Specificities of One-Dimensional Dissipative Magnetohydrodynamics

One-dimensional dynamics of a plane slab of cold (beta << 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit beta -> 0 is analyzed in detail. It is shown that, at beta=0 the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at beta > 0 and the conditions for the electric field at beta = 0 is found. The stability of the solution against one-dimensional longitudinal perturbations is analyzed. It is shown that, in the limit beta -> 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.