PROPAGATION OF ION ACOUSTIC SOLITON AROUND THE CRITICAL VALUES OF ANY SPECIFIC PARAMETER IN UNMAGNETIZED COLLISIONLESS RELATIVISTIC PLASMAS

Abstract

The main purpose of the present work is to investigate how electrostatic plasma parameters

modify the nonlinear ion acoustic soliton (IAS) propagation in unmagnetized collisionless

plasma including higher order Lorentz relativistic expansion terms. The study of

IASs in an unmagnetized collisionless relativistic plasma made of relativistic ion fluids,

Cairns-distributed electrons and Cairns-distributed positrons. In one dimensional analysis,

the reductive perturbation technique is employed to reduce the dynamics of the whole

system to the Korteweg-de Vries equation (KdVE) involving various nonlinearity, whose

nonlinear and dispersion coefficients are dependent on the related plasma parameters. This

indicates that KdVEs have been derived incorporating quadratic, cubic, and quartic nonlinearities.

However, as the coefficient of KdVE associated with quadratic nonlinearity

approaches zero, the method encounters limitations. To overcome this challenge, adjustments

are made to the stretching coordinates, resulting in a cubic nonlinearity KdVE that

effectively describes soliton propagation near critical values in these plasma conditions.

Additionally, a KdVE with quartic nonlinearity is derived to model super-critical values of

specific plasma parameters in relativistic plasmas.

Previous studies have primarily focused on relativistic effects on soliton propagation using

Lorentz relativistic factor expansions up to three terms. In contrast, this thesis expands

this consideration to more higher order Lorentz relativistic expansion terms to minimize

truncation errors in modeling nonlinear soliton propagation within these plasmas. The investigation

reveals that the relativistic streaming factor significantly alters the wave potential

functions with the presence of more higher order Lorentz relativistic expansion terms.

Notably, the derived KdVE shows that quadratic nonlinearity supports both compressive

and rarefactive soliton propagation, whereas cubic and quartic nonlinearities exclusively

support compressive solitons. Furthermore, this study explores how plasma parameters, incorporating

more higher order Lorentz relativistic expansion terms, influence the amplitude

and width of IASs in the unmagnetized relativistic plasma. It finds that higher order terms

of the Lorentz relativistic factor noticeably modify the propagation characteristics of IASs

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within this specific plasma environment. The effect of plasma parameters on the amplitude

and width of IASs has also been discussed with the physical interpretations.