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Definition of electron temperature of nonequilibrium plasma based on Tsallis and Rényi entropy maximization principles

Koji Kikuchi1 and Hiroshi Akatsuka2

  • 1Graduate Major in Nuclear Engineering, Department of Electrical and Electronic Engineering, Institute of Science Tokyo, 2-12-1-N1-10, O-Okayama, Meguro-ku, Tokyo 152-8550, Japan
  • 2Institute of Integrated Research, Institute of Science Tokyo, 2-12-1-N1-10, O-Okayama, Meguro-ku, Tokyo 152-8550, Japan

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Phys. Rev. E 112, 015201 – Published 7 July, 2025

DOI: https://doi.org/10.1103/6zfg-q1b9

Abstract

Nonequilibrium plasma has attracted significant attention owing to its excellent physical properties, which are highly valued by the industrial community. However, determining the electron temperature in nonequilibrium plasmas proves challenging unless the energy distribution function is approximated as an ideal Maxwell-Boltzmann distribution, where the slope of the Boltzmann plot is directly related to temperature based on traditional Boltzmann-Gibbs statistics. To overcome this problem, Tsallis and Rényi entropies are applied to nonequilibrium systems using nonextensive Tsallis and extensive Rényi statistics, respectively. Here, the temperature is determined through a power-law distribution derived from the entropy maximization principle, which accounts for the influence of previously neglected high-energy electrons. However, because the resulting distribution function requires a self-consistent function that cannot be solved analytically, a self-consistent iterative scheme is proposed to calculate the temperature. Consequently, the electron temperature is uniquely determined in nonequilibrium plasmas, satisfying the entropy maximization principle. This study may open additional avenues for understanding plasma properties using an additional parameter q expanding the meaning of temperature T.

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Phys. Rev. E 112, 015201– Published 7 July, 2025
  • Received 8 February 2025
  • Accepted 22 May 2025
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