Numerical approximation of the equations describing a partially ionized plasma

Abstract

A two-dimensional, time-dependent finite-difference model of a partially ionized, highly magnetized MHD plasma is discussed. The electron energy equation and the Saha equation are solved, together with the Ohm's law and field equations. Boundary conditions are described for the plasma in a segmented electrode duct, and for the plasma in a continuous insulator wall duct. It is shown that the time-differencing possesses a slow instability to space-centered terms describing convection and compressional processes, but that as a result of the energy conduction damping, the instability can only develop when the plasma is extremely close to a physical stability threshold. The results of the model are compared in the linear phase with approximate analytic formulas for the growth rates of ionization instabilities in a continuous insulator wall duct. Finally, some results are given for the relaxation of plasma nonuniformities in a segmented electrode duct for small values of the electron Hall parameter.