Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions

Abstract

The propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains has been investigated. The Boltzmann distribution is suggested for electrons whereas vortex-like distribution for ions. In the linear analysis, the dispersion relation is obtained, and the dependence of damping rate of the waves on the carrier wave number k, the dust kinematic viscosity coefficient g d and the ratio of the ions to the electrons temperatures r i is discussed. In the nonlinear analysis, the modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation is derived via the reductive perturbation method. Bifurcation analysis is discussed for non-dissipative system in the absence of Burgers term. In the case of dissipative system, the tangent hyperbolic method is used to solve mKdV-Burgers equation, and yield the shock wave solution. The obtained results may be helpful in better understanding of waves propagation in the astrophysical plasmas as well as in inertial confinement fusion laboratory plasmas.

Low-frequency shock waves in a magnetized superthermal dusty plasma

“…A large number of investigations have been reported for the study of shock structures in plasmas both theoretically [15,[17][18][19][20][21][22] and experimentally [23][24][25][26]. Dust acoustic shock waves for two temperature ions in unmagnetized dusty plasma were investigated by Zhang and Wang [17].…”

“…It was also noticed that the effect of dust fluid temperature modifies the basic properties of shock structures. El-Hanbaly et al [21] derived the modified KdVBurgers equation in a dusty plasma consisting of Boltzmann-distributed electrons and trapped ions obeying vortex-like distribution and studied the shock solution in a dissipative space plasma. Recently, Tansim et al [22] have studied dust acoustic shock waves in a four-component unmagnetized dusty plasma consisting of cold dust fluid, Boltzmann-distributed electrons and two temperature ions obeying q-nonextensive and Cairns distribution respectively.…”

A study on dust acoustic traveling wave solutions and quasiperiodic route to chaos in nonthermal magnetoplasmas

“…Sabetkar and Dorranian [19] investigated the effect of obliqueness and external magnetic field on the characteristics of dust acoustic solitary waves in dusty plasma with two temperature nonthermal ions. El-Hanbaly et al [20] studied the propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains. Tomar et al [21] also investigated the evolution of solitons and their reflection and transmission in a plasma having negatively charged dust grains.…”

Korteweg–deVries–Burgers (KdVB) equation in a five component cometary plasma with kappa described electrons and ions

“…If the dissipative effect is negligible the KdVB equation transforms into the KdV equation which permits a soliton solution. The KdVB equation has thus been extensively used to study the properties of solitons and shock waves in dusty plasmas [8][9][10][11][12].…”