Eur. Phys. J. Plus (2017) 132: 109
https://doi.org/10.1140/epjp/i2017-11367-2

Regular Article

Ion acoustic shock waves in a degenerate relativistic plasma with nuclei of heavy elements

¹ Department of Physics, Faculty of Science, Alexandria University, P.O. 21511, Alexandria, Egypt
² Department of Physics, Faculty of Science, Damietta University, P.O. 34517, New Damietta, Egypt

^* e-mail: eebehery@gmail.com

Received: 25 October 2016
Accepted: 27 January 2017
Published online: 2 March 2017

Abstract

Based on the quantum hydrodynamics theory, a rigorous model for ion acoustic shock waves (IASWs) in a degenerate relativistic plasma with heavy ion nuclei is presented. Two cases are considered: the ultra-relativistic case and the non-relativistic case. A Korteweg-de Vries-Burger's (KdVB) equation describing IASWs in such plasma is derived, then its explicit as well as oscillatory solutions are deduced. It is found that the shape of IASWs is influenced by the particle density of degenerate electrons, the concentration of heavy elements, the viscosity coefficient, and the quantum Bohm potential term. The results should be useful in understanding the shock wave characteristics in degenerate plasma which is found in compact astrophysical objects.