The effect of magnetic field quantization on the propagation of shock waves in quantum plasmas

Abstract

Nonlinear ion acoustic shock structures are investigated in the presence of trapping effects and Landau quantization in quantum plasmas. Ion electron plasma is under consideration in which ions are classical and quantum mechanical effects of electrons are taken into account. We assume that the orbital motion of electrons is quantized such that the condition kBT≪ℏωce is satisfied. To study the energy transfer mechanism in such conditions, the reductive perturbation technique has been employed to derive the nonlinear differential equation. In the presence of dissipation, which appears through kinematic viscosity of ions, the Korteweg-de Vries Burgers (KdVB) equation is obtained. The different solutions of KdVB are presented, and excitation from KdV oscillations to shock solution is explained in the presence of orbital motion of electrons which are discussed. The devastating effect of Landau quantization on the height (strength) of the nonlinear shock structure is pointed out.