Self-consistent kinetic theory of a plasma sheath

A fully kinetic theory model of the sheath of a dc glow discharge is presented. This model includes a direct numerical solution of Boltzmann equations for the spatial and velocity dependence of the electron and Ar+ distribution functions with a self-consistent electric field calculated from the Poisson equation. The solution is obtained using a collocation method that employs Legendre quadrature points for both angular and spatial variables, and nonclassical speed quadrature points for velocity. The results of the steady state direct numerical solution are compared with a particle-in-cell Monte Carlo simulation. As anticipated, it is found that the space- and energy-dependent ion distribution function varies strongly with a decrease in the ratio of the Debye length to the ion mean free path.