Calculation of two-Temperature plasma composition: I. Mass action law methods and extremum searching methods

Composition of species is one of the key parameters in calculating the plasma properties and assessing the plasma chemical processes. Unlike the calculation of LTE plasma composition, the calculation of 2T plasma composition still remains in dispute. Different researchers have chosen different methods which lead to different results. In this work, we compare two kinds of methods for calculating 2T plasma composition: The mass action law methods and extremum searching methods. The former methods include the two described by Potapov and van de Sanden et al mass action laws, respectively. The latter methods include those of searching minimum Gibbs free energy and maximum entropy of a plasma system respectively. The entropy maximization method is first reported in this work and has the same power as the commonly used Gibbs free energy minimization method. We demonstrate both mathematically and numerically that the method of 2T Gibbs free minimization is completely the same as the 2T Potapov mass action law, and the method of 2T entropy maximization is exactly consistent with the 2T van de Sanden et al mass action law if we assume that the term μ _i/T _i is independent of the number density n _i. It is also found that the assumption of number density-independent μ _i/T _i mainly affects the density of charged particles. When the plasma reaches the LTE state, the composition obtained by the methods of entropy maximization with and without this assumption will be exactly the same.