Rarefactive electron-scale shock excitations in a degenerate quantum plasma

The nonlinear propagation of the electron-acoustic shock waves (EASWs) in an unmagnetized, collisionless degenerate quantum plasma system has been investigated theoretically. The plasma system is assumed to contain two distinct groups of electrons (one inertial non-relativistic cold electrons and other inertialess ultra-relativistic hot electrons) and positively charged static ions. The Burgers equation has been derived by employing the reductive perturbation method and numerically examined to identify the basic features (speed, amplitude, width, etc.) of EASWs. It is shown that only rarefactive shock waves can propagate in such a quantum plasma system. It is found that the effect of degenerate pressure and number density of hot and cold electron fluids, and positively charged static ions significantly modify the basic features of EASWs. It is also noted that the inertial cold electron fluid is the source of dissipation for EA waves and is responsible for the formation of shock structures. The implications of this investigation in astrophysical compact objects (viz. non-rotating white dwarfs, neutron stars, etc.) are briefly mentioned.