Shock wave solution in a hot adiabatic dusty plasma having negative and positive non-thermal ions with trapped electrons

Abstract

In this report an investigation of the properties of a dust acoustic (DA) shock wave propagating in an adiabatic dusty plasma, including the effect of the negative-ion-rich non-thermal ions and trapped electrons, is presented. The reductive perturbation method is employed to derive the modified Burgers equation and a new form of the lower-order nonlinear modified Burgers equation for DA shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are electrons, singly-charged positive ions, singly-charged negative ions and massive, charged dust particles. The stationary analytical solution of the Burgers equation and the new analytical solution of the lower-order nonlinear modified Burgers equation are numerically analyzed, and the effects of various dusty plasma constituents on the DA shock wave’s propagation are taken into account. Both positive and negative ions in the dusty plasma are observed to play a key role in the formation of both positive, as well as negative, DA shock waves, and the ion concentration can be used to control the transformation from negative to positive potentials of the waves.