The Bohm criterion and the field singularity at the sheath edge

Abstract

In the asymptotic limit of a small Debye length (λ D →0) the analysis of the plasma boundary layer leads to a two-scale problem of the space-charge sheath and the quasineutral presheath. Usually the presheath solution ends at the sheath edge with a field singularity indicating the scale transition in the potential variation. Recently, two special presheath solutions were published in which this typical field singularity is missing [Phys. Fluids 23, 803 (1980); Phys. Fluids 31, 1748 (1988 ) ]. In this Brief Communication a kinetic investigation of the plasma sheath transition under quite general conditions is presented. It is shown that the (generalized) Bohm criterion is fulfilled with the equality sign. A sheath edge without field singularity is possible only for a few special cases. © 1989 American Institute of Physics.