Interaction of Dust-Acoustic Shock Waves in a Magnetized Dusty Plasma under the Influence of Polarization Force

N S Saini,Papihra Sethi,Kuldeep Singh

doi:10.1155/2021/6679085

Abstract

The interaction of dust-acoustic (DA) shock waves in a magnetized dusty plasma under the influence of nonextensively modified polarization force is investigated. The plasma model consists of negatively charged dust, Maxwellian electrons, nonextensive ions, and polarization force. In this investigation, we have derived the expression of polarization force in the presence of nonextensive ions and illustrated the head-on collision between two DA shock waves. The extended Poincaré–Lighthill–Kuo (PLK) method is employed to obtain the two-sided Korteweg–de Vries–Burgers (KdVB) equations and phase shifts of two shock waves. The trajectories and phase shifts of negative potential dust-acoustic shock waves after collision are examined. The combined effects of various physical parameters such as polarization force, nonextensivity of ions, viscosity of dust, and magnetic field strength on the phase shifts of DA shock waves have been studied. The present investigation might be useful to study the process of collision of nonlinear structures in space dusty plasma such as planetary rings where non-Maxwellian particles such as nonextensive ions, negatively charged dust, and electrons are present.

Highlights

Dusty plasma has fascinated the attention of many researchers for the study of different kinds of linear as well as nonlinear structures over the past many years. e presence of dust in an electron-ion plasma modifies the behaviour of nonlinear structures and generates new modes such as dust ion-acoustic waves [1] and dustacoustic waves [2], which have been frequently studied theoretically and experimentally [3,4,5,6]
Dust particulates in a dusty plasma are affected by various forces due to the large amount of dust charge on them, among which electrostatic force Fe qdE has a significant influence on dust
Spatial nonuniform dust density means that the dust charge is nonuniformly distributed in plasmas. e polarization force acts in the direction in which Debye length decreases and acts in the direction opposite to the electrical force independent of the sign of dust charge [17]. us, the polarization force has a significant influence on the propagation characteristics of low-frequency linear DA waves

Summary

Introduction

Dusty plasma has fascinated the attention of many researchers for the study of different kinds of linear as well as nonlinear structures over the past many years. e presence of dust in an electron-ion plasma modifies the behaviour of nonlinear structures and generates new modes such as dust ion-acoustic waves [1] and dustacoustic waves [2], which have been frequently studied theoretically and experimentally [3,4,5,6]. E investigations of the head-on collision of nonlinear shock waves under the influence of polarization force have been reported by numerous researchers in the framework of Maxwellian and non-Maxwellian distributions in different plasma systems [26, 27, 31]. Ey considered negatively charged dust grains and Maxwellian electrons and ions and studied modulational instability and effect of polarization force on the phase shifts of dust-acoustic solitary waves. Singh et al [31] investigated the head-on collision in a dusty plasma among DA multisolitons with ions following the hybrid distribution under the effect of the polarization force. Numerical analysis and discussion are presented in Section 4. e last Section 5 is devoted to the conclusions

The Fluid Equations

Derivation of KdVB Equations and Phase Shifts

Numerical Analysis and Discussion

Conclusions