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Title
Japanese: 
English:Discussion on Electron Temperature of Gas-Discharge Plasma with Non-Maxwellian Electron Energy Distribution Function Based on Entropy and Statistical Physics 
Author
Japanese: 赤塚洋, 田中昌徳.  
English: Hiroshi Akatsuka, Yoshinori Tanaka.  
Language English 
Journal/Book name
Japanese: 
English:Entropy 
Volume, Number, Page Vol. 25    No. 2    276
Published date Feb. 2, 2023 
Publisher
Japanese: 
English:MDPI 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
Official URL https://www.mdpi.com/1099-4300/25/2/276
 
DOI https://doi.org/10.3390/e25020276
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 10^{17}m^{-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 T^{st}_e is calculated as T^{st}_e=[∂S/∂U]^{-1}. The difference between T^{st}_e and the electron kinetic temperature T^{kin}_e 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.

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