Solution for jump conditions at fast shocks in an anisotropic magnetized plasma

We study the magnetic field and plasma parameters downstream of a fast shoc k as functions of normalized upstream parameters and the rate of pressure a nisotropy (defined as the ratio of perpendicular to parallel pressure). We analyse two cases: with the shock (i) perpendicular and (ii) inclined with respect to the magnetic field. The relations on the fast, shock in a magnet ized anisotropic plasma are solved taking into account the criteria for the mirror instability and firehose instability bounding the pressure anisotro py downstream of the shock. Our analysis shows that the parallel pressure a nd the parallel temperature as well as the tangential component of the velo city are the parameters that are most sensitive to the rate of pressure ani sotropy. The variations of the other parameters, namely density, normal vel ocity, tangential component of the magnetic field, perpendicular pressure, and perpendicular temperature are much less pronounced, in particular when the perpendicular pressure exceeds the parallel pressure. The variations of all parameters increase substantially for a very low rate of anisotropy, w hich is bounded by the firehose instability in the case of inclined shocks. Using the criterion for mirror instability as a closure relation for the j ump conditions at the fast shock, we obtain the plasma parameters and the m agnetic field downstream of the shock as functions of the Alfven Mach numbe r. For each Alfven Mach number, the criterion for mirror instability determ ines the minimum jumps in such parameters as density, tangential magnetic f ield component, parallel pressure, and temperature. and determines the maxi mum values of the velocity components and the perpendicular temperature. Id eal anisotropic magnetohydrodynamics (MHD) has wide applications for space plasma physics. Observations of the field and plasma behaviour in the solar wind as well as in the Earth's magnetosheath have highlighted the need for an MHD model where the plasma pressure is treated as a tensor.