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

Shack waves in plasmas with strongly anisotropic viscosity and thermal cond uctivity are considered. The analysis is restricted to the case where the p lasma beta is less than unity. The set of two equations that governs propag ation of small-amplitude MHD waves at small angles with respect to the unpe rturbed magnetic field in such plasmas is derived. A qualitative analysis o f this set of equations is carried out. It is shown that the shock structur e 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 th e magnetic field component, perpendicular to the direction of shock-wave pr opagation 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 w aves are calculated numerically for different values of the shock amplitude and the ratio of the coefficients of viscosity and thermal conductivity.