Numerical solution of momentum balance equations for plasmas with two ion species

In plasmas bounded by material surfaces the Bohm criterion has to be satisfied at the entrance of the Debye sheath near the surface. With a single ion species this constraint prescribes a boundary condition for the momentum balance equation governing the ion mass velocity. If, however, several ion species are present a generalization of the Bohm criterion does not provide enough number of boundary conditions. Additional “intermediate” conditions follow from the requirement that spatial derivatives of the ion velocities are finite everywhere within the plasma volume. The amount of such independent conditions is sufficient to determine, in an iterative way, also the position in the plasma where they have to be imposed. A numerical approach to find unique regular solutions of fluid motion equations, satisfying the generalized Bohm criterion at the plasma boundary, is elaborated and realized for the case of two ion species.