Post on 26-Dec-2021
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