Reduced formulation and efficient algorithm for the determination of equilibrium composition and partition functions of ideal and nonideal complex plasma mixtures.

Abstract

The system of coupled nonlinear Saha equations supplemented by electroneutrality and conservation of nuclei for complex plasma mixtures is reformulated into a reduced form, which allows the development of an efficient numerical algorithm to solve the set of nonlinear equations. The efficient algorithm is based on the solution of an equivalent single transcendental equation. Nonideality corrections have been taken into consideration in terms of depression of ionization potentials and truncated partition functions. Implementing this simple efficient methodology simplifies the problem and considerably reduces the computational effort needed to compute the detailed plasma composition for different cases. The algorithm is analytically known to be safe, fast, and efficient. It also shows no numerical instabilities, no convergence problems, and no accuracy limitations or lack of change problems, which have been reported in the literature. A nontrivial sample problem has been worked in detail showing the usefulness of the method for applied and industrial plasma physicists. Effects of the nonideality corrections and the exclusion of excited states are quantified and presented. A criterion for the validity of the assumption of local thermodynamic equilibrium is applied to the results from the sample problem to show the region of the temperature-density phase space over which the assumption is valid.