Large-amplitude compression waves in an adiabatic two-fluid model of a collision-free plasma

The development of large amplitude compression waves in a collision-free plasma is studied by considering the motion of a plane piston into a uniform stationary plasma containing a magnetic field parallel to the plane of the piston. The adiabatic two-fluid equations are solved by finite-difference methods and the form of the waves after a long time is compared with the possible steady-state solutions.

A generalized discontinuous solution of the steady-state equations is found for sufficiently high Mach numbers. At the highest Mach numbers this leads to a constant state at the piston; while at lower speeds a wave train results whose amplitude increases as the speed decreases. In each of these cases the numerical solutions of the time-dependent equations converge rapidly to the steady-state solutions. At still lower speeds, where the solitary-wave solution exists, the situation is less clear.