Kinetic theory of the plasma sheath transition in a weakly ionized plasma

Abstract

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 λ_D. This model represents a collision‐dominated counterpart to the well known Tonks–Langmuir model of the collision‐free plasma.