Free-energy functional of the Debye–Hückel model of two-component plasmas

Abstract

We present a generalization of the Debye-Hückel free-energy-density functional of simple fluids to the case of two-component systems with arbitrary interaction potentials. It allows one to obtain the two-component Debye-Hückel integral equations through its minimization with respect to the pair correlation functions, leads to the correct form of the internal energy density, and fulfills the virial theorem. It is based on our previous idea, proposed for the one-component Debye-Hückel approach, and which was published recently [1]. We use the Debye-Kirkwood charging method in the same way as in [1], in order to build an expression of the free-energy density functional. Main properties of the two-component Debye-Hückel free energy are presented and discussed, including the virial theorem in the case of long-range interaction potentials.

Free-energy functional of the Debye-Hückel model of simple fluids

“…which is identical to Eq. ( 21) of [2]. Once again, the identity, in the sense of thermodynamical functions, of both free-energy functionals taken at equilibrium immediately yields the identity of all thermodynamical functions.…”

“…On the other hand, in the two-component case, one can compare the equilibrium value of the present functional to that of [2]. For a two-component fluid, the equilibrium correlation functions are given by:…”

“…( 13). Moreover, it was shown that the functional of [2] reduces to that of [1] in the one-component case. Therefore, it is clear that the functional of Eq.…”

“…

In previous publications [1,2], the authors have proposed Debye-Hückel-approximate free-energy functionals of the pair distribution functions for one-component fluid and two-component plasmas. These functionals yield the corresponding Debye-Hückel integral equations when they are minimized with respect to the pair distribution functions, lead to correct thermodynamic relations and fulfill the virial theorem.

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A New Implementation of the STA Method for the Calculation of Opacities of Local Thermodynamic Equilibrium Plasmas

“…This procedure enables the handling of situations where the number of populated configurations is too large, as shown in Figure 1. STAR also implements several additional advanced capabilities, such as (i) an adaptive integration of resonances in the electronic density of state [27][28][29][30], which has an effect on the bound-free structure and on the self-consistent field average-atom calculation, (ii) ion-sphere and ion-correlation models for the plasma environment [7,27,[31][32][33][34] and (iii) stable recursive calculation of partition functions, as in Refs. [8,[35][36][37].…”