Characteristic velocity of MHD shock

A physical quantity called the characteristic velocity of MHD shock that is based on the similarity of between the boundary conditions on the MHD discontinuity and the equations of the MHD simple wave is introduced. The quantity is defined as the ratio of the jump of total pressure to that of the density, equal to the geometric mean value of the shock velocities relative to the up and down streams, and approaching the MHD wave velocity in the weak shock limit. A system of equations is given which expresses the shock relations using the defined quantity as the strength parameter. These relations simplify the usual shock calculations and degenerate into the formulas for the MHD simple wave in the infinitesimal jump limit. Equations which distinguish fast, slow, and intermediate shock and jump formulas which explicitly show the transmission relations among the various modes of MHD shock and wave are presented.