Current-Layer Diffusion in a One-Dimensional Pinch

Diffusion of the current layer at the surface of a compressible electrically conducting gas in a one-dimensional pinch is analyzed in the limit of large time. Magnetohydrodynamic equations including finite scalar electrical and thermal conductivities are used, and the degree of ionization is taken to be constant. A parameter, which is proportional to the diffusion speed divided by the sound speed, is used to show that the inertia terms may be discarded in large-time high-electrical-conductivity problems. Some numerical results for the temperature, velocity, and magnetic field within the current layer are presented in terms of a similarity variable. In the cases analyzed the gas boundary is displaced from its infinite conductivity position by an amount which is of the order of magnitude of the current-layer thickness. Comparison of constant conductivity with temperature-dependent conductivity results shows that Joule heating at the gas boundary improves confinement if the initial conductivities are low.