Vlasov Equation Study of Plasma Motion across Magnetic Fields

A description is given, in terms of distribution functions, of the phenomenon of a plasma crossing magnetic field lines by virtue of beam polarization. The task requires solving two steady-state, nonlinear Vlasov equations for ions and electrons, coupled with Maxwell's equations. Studying the plasma in a neighborhood of the moving beam surface, a distinction is made between two asymptotic regions of plasma in equilibrium, and an intermediate, transition region. In the so-called charge-neutral approximation, actual transition profiles are computed in closed form, in terms of quadratures. Some general conclusions are drawn concerning the minimum width of the transition region and the maximum change in the macroscopic velocity that the plasma can support over such minimum distance.