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Abstract
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We present a generalized nonlinear theory for large-amplitude electrostatic (ES) ion shocks in collisional
quantum plasmas composed of mildly coupled degenerate electron fluid of arbitrary degeneracy and
nondegenerate strongly correlated ion fluid with arbitrary atomic number. For our purposes, we use the inertialess
electron momentum equation including the electrostatic force, pressure gradient, and relevant quantum forces, as
well as a generalized viscoelastic ion momentum (GVIM) equation for strongly correlated nondegenerate ions.
The ion continuity equation, in the quasineutral approximation, then closes our nonlinear system of equations.
When the electric field force is eliminated from the GVIM equation by using the inertialess electron momentum
equation, we then obtain a GVIM and ion continuity equations, which exhibit 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 arbitrarily-large-amplitude planar and nonplanar ES shocks arising from a balance between
harmonic generation nonlinearities and the ion fluid viscosity for a wide range of plasma mass densities and
ion atomic numbers that are relevant for the cores of giant planets (viz., 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, ion density perturbations propagate with
Mach numbers which significantly depend on the studied plasma fractional parameters. It is concluded that the
dynamics of the ES shocks in the superdense degenerate plasma is quite different in the core of a white dwarf
star from that in the lower density crust region.
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