On simplifying approaches to the solution of the Boltzmann equation in spatially inhomogeneous plasmas

With the continuing progress of plasma modelling in recent years the desire arose to develop simplified approaches to the kinetic description of the electron component in weakly ionized plasmas. Methods which are based on the direct solution of the Boltzmann equation in some limiting situations, namely the `nonlocal' approximation in a weakly collisional plasma and the `local' approximation in a highly collisional plasma, may be much more efficient than conventional simulation techniques. In this paper the foundation of these approaches is reviewed. Their quantitative accuracy and their applicable range is examined on the basis of a comparison to the numerical solution of the complete, space-dependent Boltzmann equation for a positive column plasma.