Modeling of nonlocal electron kinetics in a low-pressure afterglow plasma

Abstract

The electron kinetics in a low-pressure afterglow plasma is studied by means of the time- and space-dependent Boltzmann (kinetic) equation. A method based on the nonlocal approach is presented, which enables the nonlocal nature of the electron distribution function (EDF) to be accounted for in a simple manner, without solving a complicated kinetic equation. Simplified kinetic equations are derived, as well as some analytic solutions, for obtaining the EDF in terms of its energy-averaged parameters, such as the electron density and temperature. This allows an energy-balance equation to be used to describe the electron-energy decay at the kinetic level. To validate the proposed method, the full time- and space-dependent kinetic equation is solved numerically for an afterglow in Ar. It is observed that under nonlocal conditions the EDF is strongly non-Maxwellian. As a consequence, the values of the wall potential predicted using the kinetic approach differ drastically from those obtained on the premise of a Maxwellian EDF. Another striking nonlocal effect manifests itself in a strong spatial inhomogeneity of the electron temperature. The derived energy-balance equation coupled with the simplified nonlocal kinetic equations reproduce accurately both the spatial profiles and absolute values of the electron temperature obtained from the full kinetic simulations. An interesting phenomenon, obtained numerically and explained in terms of the nonlocal EDF, is that the radial fluxes of different portions of the EDF have opposite directions. A direct comparison between the fluid and kinetic approaches is carried out, and it is concluded that the fluid approach fails to describe correctly the essential properties of a low-pressure afterglow plasma, such as the temporal and spatial evolution of the electron temperature. It is further demonstrated that the volume-averaged (zero-dimensional) kinetic models can also lead to erroneous results in describing such plasmas. It is shown that superthermal electrons produced in processes involving metastables can have a great influence on the plasma decay, particularly on the wall potential and the diffusion-cooling rate. The present method has the advantage of being simple and semianalytic, and thus can be very useful in solving complex self-consistent problems.