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 vi 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.