The solution of the Rankine–Hugoniot equations for fast shocks in an anisotropic kappa distributed medium

In this paper, we concentrate on the analysis of the anisotropic Rankine–Hugoniot equations for perpendicular and oblique fast shocks. In particular, as additional information to the anisotropic set of equations, the threshold conditions of the fire-hose and mirror instability are used to bound the range of the pressure anisotropy downstream of the discontinuity. These anisotropic threshold conditions of the plasma instabilities are obtained via a kinetic approach using a generalized Lorentzian distribution function, the so-called kappa distribution function. Depending on up-stream conditions, these instabilities further define stable and unstable regions with regard to the pressure anisotropy downstream of the shock. The calculations are done for different upstream Alfvén Mach numbers. We found that low values of the parameter kappa reduce the pressure anisotropy downstream of the shock.