A self-consistent kinetic plasma model with rapid convergence

W.N.G. Hitchon, T.J. Sommerer, J.E. Lawler
1991 IEEE Transactions on Plasma Science  
Algorithms for very efficient solution of kinetic equations have previously been developed and used to obtain a self-consistent kinetic description of electrons and ions in various plasmas, including RF glow discharges [1]-[4] . Since RF discharge calculations may take many thousands of cycles to converge, a solution which follows the time evolution throughout this process is inevitably computationally costly. We have implemented a "scaleup" procedure which obviates the need to follow the
more » ... time evolution in this or other plasma models. By running the full calculation for a short time, we extract information which permits an extrapolation of the time evolution over a very long time, or a "scaleup." A detailed description of the basis for the scaleup is given, as well as an example of the use of a scaleup procedure, as applied to a moderately high-pressure RF discharge in helium. I . INTRODUCTION ISCHARGE plasmas are extremely complex and subtle. D Almost any ad hoc assumption made to simplify a discharge model tends to omit vital physical effects. A modest error in one aspect of a model leads to a chain of others, and the nonlinearity of the system allows the inaccuracies to build to an unpredictable extent. On the other hand, a kinetic description of the plasma, with a "self-consistent" electric field, can be constructed which provides a very accurate and complete discharge model with a minimum of ad hoc assumptions. A numerical calculation has been developed [1]-[4], which is much faster than finite differences and exhibits less numerical diffusion when applied to solve a kinetic equation (or other transport problems having significant convection; we refer to the method as a "convective scheme," or CS). This permitted calculation of electron and ion distribution functions, fe(z, v" vL, t ) and f,(z, w" t ) , respectively, and the self-consistent electric field E, (z,t) in a parallel-plate RF discharge [4]. The independent variables are x, the perpendicular distance from one plate, v, 2, and w1 is the velocity perpendicular to the x direction. E, is found from fe and fi by solving Poisson's equation and is used to determine their time evolution. The first calculations have been done for He, using detailed cross-section data given by Alkhazov [5], LaBahn and Callaway [6], and Helm [7]. A calculation of this scope (with this set of independent variables) is made feasible by the CS. It is possible but still not convenient to run for thousands of cycles, however. The present
doi:10.1109/27.106804 fatcat:kl3hs5c6yvhrpmxelphhyzwfze