The influence of collisions on the plasma sheath transition

In the asymptotic limit λD/λ→0 (where λD is the electron Debye length and λ represents the ion mean free path) the boundary layer of a collision dominated plasma is split up in a collision free planar sheath (scale λD) and a quasi-neutral presheath (scale λ). The “sheath edge” separating the presheath and the sheath is defined by the Bohm criterion. To clear up controversial statements on the validity of the plasma sheath concept and on the role of the Bohm criterion for finite values of λD/λ, a simple fluid model of the ions is used to account for collisions and for space charges in the boundary layer. It is shown that the asymptotic solution on an “intermediate scale” (scale length λ1/5λD4/5) is suitable to match the presheath and sheath solutions smoothly and to construct a convenient approximation for small but finite λD/λ. The intermediate scale, again, is closely related to the Bohm criterion. Various attempts to derive a “generalized” Bohm criterion accounting for collisions are inconsistent.