In the limit of a small Debye length (,ID+ 0) the analysis of the plasma boundary layer leads to a two-scale problem of a collision free sheath and of a quasi-neutral presheath. Bohm's criterion expresses a necessary condition for the formation of a stationary sheath in front of a negative absorbing wall. The basic features of the plasma-sheath transition and their relation to the Bohm criterion are discussed and illustrated from a simple cold-ion fluid model. A rigorous kinetic analysis of the vicinity of the sheath edge allows one to generalize Bohm's criterion accounting not only for arbitrary ion and electron distributions, but also for general boundary conditions at the wall. It is shown that the generalized sheath condition is (apart from special exceptions) marginally fulfilled and related to a sheath edge field singularity. Due to this singularity smooth matching of the presheath and sheath solutions requires an additional transition layer. Previous investigations concerning particular problems of the plasma-sheath transition are reviewed in the light of the general relations.

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.

In the limit of a small Debye length (11,0->0), the plasma boundary layer in front of a negative absorbing wall is split up into a collision-free planar space charge sheath and a quasineutral presheath, where the ions are accelerated to ion sound speed (Bohm criterion). Usually the presheath mechanism depends decisively on collisional friction of the ions, on ionization, or on geometric ion current concentration. If the ion dynamics in the presheath is dominated by a magnetic field (nearly) parallel to the wall, an additional effect must be considered to provide an ion transport to the wall. The special cases (a) of an ion transport by field lines intersecting the wall at a finite angle and (b) of an ion transport by collisions result in somewhat contradictory conclusions. To get a coherent picture, a hydrodynamic model of the presheath is investigated accounting for an oblique magnetic field and for collisions. The limiting cases (a) and (b) are discussed, and it is shown that (in plane geometry) the presheath ion acceleration depends always on elementary processes. The main effect of a strong magnetic field is to "compress" the collisional presheath into a thin layer with a characteristic extension of the ion gyroradius Pi'

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The boundary layer of a weakly ionized rare gas discharge is treated using kinetic theory. A self-consistent two-scale analysis is performed and the exact presheath and sheath solutions are constructed for the following model: A plasma consisting of Boltzmann distributed electrons and singly charged atomic ions is in contact with a negative absorbing wall. The ion kinetics is dominated by charge exchange with cold neutrals (T0≪T−). The mean-free-path λ is constant and large compared with the electron Debye length λD. This model represents a collision-dominated counterpart to the well known Tonks–Langmuir model of the collision-free plasma.