Relaxation of Electrons in the Boundary Layer of a Weakly Ionized Plasma
We study the kinetics of fast electrons in a weakly ionized collision dominated plasma in front of a planar negative wall. For small Debye lengths the potential variation in the boundary layer can be approximated by a potential jump representing the space charge sheath. We propose an approximation method to calculate the electron distribution function which accounts for general boundary conditions (absorption, reflection and emission). This method is based on a parametrization of the angular dependency, the unknown parameters being determined by a suitable adaption of the Method of Weighted Residuals. The error inherent in our approximation procedure is discussed and shown to be small. As result we get a straightforward analytic representation of the electron distribution function in the boundary layer. For the special case of a totally absorbing wall our results are in good agreement with exact analytical solutions in the literature.