Theory for large amplitude electrostatic ion shocks in quantum plasmas

Abstract

We present a generalized nonlinear theory for large amplitude electrostatic (ES) ion shocks in collisional quantum plasmas composed of mildly coupled degenerate electron fluids of arbitrary degeneracy and non-degenerate strongly correlated ion fluids with arbitrary atomic number. For our purposes, we use the inertialess electron momentum equation including the electrostatic, pressure gradient and relevant quantum forces, as well as a generalized viscoelastic momentum (GVEM) equation for strongly correlated non-degenerate ions. The ion continuity equation, in the quasi-neutral approximation, then closes our nonlinear system of equations. When the electric field is eliminated from the GVEM equation by using the inertialess electron momentum equation, we then obtain a generalized GVEM and the ion continuity equations exhibiting nonlinear couplings between the ion number density and the ion fluid velocity. The pair of nonlinear equations is numerically solved to study the dynamics of arbitrary large amplitudes planar and non-planar ES shocks arising from the balance between harmonic generation nonlinearities and the ion fluid viscosity for a wide range of the plasma mass-density and the ion atomic-number that are relevant for the cores of giant planets (viz. the Jupiter) and compact stars (viz. white dwarfs). Our numerical results reveal that the ES shock density profiles strongly depend on the plasma number density and composition (the atomic-number) parameters. Furthermore, density perturbations propagate with Mach numbers which significantly dependent on the studied plasma fractional parameters. It is concluded that the dynamics of the ES shocks in the super-dense degenerate plasma is quite different in the core of a white dwarf star from that in the lower density crust region.