Recent advances in the application of Boltzmann equation and fluid equation methods to charged particle transport in non-equilibrium plasmas

Abstract

The kinetic theory of charged particles in gases has come a long way in the last 60 years or so, but many of the advances have yet to find their way into contemporary studies of low-temperature plasmas. This review explores the way in which this gap might be bridged, and focuses in particular on the analytic framework and numerical techniques for the solution of Boltzmann's equation for both electrons and ions, as well as on the development of fluid models and semi-empirical formulae. Both hydrodynamic and non-hydrodynamic regimes are considered and transport properties are calculated in various configurations of dc and ac electric and magnetic fields. We discuss in particular the duality in transport coefficients arising from non-conservative collisions (attachment, ionization).

High-order fluid model for streamer discharges: I. Derivation of model and transport data

“…Thus, particular care should be taken with the closure through specification of the energy flux. Even for charged particle swarms under non-hydrodynamic conditions one must be careful how to specify the heat flux vector [35,40,41,51]. We now discuss how the fluid equations should be closed for streamers, while we stress that the method itself is applicable to a much wider range of phenomena.…”

“…There are many examples which illustrate this issue and the reader is referred to [35,40,41] for a detailed discussion. In the context of streamer and breakdown studies beyond first order fluid models, it has become common practice to evaluate the collision terms and averages by assuming some particular form of the velocity distribution function, usually Maxwellian [48,49,52,53,54].…”

“…It is discussed comprehensively in the textbook of Mason and McDaniel [44] and in references [35,40,41,45,55,56,57]. The main ideas can be briefly summarized as follows: (1) We need to express the average collision frequencies as a function of the mean energy in the center-of-mass reference frame.…”

“…In plasma modeling, transport coefficients of electrons and/or ions may be obtained either from swarm experiments, from solutions of the Boltzmann equation, or from Monte Carlo simulations. We note that swarm transport data are usually given in the literature in the form of tables as a function of reduced electric field, E/n 0 [35,40]. In fluid plasma modeling, however, several important issues have to be considered before directly implementing data from the literature.…”

“…This is done by approximating the high order tensors in the energy flux balance equation by a product of two lower moments while the collision transfer terms are evaluated using momentum transfer theory. In section 3, electron transport properties as an input in fluid models are calculated using a multi term theory for solving the Boltzmann equation [35,36]. We pay particular attention to the accuracy of the calculation and the proper use in both the first and high order fluid models.…”