The anisotropic jump equations for oblique fast shocks in a kappa distributed medium

In this paper, we concentrate on the solution of the anisotropic Rankine-Hugoniot equations for inclined fast shocks taking into account a new approach in closing the set of equations. In particular, the threshold conditions of the fire-hose and that of the mirror instability, obtained in a kinetic approach using the so-called kappa distribution function, are used to bound the range of the pressure anisotropy downstream of the discontinuity. We study the variation of the density across the shock for a given Alfvén Mach number and upstream pressure anisotropy and find that the parameter kappa is most sensitive to stable plasma conditions, i.e. low values of kappa reduce the pressure anisotropy downstream of the discontinuity.