Solution of Time-dependent Boltzmann Equation

The time-dependent Boltzmann equation (BE) is solved in a two-term and a multi-term approximation in order to study the time evolution of the electron energy distribution function (EEDF) in argon plasma in a constant electric field. The initial distribution is taken to be isotropic Gaussian distribution, its center is set to the area of increasing elastic collision cross-section in order to study the effect of negative mobility. This effect is described and explained in detail. The results of the solution of the BE are compared with the results from the Monte Carlo simulation. Introduction In the last twenty years there have appeared several articles on the negative mobility of electrons in low-temperature plasma. This interesting phenomenon appears for example in a weakly ionized relaxing plasma in rare gases. At first it was theoretically predicted [McMahon et al., 1985 ] and this prediction enforced the publication of previous unpublished experiments [Warman et al., 1985]. In these experiments the phenomenon was observed on a nanosecond time scale in relaxing Xe plasma, ionized by a hard x-ray pulse. The possibility of steady state conditions leading to the negative mobility was theoretically studied in externally ionized gas mixtures [Rozenberg et al.,1988]. The theoretical studies mentioned above were made by solving an appropriate Boltzmann equation using so-called two-term approximation for the EEDF. The applicability of this approximation—for a steady state—was studied by [Dyatko et al., 2000] using two different methods: a Monte Carlo (MC) simulation and the solution of Boltzmann equation in two-term approximation. The main aim of the presented paper is to demonstrate the applicability of a strict timedependent two-term approximation (STTA) and higher order terms—so called multi-term— approximation (MTA). The correctness of results of STTA is tested by the MC simulation. As a testing example the relaxing argon plasma was chosen. The reasons how can electrons move against the acting electric force (which leads to a negative mobility) are discussed in more details. Model Suppose, we have a spatially homogeneous argon plasma. The neutral gas particles of mass M and density N are assumed to be at rest (Tgas = 0K). We are interested in the behavior of electrons (mass me and charge −e0) under the action of external electric field E that is suddenly switched on at time t = 0 s and remains constant. Electrons collide with neutral gas particles only, there is neither electron–electron nor electron–ion interaction. There is also no self-consistent space charge electric field. For simplicity only conservative inelastic collisions (including ionization) were considered and the elastic and all inelastic collisions were assumed to be isotropic. WDS'05 Proceedings of Contributed Papers, Part III, 613–619, 2005. ISBN 80-86732-59-2 © MATFYZPRESS