Kinetic theoretical and fluid modelling of plasmas and swarms: the big picture

Abstract

Since the 1950s there has been great progress in the fundamental kinetic theory of charged particles (electrons, positrons, muons and ions) in gases, but many of the ideas and results have still to find their way into modern low temperature plasma physics. This paper stresses the bigger picture, in the context of the kinetic theory of gases and fluid modelling, with a view to reconciling the plasma and swarm literature. We focus especially on the importance of a unified approach to transport analysis, appropriate to all types of charged particles in all situations. We discuss both plasmas and swarms in general, and make recommendations for 'best practice' in both kinetic theoretical and fluid modelling.

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].…”

Electron attachment properties of c-C4F8O in different environments

“…Electron swarm parameters such as the effective ionization rate, the electron drift velocity and the electron diffusion coefficient are useful for modeling low temperature plasmas in general [4,5], and in particular for modelling non-thermal gas discharges and assessing the performance of an electronegative gas for high voltage insulation [6,7]. It is common practice to calculate the effective ionization rate by solving the electron Boltzmann equation [8], or by means of Monte-Carlo simulations [9,10].…”

Uniform Moment Theory for Charged Particle Motion in Gases

“…Before Equation (6) can be solved for the ion number density, it is necessary to know the dependence of the moment of the average ion velocity, Gv9, upon space and time. This is a familiar problem [7] in moment methods for solving Equation (5), since the moment equation for a simple quantity involves one or more moments of more complicated functions. Thus, the equation forGv9, called the momentum-balance equation [16], involves the tensorGvv9 that is related to the temperature tensor.…”

“…We will present a closed system of differential equations governing the moments retained in the first of a series of approximations that provide progressively higher accuracy in describing the motion of trace amounts of ions through gases under the influence of arbitrary electric and magnetic fields. The assumption of trace ions means that we are considering swarm experiments and not plasmas [7] (i.e., ion-ion interactions are neglected).…”