Structure of small-amplitude quasiparallel magnetohydrodynamic shock waves in plasmas with anisotropic viscosity and thermal conductivity

Abstract

Shock waves in plasmas with strongly anisotropic viscosity and thermal conductivity are considered. The analysis is restricted to the case where the plasma beta is less than unity. The set of two equations that governs propagation of small-amplitude MHD waves at small angles with respect to the unperturbed magnetic field in such plasmas is derived. A qualitative analysis of this set of equations is carried out. It is shown that the shock structure is described by a solution that is a separatrix connecting two stationary points: a stable node and a saddle. This solution describes the structure of a fast quasiparallel shock wave, and it only exists when the ratio of the magnetic field component, perpendicular to the direction of shock-wave propagation after and before the shock is smaller than a critical value. This critical value is a function of the plasma beta. The structures of shock waves are calculated numerically for different values of the shock amplitude and the ratio of the coefficients of viscosity and thermal conductivity.