Convected Scheme Simulations of the Electron Distribution Function in a Positive Column Plasma

A numerical procedure that provides an accurate and efficient solution of the Boltzmann equation in cylindrical geometry with coordinates (p, v) is discussed. The procedure, based primarily on the convected scheme, propagates the particle phase-space density on a computational mesh. A combination of the choice of independent variables, the design of the mesh structure and the use of a moving mesh can provide an exact solution of Vlasov's equation. A variant of the method is also presented which first iterates the scattering rate throughout phase space then finds the distribution function from the scattering rate. We describe the methods and apply them to a kinetic model of a dc positive column. Results are compared to Monte Carlo simulations.