Fast algorithms for multiple time scales problems in glow discharge physics

Summary form only given. Glow discharges are characterized by very different time scales. The ions, the electrons and the metastable atoms have very different dynamic responses. In most cases, the evolution of the plasma must be simulated for thousands of RF cycles until the system relaxes to steady state. If the evolution of the system is followed on the electron time scale, the cost of the simulation is high. In the present paper, different techniques to speed-up the convergence to steady state are studied on a common mathematical basis. The proposed methods take into account the tendency of the electrons to follow the ions very closely to give quasineutral plasmas. The ion motion can be followed in its own time scale by assuming that the electrons are in equilibrium. Thus, the electron time scale is eliminated, leading to very fast schemes, potentially hundreds of times faster than conventional methods. The methods considered are applied to a drift-diffusion model. This simple model is used to develop the numerical analysis of the convergence properties of the various schemes. The methods presented can be applied to more complex models (e.g. kinetic models). Finally, the algorithms will be applied to paradigmatic cases.