Relativistic oblique magnetohydrodynamic shocks

Abstract

Special relativistic magnetohydrodynamic shock waves in a perfect gas of infinite conductivity and constant adiabatic index are analysed. It is shown that the Rankine-Hugoniot equations for such shocks may be reduced to a seventh degree polynomial for the downstream dynamical volume ω, with the polynomial coefficients depending on the upstream state (ω equals the specific volume times the ratio of the energy density of the fluid (omitting electromagnetic terms) to the fluid rest mass energy density). In the non-relativistic limit, the polynomial equation reduces to a relation between the upstream and downstream Alfvénic Mach numbers, previously obtained by Cabannes. The equation for ω classifies in a natural way both shocks in which the electric field may be eliminated by transforming to the de Hoffman–Teller frame, and shocks for which this is not possible. The equation is used to determine the downstream state of relativistic shocks for a given upstream state as specified by the plasma beta, magnetic field obliquity, and flow speed.