Supersonic Shock Wave with Landau Quantization in a Relativistic Degenerate Plasma^*

Abstract

A three-dimensional (3D) Burgers’ equation adopting perturbative methodology is derived to study the evolution of a shock wave with Landau quantized magnetic field in relativistic quantum plasma. The characteristics of a shock wave in such a plasma under the influence of magnetic quantization, relativistic parameter and degenerate electron density are studied with assistance of steady state solution. The magnetic field has a noteworthy control, especially on the shock wave’s amplitude in the lower range of the electron density, whereas the amplitude in the higher range of the electron density reduces remarkably. The rate of increase of shock wave potential is much higher (lower) with a magnetic field in the lower (higher) range of electron density. With the relativistic factor, the shock wave’s amplitude increases significantly and the rate of increase is higher (lower) for lower (higher) electron density. The combined effect of the increase of relativistic factor and the magnetic field on the strength of the shock wave, results in the highest value of the wave potential in the lower range of the degenerate electron density.

MHD waves with Landau diamagnetic pressure and Pauli paramagnetizim in degenerate plasmas

“…This is a unique property arising from the short wavelength quantum electro dynamical (QED) correction. In Landau quantized plasma, shock waves are studied with lower (higher) electron density and magnetic field strength byDeka and dev [19]. On the other hand linear spin magnetoacoustic wave modes are analyzed in the presence of spin-up and spin-down electrons as two different fluids [20] and it is found that in the presence of strong magnetic field, the energy of electrons in the perpendicular direction becomes quantized into Landau levels.…”