Discussion on Electron Temperature of Gas-Discharge Plasma with Non-Maxwellian Electron Energy Distribution Function Based on Entropy and Statistical Physics

Abstract

Electron temperature is reconsidered for weakly-ionized oxygen and nitrogen plasmas with its discharge pressure of a few hundred Pa, with its electron density of the order of 1017m−3 and in a state of non-equilibrium, based on thermodynamics and statistical physics. The relationship between entropy and electron mean energy is focused on based on the electron energy distribution function (EEDF) calculated with the integro-differential Boltzmann equation for a given reduced electric field E/N. When the Boltzmann equation is solved, chemical kinetic equations are also simultaneously solved to determine essential excited species for the oxygen plasma, while vibrationally excited populations are solved for the nitrogen plasma, since the EEDF should be self-consistently found with the densities of collision counterparts of electrons. Next, the electron mean energy U and entropy S are calculated with the self-consistent EEDF obtained, where the entropy is calculated with the Gibbs’s formula. Then, the “statistical” electron temperature Test is calculated as Test=[∂S/∂U]−1. The difference between Test and the electron kinetic temperature Tekin is discussed, which is defined as [2/(3k)] times of the mean electron energy U=⟨ϵ⟩, as well as the temperature given as a slope of the EEDF for each value of E/N from the viewpoint of statistical physics as well as of elementary processes in the oxygen or nitrogen plasma.