Time reversal duality of magnetohydrodynamic shocks

The shock conditions in magnetohydrodynamics (MHD) are reduced to their most concise, three-parameter, distilled form by consistent use of the scale independence of the MHD equations and of the de Hoffmann–Teller transformation. They then exhibit a distinct time reversal duality between entropy-allowed shocks and entropy-forbidden jumps. This yields a new classification of MHD shocks by means of the monotonicity properties with respect to upstream and downstream Alfvén Mach numbers, it exhibits the central role of intermediate discontinuities, and permits straightforward construction of all relevant dimensionless quantities of the shocks. An exhaustive overview is presented of solutions in the different parameter regimes.