The mathematical justification of the Bohm criterion in plasma physics

Abstract

In plasma physics, the Bohm criterion is known as a necessary condition for the formation of the boundary layer called sheath. Our aim is to validate the Bohm criterion from the mathematical point of view. First, we define the sheath as a stationary solution to the Euler–Poisson equations over a half space since the Bohm criterion is proved to be sufficient for the existence of the stationary solution. Then we study the asymptotic stability of the stationary solution under the degenerate or nondegenerate Bohm criterion.