A regularized high-order moment model to capture non-Maxwellian electron energy distribution function effects in partially ionized plasmas

Abstract

A model for electrons in partially ionized plasmas that self-consistently captures non-Maxwellian electron energy distribution function (EEDF) effects is presented. The model is based on the solution of scalar and vectorial velocity moments up to the contracted fourth-order moment. The set of fluid (macroscopic) equations is obtained with Grad's method and exact expressions for the collision production terms are derived, considering the electron–electron, electron–gas, and electron–ion elastic collisions as well as for electron–gas excitation and ionization collisions. A regularization of the equations is proposed in order to avoid spurious discontinuities, existing in the original Grad's moment model, by using a generalized Chapman–Enskog expansion that exploits the disparity of mass between the electrons and the heavy particles (ions and atoms) as well as the disparity of plasma and gas densities, typical of gas discharges. The transport model includes non-local effects due to spatial gradients in the EEDF as well as the impact of the EEDF in the calculation of the elastic and inelastic collision rates. Solutions of the moment model under spatially homogeneous conditions are compared to direct simulation Monte Carlo and a two-term Boltzmann solver under conditions that are representative of high plasma density discharges at low-pressure. The moment model is able to self-consistently capture the evolution of the EEDF, in good quantitative agreement with the kinetic solutions. The calculation of transport coefficients and collision rates of an argon plasma in thermal non-equilibrium under the effect of an electric field is in good agreement with the solutions of a two-term Boltzmann solver, largely improving models with a simplified Bhatnagar–Gross–Krook collisional operator.