and upper sideband(r~~2 ) is neglected e

being off-resonant, the three-wave decay process is known

as stimulated scatterings. If the low frequency electro-

static mode (Wy k) is an electron plasma wave, the scatter-

ing is known as the stimulated Raman scattering. If the

electrostatic mode ([420!) is an ion acoustic mode, the

decay is known as the stimulated Brillouin scattering.

When the low frequency perturbation satisfies the

conditions Cji both the high frequency

Ne - e' s. 0

sidebands are again important. Further, if is perpen-

dicular to IZo

the instability is called the

(cc11. = w ) 0 is an electromagnetic mode

filamentation instability.

The phenomena of parametric instabilities in unmag-netized plasmas have been studied in recent years by a

number of workers9-14

. iith the observation of self—

generated magnetic field 15-26 in pellet fusion, a new

dimension has been added to these processes. In the presence

of a magnetic field a plesMa supports many new modes and

offers many new channels of decay27. The stimulated

Orillouin'and Raman scatterings in magnetized plasma have

been studied previously by a number of workers28-32

The heating of magnetically confined plasmas by

pump waves of ion cyclotron range of frequencies has been

studied extensively33-41.

A good review is given by

Ferkins42. The power usually employed in ion cyclotron radio frequency (ICRF) is sufficiently high to initiate

parametric processes. We have studied the stimulated

Brillouin scattering of ion cyclotron waves in chapter II

where the nonlinearity%arises predominantly through the

ions.

Grebogi and Liu43

have recently studied the enhanced •

Raman and Brillouin scatterings in the presence of self—

generated magnetic field in laser produced plasmas. For stimulated Brillouin and Raman scatterings the low

frequency mode must possess long perpendicular wavelengths.

In the limit of short perpendicular wavelengths of the low frequency electrostatic mode (i.e., electron Bernstein

mode and fast ion mode), no work is reported so far. We

have, therefore, studied the scattering of an upper hybrid

laser radiation by electron Bernstein modes in a magnetized

plasm. in chapter II.

It is well known that a semiconductor subjected to

a high d.c. electric field is unstable for an acoustic

perturbation, when the pump induced drift velocity of

electrons exceeds the velocity.of sound in the semiconduc.,

tor44-47

Sharma and Tripathit7 have investigated SBS of

a laser radiation in CdS. Sodha and Sharma48 have also

studied SBS of helicon wave in piezoelectric n-InSb. We

have studied the effect of an external static magnetic

field on the SBS of a high power laser radiation'An n-InSb

in chapter III. The stimulated Raman scattering of laser

radiation in n-InSb and CdS in the presence of a d.c.

electric field has also been investigated in the same

chapter.

The phenomena of filamentation instability has been

studied in gaseous plasmas by a number of workers49-53

Sodha f Ghatak and Tripathi54 have made a detailed investi-

gations of this instability in germanium and indium anti-

monide. In chapter IV, we have studied the filamentation of

laser beam in GaAs where, the nonlinearity arises through

ponderomotive force as well as through the field depended

effective mass of electrons. The phenomenon of nonlinear

absorption and over modulation of a high power EH wave in

GaAs has also been studied in the same chapter.

2. Harmonic Generation

In the presence of a high amplitude EV' wave' the

electrons of a plasma experience a strong ponderomotive

force having two components (i) a time independent

component which results in the redistribution of plasma

density, and (ii) a time dependent component at twice the

frequency of the pump. The oscillatory component of the

pondoromotive force produces a second harmonic current

density, which results in the generation of second

harmonic. In the presence of a plane uniform pump wave

propagating in a homogeneous plasma, the second harmonic

is purely electrostatic. However, in the presence of a

gradient either in the intensity distribution of the pump

or in the density of the plasma, the generated second harmonic

is a mixture of electrostatic and electromagnetic modes.

The generated second harmonic might interact with

the fundamental to produce a third harmonic and so on.

There is also a different mechanism for the generation of

third harmonic in a collisional plasma. In the presence

of a high amplitude EM wave of frequency bj y the

electrons of the plasma absorb considerable energy rion the

wave (—eE0.vo) and are heated above thermal equilibrium

temperature. Consequently, both the temperature and the

conductivity 0' , which are functions of electron collision

Frequency, acquire an oscillatory component.at 2c4)0 .

Through the relation Strz.-6-4E , the current density contains

a 3C00 component and thus a third harmonic is generated.

For highly collisional plasmas, the collisional nonlinearity

dominates over the ponderomotive nonlinearity in the

generation of the third harmonic waves.

In recent years, the general problem of harmonic

generation and nonlinear mixing have been investigated in

considerable detail by a number of workers55-72.

In these

studies the nonlinearity arises either from the pondero-

motive force or from modulation of collision frequency of

electrons. All these theories are mostly restricted to

unbound plasmas. But all the laboratory plasmas63,73,74

for harmonic generation experiments are limited to size

and one would expect the boundary effects to play an

important role in the process of wave conversion. Recently,

Sharma and Sharma75

have examined harmonic generation in

unmagnetized plasma filled waveguide. They have shown that

the power conversion efficiency could be resonantly enhanced

by the choice of plasma configuration and plasma parameters.

We have studied the microwave harmonic generation in a

plasma filled rectangular waveguide in the presence of a

homogeneous static magnetic field.

3. Beat Heating

Beat heating of plasmas by two laser beams has

recently been suggested as a very efficient technique for

heating a plasma up to thermonuclear temperature, This

10

method Utilizes the excitation of longitudinal plasma wave

by resonance at difference freqUencies of the two transverse

waves. On account of the interaction of two pump waves,

the ponderomotive force becomes finite at the difference

frequency. If the difference frequency and the difference

of the propagation vectors of the two pump waves satisfy the

dispersion relation of the plasma waves, resonant excitation

of the plasma wave occurs. The excited plasma wave, after

damping, transfers its energy to the plasma particles and

this leads to the enhanced heating of the plasma.

The earlier investigations on beat heating of plasmas

by two pump waves are limited to the situation when the

pump waves are purely EN waves76-78.

However, in many

realistic situations of plasma heating, the pump waves are

not necessarily pure Eli waves but may be mixed modes

having both electromagnetic and electrostatic components.

Moreover, the earlier studies are limited to normal

incidence of the pump waves. In chapter VI, we have studied

the excitation of plasma waves at the difference frequency

when the two p-polarized pump waves are incident at a

finite angle of incidence at the vacuum-plasma interface.

Recently, in laser-plasma interaction experiments

many workers79-81 have observed the third harmonic generation.

Sodha et el.82

gave an explanation for the generation of

third harmonic when the pump wave is normally incident on

a homogeneous plasma. We have investigated, in chapter VII,

11

the plasma wave and third harmonic generation by a o-

polarized wave incident obliquely at the vacuum-plasma

interface.

4. Self-focusing

One of the important nonlinear effects is the self-

focusing of laser beams, which in turn affects many nonlinear

phenomena in a plasma. Following are the two principal

mechanisms of self-focusing:

1) Nonuniform (generally Gaussian) intensity

distribution of the high power EM beam causes the electrons

of the plasma to be heated nonuniformly, resulting in a

pressure gradient, which causes ambioolar diffusion. This

mechanism dominates over all Other mechanisms on a long

time scale (I'd MIMI) ).

2) Ponderomotive force exerted by the EN wave causes

redistribution of carriers. ThiS mechanism is operative

on a short time scale^-4 1.f' land is important for high

temperature collisionless plasma.

The redistribution of carriers modifies the plasma

density profile, which in turn, modifies the dielectric

constant of the medium. The dielectric constant E=1---(tiii,12" P 0

is maximum on the axis and decreases away from it.

Consequontly, the phase velocity 6:7 / 6-112) of the- EN wave

is minimum on the axis and increases away from the axis.

Thus a lens-like duct is created in which a Gaussian laser

beam, with initially plane wavefront•gets focused. This

12

phenomenon of self-focusing is opposed by the diffraction

divergence effects. Therefore, there exists a threshold

for self-focusing. The value of threshold power is

however, quite moderate and is easily achieved in the

present day experiments.

The earlier investigations on ponderomotive non-

linearities are limited when the pulse width is much larger

than the characteristic diffusion time of carriers across

the pulse in a plasma. But in laser-plasma interaction

experiments the pulse width and the diffusion time may be

comparable. Hence, the earlier theories05

are no longer

valid. In the last chapter of the present thesis, ue

have investigated the transient behaviour of ponderomotive

nonlinearity and excitation of an ion acoustic pulse at the

difference frequency of two EM laser pulses.

The thesis is divided into eight chapters. f.

chapterwise brief summary is presented below:-

Chapter-I: Stimulated Brillouin Scattering of Electro- ftasaetpn in o Cyclotrn Waves a Plasma

This chapter presents an investigation of stimulated

Brillouin scattering of EM ion cyclotron waves in a plasma.

The EM ion cyclotron wave decays parametrically into an

ion acoustic wave and a scattered EM ion cyclotron wave.

For typical plasma parameters: no = 10

10 cm

-32 B

s - 1 KGauss, -

Te— 1KeV Ti fY 0.1 Te' the threshold power for this instability

turns out to be-_` 10-3 watts/cm2, Above the threshold, the

13

growth rates for forward and backward scatterings are

103 rad. sec

-1 and 104 rad.sec-1 respectively. The

results of this chapter are an additional vivid support

for the ion cyclotron radiofrequency (ICRF) heating of

magnetically confined plasmas.

Chapter7IJ: Nonlinear Scattering of _Upper Hybrid Laser Radiation by .El.ectron_Bernstein f.:■pdes in a Plasma

In this chapter we have investigated the , nonlinear

scattering of an upper hybrid laser radiation by electron

Bernstein modes in a homogeneous plasma. The kinetic model

'approach has been used to obtain the nonlinear electron

density perturbation of magnetized electron Bernstein modes

and nonlinear current density of unmagnetized scattered

laser radiation. The threshold for the scattering is

found to be considerably low. It is found that the decay

of the upper hybrid laser radiation in a plane perpendicular

to the magnetic field, into electron Bernstein wave and

scattered laser radiation in the ordinary mode is not

possible. Our analysis for CO2

laser produced plasma is

valid marginally, whereas, for Nd:glass laser produced

plasma, the validity of this investigation is very well

described. The growth rate for the scattering by fundamental

electron Bernstein mode in Nd:glass laser (power density ft.!

1012 wicm2) produced plasma having a temperature of about

a few KeV„ turns out to be 6.0x1011 rad.sec-1.

14

Chapter {III ! StiMUlated BrilloUin and Raman katteriag of Laser Radiation in Semiconductors

In patt A Of this chapter, we have studied the

stimulated BrilloUin scattering of a right handed circularly

polarized laser radiation in a piezoelectric semiconductor

When the laser beam propagates in (i) the direction of the

externally applied Maghetic field, and (ii) perpendicular

to the magnetic field, The nonlinearity in the low

fteqUency ion acoustic wave arises dUe to equation of

motion of electrons and in the high frequency sideband

through the equation of continuity; For ToLY 77°K,

0s

1 KG, n° = 1014 cm-3, rs

=30°, the growth rates

above the threshold are rwr 106 rad, sec

-1 and r•./ 10

5 rad.

sec-1

for longitudinal and transverse propagation,

respectively.

In the second part, the stimulated Raman scattering

of laser radiation in n-InSb and CdS has been studied.

The effect of externally applied d.c. electric field on the

growth rates has also been shown,

Chapter-IVs Filamentation of Laser Radiation and Over- - Mietilh-t7r a a H'ilFildwer -IM 'lave in GaAs

In the first part of this chapter, we have investi-

gated filamentation of laser radiation in d.c. based GaAs.

The nonlinearity arises through ponderomotive force on

electrons and field dependent effective mass of electrons.

In the negative differential resistivity (n.d.r.) region,

15

the d.c. field help the laser beam to initiate the

instability which has considerable groWth rate.

In the second part,nonlinear absorption and over—

modulation of a high power EM wave in n—GaAs has been

studied. In the n.d.r. region the attenuation coefficient

is drastically reduced and consequently, an amplitude

modulated EM beam suffers a severe overmodulation.

Chapter—V: Nonlinear MicrowaveHarmonicGeneratipnin_a Plasqpflled qayequide lnthe Presence of_a paqfletip Field.

In this chapter, we have studied the phenomena of

nonlinear harmonic generations in a plasma filled

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

in

3.1 Introduction 54

3.2 Nonlinear DisperSion Relation 56 (Longitudinal Propagation)

3:43 Growth rates 62

3.4 Growth rates (Transverse Propagation) 65

3.5 Discussion 67

PART_

Stimulated Raman Scattering of Laser Radiation in Semiconductors.

3.6 Introduction 69

3.7 Nonlinear dispersion relation and growth rates 70

3.8 Discussion 75

CHAPTER,JK

PA 31 A

Filamentation of Laser Radiation in DC Biased GaAs

4.1 Introduction 77

4.2 Nonlinear response of electrons 79

4.3 Growth rate 84

4.4 Discussion

88

PART

Nonlinear Absorption and Overmodulation of a high

power En wave in GaAs.

4.5 Introduction 89

4.6 Nonlinear attenuation of EM radiation 91

4.7 Self distortion of amplitude modulated wave 94

4.8 Discussion

95

CHAPTER U

Nonlinear microwave Harmonic Generation in a Plasma Filled Waveguide in the Presence of a Magnetic Field

5.1 Introduction 97

5.2 Nonlinear second harmonic current density 100

5.3 Power conversion efficiency for second 103

harmonic.

5.4 Nonlinear current density for.third harmonic 110

5.5 Power conversion efficiency for third 113

harmonic

5.6 Discussion 117

CHAPTER VI

Excitation of a Plasma Wave by two p—Polarized Waves at the Difference Frequency in a Plasma

6.1 Introduction 120

6.2 Generation of electron plasma wave at the 122 difference frequency

6.3 Field components of the excited electron plasma wave at the difference frequency 126 in a homogeneous plasma.

6.4 Discussion 135

CHAPTER VII

Plasma WaVe and Third Harmonic Generation by a p—Polarized Laser Beam in a Plasma

7.1 Introduction 139

7.2 Equations for the pump wave 140

7.3 Equations for the generated plasma wave at 2600 142

7.4 Equations for the third harmonic generation 145

7.5 Solutions for the pump equations 146

7.6 Solutions for the generated plasma wave at 2(1/4) 146

7.7 Solutions for the third harmonic generation 151

7.2 Po0er conversion efficiency of the generated 153 third harmonic

7.9 Discussion of numerical results 155

Appendix 157

CHAPTER VIII

Generation of an Ion Acoustic Pulse by two EM Pulses at the Difference Frequency in a Collisionless Plasma

8.1 Introduction 166

8.2 Transient behaviour of ponderomotive 167 nonlinearity

8.3 Transient cross—focusing of the two EM pulses 172

8.4 Generation of the ion acoustic pulse at 176 difference frequency

8.5 Discussion 186

REFERENCES 192