The application of the generalized Bohm criterion to Emmert’s solution of the warm ion collisionless plasma equation

Abstract

Emmert et al. [Phys. Fluids 23, 803 (1980)] have modeled the flow of a one-dimensional collisionless plasma to a material wall by formulating and solving the warm-ion plasma equation. In contrast to the result of the cold-ion plasma equation it was found that the electric field at the plasma–sheath boundary was finite. It is first shown that Emmert’s solution satisfies the generalized Bohm criterion, and is thus a valid solution, before discussing the cause of the difference in the results of the two models in calculating the boundary electric field.