Formation of inverse electron distribution function in glow discharges with hollow cathode.

Abstract

This study formulates a two-dimensional self-consistent kinetic model for numerical simulations a hollow-cathode glow discharge. This model includes a solution of the spatially inhomogeneous Boltzmann kinetic equation for electrons, taking into account both energy and two spatial variables: the longitudinal and radial coordinates. The model also incorporates fluid balance equations for the densities of heavy particles (ions and metastable excited atoms) and the Poisson equation for finding the electric field. It is shown based on the calculations results that extended regions of electron energy distribution function (EEDF) inversion can be realized both inside and outside the hollow cathode. An approximate analytical model is developed which explains the obtained results and allows scaling the results for varying external conditions. Thus, this study clarifies the formation mechanisms of EEDF and makes it possible to develop recommendations for the further experimental detection of an inverse EEDF.