PHYSICAL AND NUMERICAL VERIFICATION OF DISCHARGE CALCULATIONS

Calculations of radio frequency discharge parameters, and to a lesser extent d.c. discharge parameters, are apparently highly sensitive to the physical model used. It is essential to use an accurate, kinetic description of the plasma to obtain quantitatively correct results. Numerical schemes also introduce possible errors, which must be tested for both versus alternative formulations and versus simple physical models. This testing process is carefully considered in this paper. Within kinetic models a number of options exist, having different capabilities, the implications of which are examined here. Particle simulations are discussed and ''mesh-based'' kinetic calculations are considered in detail. A mesh-based kinetic model is presented which closely replicates the physical processes taking place and is consequently very efficient and accurate. Its accuracy is nevertheless limited by the resolution of the mesh. Ways to improve accuracy, and their effects, are presented. Cross-checking of various different numerical formulations of the calculations performed here shows that the results of each are essentially the same. Physical reasoning and simple estimates of discharge parameters are used to further substantiate the predictions for a particular discharge, and the processes taking place in an rf discharge in helium are described in detail. It is argued that this sort of procedure should be part of any numerical model, but especially in complex systems such as plasmas.