Abstract
In this thesis we discuss nonlinear effects in
multicomponent plasmas. By multicomponent we mean electronion,
electronpositronion, and dustelectronion etc. type plasmas.
Different types of solitary waves and soliton, are the main focus in
this work. A soliton is a solitary wave with constant profile that
preserves its shape during collisions. First of all we consider
magnetosonic soliton propagating obliquely at an angle
θ
to an external magnetic
field in ElectronPositronIon plasma, using the effective one fluid
MHD model. Two separates modes (fast and slow) for the waves are
discussed in the linear approximation and the
KadomstevPetviashvilli (KP) equation is derived by using the
reductive perturbation scheme for these modes in the nonlinear
regime. The KP equation is the two dimensional analogy of the KdV
equation and it admits solitary wave solution. We also obtain a
nonlinear dispersion relation that relates the nonlinear wave number
with different parameters. It is observed that for both the modes
the angle θ,
positron concentration, ion temperature, and plasma
βvalue
affect the propagation properties of solitary waves and are from
those of the simple ElectronIon plasmas. Like wise current density,
electric field and magnetic field for these solitons are
investigated, for their dependence on the abovementioned parameters.
Ion Acoustic wave (IAW) is a low frequency electrostatic wave, which
is supported by the ion inertia in plasma physics. The lighter
particles (e.g. electrons or positrons) play the role of restoring
force to this wave. Due to the compressions and rarefaction of ion
number density these low frequency waves propagate in plasma. In the
third chapter we investigate the linear and nonlinear properties of
the IAW, propagating obliquely to an external magnetic field in
weakly relativistic, rotating magneto ElectronPositronIon plasmas.
The ZakharovKuznetsov equation is derived by employing again the
reductive perturbation technique for this wave in the small
amplitude nonlinear regime. This equation admits solitary wave
solution. The amplitude and width of this solitary wave have been
discussed with effects of obliqueness, relativity, ion temperature,
positron concentration, magnetic field and rotation of the plasma
and observed that for IAW these parameters affect the propagation
properties of solitary waves and behave differently from the simple
ElectronIon plasmas. Most often, the velocity distribution function
of particles in space plasmas has a nonMaxwellian superthermal
tail. The distribution function decreases generally as a power law
of the velocity instead of an exponential decrease associated with a
Maxwellian distribution. A useful distribution to model plasma
containing suprathermal and superthermal particles is the
generalized Lorentzian, or kappa, distribution function. The kappa
distribution indeed possesses the desired property that particles
with velocities greater than the thermal velocity obey a power law
distribution. Another Nonmaxwellain distribution named
(r,q)
distribution, which is a
generalized version of the Lorentzian (kappa) distribution, and
gives better fits to real space plasma, has been introduced. In the
third problem (4th
chapter) we discuss
the basic properties of generalized
(r,q)
distribution function and
then using this distribution, we consider particle (electron)
trapping in wave electrostatic potential well. The effect of
particle trapping on the linear and nonlinear evolution of an ion
acoustic wave in electronion plasmas has been discussed. The
spectral indices q
and
r
represent the highenergy tails, flatness or pointedness on top of
the distribution function respectively. The generalized KdV
equations with associated solitary wave solutions for different
ranges of parameter r are derived by employing a perturbation
technique. It is shown that spectral indices r and q affect the
trapping of electrons and subsequently the dynamics of ion acoustic
solitary wave significantly. Dusty plasmas (plasmas containing
charged dust grains of micron to submicron size) occur in a wide
variety of space and laboratory environments. Dustacoustic wave on a
very slow time scale of dust dynamics emerges as a result of the
balance between dust grain inertia and plasma pressure. In the fifth
chapter we examine the characteristics of obliquely propagating Dust
Acoustic Waves (DAW) in positively charged, rotating and magnetized
dusty plasma, apply the results to the day side tropical mesosphere
by incorporating adiabatic dust charge fluctuation. The nonlinear
evolution equation here is the Kortewegde Vries (KdV) equation that
is derived by employing the reductive perturbation technique. This
KdV equation may support nonlinear DAWs on a very slow time scale.
The meteoritic dust in mesospheric plasma on day side is charged
positively due to plasma currents and photo and thermionic
emissions. The sum of Lorentz force frequency and rotational
frequency give the effective gyrofrequency. The dynamics of DAW
with effect of electronic, ionic, thermionic and photoelectric
currents along with obliqueness and effective gyro frequency are
studied. It is observed that obliqueness θ and effective
gyrofrequency modify the width, in inverse proportion. Also the
amplitude of dust acoustic soliton modifies directly and width
modifies inversely with positively dust charge variation for this
model.
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