Discussion on electron temperature of non-equilibrium plasma based on Tsallis and Rényi entropies maximization principle

Non-equilibrium plasma has attracted enormous attention due to its excellent physical phenomena, which are highly regarded by the industrial community. To utilize the excellent properties of plasma across various industries, it is important to accurately describe the state of plasma using its temperature as a parameter. However, in non-equilibrium plasmas, the electron temperature cannot be uniquely determined unless the energy distribution function is approximated as an ideal Maxwell–Boltzmann distribution based on traditional Boltzmann–Gibbs statistics, where the slope of the Boltzmann plot has physical significance as the temperature. To overcome this problem, the Tsallis and the Renyi entropies are applied to non-equilibrium systems based on non-extensive Tsallis and extensive Renyi statistics. Consequently, the temperature can be determined not from an approximated exponential distribution as a straight line in the Boltzmann plot, but from a power-law distribution under the entropy maximization principle, considering the effects of high-energy electrons that were previously ignored. However, since the distribution function under the Tsallis and the Rényi entropies maximization principle requires a self-consistent function that cannot be solved analytically, a self-consistent iterative scheme is proposed and demonstrated to calculate the temperature. As a result, the electron temperature is uniquely determined in non-equilibrium plasmas while satisfying the entropy maximization principle. This study may open up new prospects for describing more detailed properties of plasma using another parameter q, expanding the meaning of temperature T.