Discontinuous transitions in a current-carrying plasma

The properties of 'discontinuous' transitions in a current-carrying plasma are investigated by adopting an approach based on the two-fluid equations for a plasma. Braginskii's (1965) transport equations for a two-fluid plasma carrying a current are presented, and allowance is made for collisions with a background neutral gas as well as for effects of reflected particles. The speed of sound in a current-carrying plasma is derived so that the Mach number can be defined correctly as the ratio of the flow speed to the wave phase velocity in such a plasma. The various types of discontinuities permitted by the relevant jump relations in the absence of reflected particles are classified, the effect of reflected particles on such discontinuities is examined, and it is shown that the degree of indeterminacy of a discontinuity can be changed by the presence of reflected particles. Consideration of shocks containing a population of reflected particles and adiabatic transitions indicates that the pressure of reflected particles alone can give rise to both weak and strong transitions. The construction of discontinuous periodic flow solutions is also discussed.