An equation of state for partially ionized plasmas: The Coulomb contribution to the free energy

We have previously developed an equation of state (EOS) model called ChemEOS (Hakel and Kilcrease, Atomic Processes in Plasmas, Eds., J. Cohen et al., AIP, 2004) for a plasma of interacting ions, atoms and electrons. It is based on a chemical picture of the plasma and is derived from an expression for the Helmholtz free energy of the interacting species. All other equilibrium thermodynamic quantities are then obtained by minimizing this free energy subject to constraints, thus leading to a thermodynamically consistent EOS. The contribution to this free energy from the Coulomb interactions among the particles is treated using the method of Chabrier and Potekhin (Phys. Rev. E 58, 4941 (1998)) which we have adapted for partially ionized plasmas. This treatment is further examined and is found to give rise to unphysical behavior for various elements at certain values of the density and temperature where the Coulomb coupling begins to become significant and the atoms are partially ionized. We examine the source of this unphysical behavior and suggest corrections that produce acceptable results. The sensitivity of the thermodynamic properties and frequency-dependent opacity of iron is examined with and without these corrections. The corrected EOS is used to determine the fractional ion populations and level populations for a new generation of OPLIB low-Z opacity tables currently being prepared at Los Alamos National Laboratory with the ATOMIC code.