Overtaking Interactions of Multi-Ion Acoustic Shock Waves in a Magnetized Degenerate Plasma: An Application in White Dwarfs

Abstract

Overtaking interactions are examined of multi-ion acoustic shock waves in magnetized degenerate quantum plasmas comprising inertial non-relativistic heavy and light ions having positive charges ultra-relativistic degenerate inertialess electrons. A Burgers’ equation governs the nonlinear excitation of multi-ion acoustic shock waves in a plasma model at hand. The Cole-Hopf transformation and the exponential function have been used to study the overtaking interactions of multi-ion acoustic shock waves in two modes (i.e., the fast and the slow modes). Numerically, the compressive ion-acoustic shock waves exist for the fast mode, but the rarefactive ion-acoustic shock waves exist for the slow mode. A numerical simulation demonstrates that the overtaking interactions of multi-ion acoustic shock waves and their electric fields are remarkably modified with the effectiveness of the charge states of heavy ions and light ions. Furthermore, the amplitude and the steepness of multi-ion acoustic shock waves increase with the decrease in the directional cosines of the multi-ion acoustic shock waves vector along the z-axis. Numerical simulations of overtaking interaction are employed to significantly highlight the physical features of multi-ion acoustic shock waves in astrophysical situations such as white dwarfs and neutron stars.