Numerical study of ion acoustic shock waves in dense quantum plasma

Abstract

Two fluid quantum hydrodynamic equations are solved numerically to investigate the propagation characteristics of ion acoustic shock waves in an unmagnetized dense quantum plasma, whose constituents are the electrons and ions. For this purpose, we employ the standard finite difference Lax Wendroff and relaxation methods, to examine the quantum effects on the profiles of shock potential, the electron/ion number densities, and velocity even for quantum parameter at H = 2. The effects of the latter vanish in a weakly non-linear limit while obeying the KdV theory. It is shown that the evolution of the wave depends sensitively on the plasma density and the quantum parameter. Numerical results reveal that the kinks or oscillations are pronounced for large values of quantum parameter, especially at H = 2. Our results should be important to understand the shock wave excitations in dense quantum plasmas, white dwarfs, neutron stars, etc.