Electrostatic Wave Dynamics in a Dense Relativistically Degenerate Magnetised Plasma

Abstract

The propagation of three-dimensional (3-D)electrostatic solitary and shock waves with weakly relativistic and ultra-relativistic degenerate electrons and positrons is investigated in a dense magnetized plasma. For this purpose, a 3-D Zakharov-Kuznetsov-Burgers (Z-K-B) equation is derived from the pair of ion continuity and momentum equation with bulk viscosity among ion fluids, and degenerate electrons and positrons. The effect of mass of pair of ions, positron concentration, magnetic field strength and the Fermi temperature of weakly relativistic and ultra-relativistic degenerate electrons and positrons are studied in the present work. The Burgers term in our system is responsible for shock structures in pair ion plasmas. Analytical prediction and numerical analysis enable us to know that the wave yields solitary profile in absence of collisions and exhibits both oscillatory and monotonic depending on collisions between pair of ions and balanced status of diisipation and dispersion. Moreover, it is exhibited that the chaotic dynamics occur when the perturbed Z-K-B equation is perturbed by external force, and we use power spectrum, phase projection, and Lyapunov exponents to observe both weak and developed chaos. For illustration purposes, we have considered the astrophysical parameters in a white dwarf.