On the Correct Form of the Saha Equation for Two-Temperature Plasmas

Two quite different Saha equations modified to a two-temperature plasma were proposed and employed in many literatures. In order to clear up this confusion phenomenon lasted for a few decades in the community of thermal plasma science and technology, this paper re-examines the thermodynamic derivation of the two-temperature Saha equations. It is pointed out that the modified Saha equation deduced by using the minimum Gibbs or Helmholtz free energy is incorrect for the two-temperature plasma. Instead, a more rigorous derivation is presented here from the basic thermodynamic principle that the entropy in an isolated system always assumes its maximum value at chemical equilibrium.