Rankine–Hugoniot jump conditions incorporating kappa distributions

Abstract:

The effect of kappa distributions on the Rankine–Hugoniot (R-H) jump conditions of space plasma shocks is examined. The challenge is to find the connection between the plasma kappa values upstream and downstream the shock. Several past attempts to connect the upstream/downstream kappa indices were based on ill-defined first physical principles, such as the dependence of the temperature or the thermal pressure on the kappa index. However, the conservation laws of mass, momentum, and energy are independent of the kappa index, thus all different values of kappa are equivalent for describing the known R-H conditions. The upstream/downstream kappa values must be connected through a new physical concept related to the statistical origin of kappa distributions.