On Plasma Expansion in Vacuum

Abstract

In this paper, we propose a model describing the expansion of a plasma in vacuum. Our starting point consists in a two-fluids Euler system coupled with the Poisson equation. Since numerical simulations of this model are very expensive, we investigate a quasi-neutral limit of it. We show that electron emission occurs at the plasma-vacuum interface. This emission is well modelled by a Child—Langmuir law. The difficulty consists in accounting for the motion of the plasma-vacuum interface. In this paper, we formally and numerically justify why electron emission produces a reaction pressure which slows the plasma expansion down.