Cylindrical and Spherical Nucleus-Acoustic Solitary and Shock Waves in Degenerate Electron-Nucleus Plasmas

A A Mamun

doi:10.3390/physics3040068

Abstract

The basic characteristics of cylindrical as well as spherical solitary and shock waves in degenerate electron-nucleus plasmas are theoretically investigated. The electron species is assumed to be cold, ultra-relativistically degenerate, negatively charged gas, whereas the nucleus species is considered a cold, non-degenerate, positively charged, viscous fluid. The reductive perturbation technique is utilized in order to reduce the basic equations (governing the degenerate electron-nucleus plasmas under consideration) to the modified Korteweg-de Vries and Burgers equations. The latter are numerically solved and analyzed to detect the basic characteristics of solitary and shock waves in such electron-nucleus plasmas. The nonlinear nucleus-acoustic waves are found to be propagated in the form of solitary as well as shock waves in such degenerate electron-nucleus plasmas. Their basic properties as well as their time evolution are significantly modified by the effects of cylindrical as well as spherical geometries. The results of this study is expected to be applicable not only to astrophysical compact objects, but also to ultra-cold dense plasmas produced in laboratory.

Highlights

Mamun, Amina and Schlickeiser [1,2] have first used the name “nucleusacoustic (NA) waves” for the study of NA shock waves in strongly coupled degenerate plasmas [1] as well as NA solitary waves in self-gravitating degenerate plasmas [2]
The degenerate plasmas [3,4,5] containing negatively charged degenerate electron gas and positively charged nucleus or ion fluid have important applications in astrophysical compact objects [3,4,5,6,7], and in ultra-cold dense plasmas produced in laboratory devices [8,9,10,11,12]
The modified Korteweg-de Vries (MK-dV) equation for the nonlinear propagation of the NA waves (NAWs) in the cold degenerate electron-nucleus plasmas (CDENPs) is derived by the reductive perturbation technique (RPT) which requires first the stretching of the independent variables, r and t as [28]

Summary

Introduction

Mamun, Amina and Schlickeiser [1,2] have first used the name “nucleusacoustic (NA) waves” for the study of NA shock waves in strongly coupled degenerate plasmas [1] as well as NA solitary waves in self-gravitating degenerate plasmas [2]. On the basis of Mamun, Amina and Schlickeiser [1,2], a number of theoretical investigations [14,15,16,17,18,19,20,21,22] on nonlinear NAWs in degenerate quantum plasmas under different situations have been made during the last five years In these studies the length scale, phase speed and dispersion properties of the NAWs are not defined. This is not correct, since at absolute zero temperature the degenerate electron gas does not allow the IAWs to exist, but does allow the NAWs to exist This fact along with the concept of the IAWs [23,24] have lead Mamun [25] to introduce proper length scale as well as time scale of the NAWs for the study of the linear propagation of the latter.

Basic Equations

MK-dV Equation

MBurgers Equation

Discussion