Discussion on Temperatures on the basis of the Tsallis Entropy Determined by the Excited-State Populations of Hydrogen Atoms in Hydrogen Plasma

We reconsider what the temperature should be determined in plasmas in a state of non-equilibrium on the basis of Tsallis statistics. We calculate number densities N_i of hydrogen atoms with its principal quantum number i (≥ 2) of the hydrogen plasma by collisional radiative model, where we can treat N_i as functions of electron temperature T_e, density N_e, and density of the ground-state hydrogen atoms N₁. When we apply the Tsallis entropy S_q = -kΣ^N_i=1 p_i^q ln_q p_i, q-average energy U_q = (Σ^N_i=1 p_i^qε_i)/(Σ^N_j=1 p_j^q) and probabilities p_i = 1/Z_qexp_q(-β_q(ε_i-U_q)), we can determine the physical temperature as T_phys = (1+(1-q)S_q/k)/(∂U_q/∂S_q) on the basis of Tsallis statistics. Then, we can apply this equation to the excited-state N_i of hydrogen plasmas to determine T_phys. We discuss the dependence of T_phys on T_e in the range of 1 ≤ T_e [eV] ≤ 10.