On fundamental inconsistencies in a commonly used modification of a fluid model for glow discharge

Abstract

This work considers the fundamental contradictions in the concept of one of the most well-known and widely used modifications of the fluid model for simulation of a glow discharge (GD), the ‘local mean energy approximation’ (LMEA). In this model, it is proposed to determine the kinetic coefficients in the electron particle and energy balance equations as functions of the electron mean energy (temperature) rather than local electric field, using a one-to-one correspondence between these parameters through the electron Boltzmann equation. It is shown that the scope of applicability of this model, like any other modification of the fluid model, is limited by the local mode of formation of the electron energy distribution function (EEDF). Therefore, as demonstrated by the examples of typical 1D and 2D problems for a GD in argon, its extension to the region of nonlocal EEDF is in no way justified and leads not only to serious errors in the results, but also to a logically intractable situation in attempts to apply the main postulate of the LMEA model to the region of a weak (or even reverse) electric field in a negative glow plasma. At the same time, the apparent reliability of calculations within the framework of the LMEA model for a number of parameters, in our opinion, only slows down progress in modeling of gas discharge plasma.