Electrostatic Ion-Acoustic Shock Waves in a Magnetized Degenerate Quantum Plasma

Sharmin Jahan,Abdul Mannan,Nure Alam Chowdhury,Tanu Shree Roy,A A Mamun,Booshrat E Sharmin

doi:10.3390/plasma4030031

Sharmin Jahan, Abdul Mannan + Show 4 more

Open Access

https://doi.org/10.3390/plasma4030031

Copy DOI

Abstract

A theoretical investigation has been carried out to examine the ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system containing inertialess ultra-relativistically degenerate electrons, and inertial non-relativistic positively charged heavy and light ions. The Burgers equation is derived by employing the reductive perturbation method. It can be seen that under the consideration of non-relativistic positively charged heavy and light ions, the plasma model only supports the positive electrostatic shock structure. It is also observed that the charge state and number density of the non-relativistic heavy and light ions enhance the amplitude of IASHWs, and the steepness of the shock profile is decreased with ion kinematic viscosity. The findings of our present investigation will be helpful in understanding the nonlinear propagation of IASHWs in white dwarfs and neutron stars.

Highlights

Academic Editor: Andrey StarikovskiyReceived: 17 July 2021Accepted: 23 August 2021Published: 26 August 2021Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.Licensee MDPI, Basel, Switzerland.The research regarding the propagation of nonlinear electrostatic excitations in a degenerate quantum plasma system (DQPS) has received a substantial attention from plasma physicists due to its ubiquitous existence in white dwarfs [1,2,3] and neutron stars [1,2,3]
The ion-acoustic shock waves (IASHWs) are governed by the Burgers equation (28), and the positive shock potential can exist corresponding to the limit of A > 0 (A < 0)
It is really interesting that the steepness of the shock profile decreases with an increase in the value of the non-relativistic heavy and light ion’s kinematic viscosity, but the amplitude of shock profile is not affected by the kinematic viscosity of ions, and this result agrees with the previous work of Abdelwahed et al [17]

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. A number of authors investigated nonlinear waves in DQPS with positively charged heavy and light ions and electrons [11,12,13,14]. Investigated three-dimensional cylindrical waves in a self-gravitating DQPS and found that the considered plasma system supports both positive and negative electrostatic potentials and the amplitude, width, and speed are significantly modified by the effects of degenerate plasma species. Islam et al [14] investigated envelope solitions in a three-component DQPS containing relativistically degenerate electrons, positively charged heavy and light ions. To the best knowledge of the authors, no attempt has been made to study IASHWs in a magnetized DQPS with positively charged non-relativistic heavy and light ions, and ultra-relativistically degenerate electrons.

Model Equations

Derivation of the Burgers Equation

Results and Discussion

Conclusions