Study of linear and nonlinear ion acoustic waves in contaminated dusty plasma.

Abstract

This theses focus mainly on the theoretical investigation of a new low frequency electrostatic wave in an unmagnetized collisionless dusty plasma, new acoustic waves originating from a balance of dust particle inertia and plasma pressure. It is shown that these waves can propagate linearly as a normal mode in dusty plasma, also discussed linearly the electromagnetic waves that may exist in a nonuniform dusty megnetoplasma by considering the mixed mode. The different limiting cases are examined for the couple drift-Alfven-Shukla-Varma modes in a non-uniform dusty magnetoplasma. The primary objective of this study was the use of Reductive Perturbation Method (RPM) to examine and discuss the stability of the ion acoustic waves (IAWs) in unmagnetized electron-ion plasmas. The ion acoustic wave (IAWs) propagates with the phase velocity and depends upon ion mass and electron temperature. The nonlinear Schrödinger equation for low amplitude ion acoustic wave (IAWs) packet in plasmas with q-nonextensive electron distribution is obtained using the standard reductive perturbation technique and the stability of the ion acoustic wave (IAWs) is also discussed. The problem of modulational instability (MI) of ion-acoustic waves (IAWs) in a two-component plasma with Cairns--Tsallis distributed electrons is investigated, using the standard multiple scale reductive perturbation method, we derive a nonlinear Schrödinger equation NLSE and the MI of the IAWs is discussed. The nonlinear Schrödinger equation is derived and then the stability of model is explained. The stability depends on q-nonextensive parameter, wave number of ion acoustic wave (IAWs) and the velocity of cold beam. For graphical representation of models plots are made with the help of software mathematic. In this model studied frequency and group velocity of ion acoustic waves (IAWs) depends on nonextensive parameter q. There is also examined the obliquely propagating nonexrensive dust ion acoustic solitary waves in a dusty plasma. The reductive perturbation method has been employed to derive K-dV equation which admits a solitary wave solution. In this model the amplitude and width of K-dV solitons depends on q nonextensive parameter, phase shift, and ratio of number densties of dust and ions at equilibrium, and width is also depends on ωci.