Self-consistent approach for the thermodynamics of ions in dense plasmas in the superconfiguration approximation

Abstract

We propose a new thermodynamic approach to ions in dense plasmas taking into account the screening by free electrons. The ions in fundamental and excited states are represented by a group of superconfigurations. Each superconfiguration containing an integer number of bound electrons is totally screened by free electrons in a Wigner–Seitz (WS) sphere. The minimisation of the plasma free energy with respect to the WS radii of the ions, under the condition that the specific mass of the plasma is preserved, leads to the equality of the electronic pressure for all ions. This pressure, as well as the WS radii and the distribution of ionic probabilities, are calculated by iteration. In this way, our approach not only gives the charge neutrality of the plasma, but also assures that the plasma environment is the same for each ion. In principle, the proposed approach allows one to apply the superconfiguration method to calculate radiative properties of plasmas for higher densities than those encountered in transmission experiments. Numerical examples for nickel, aluminium and samarium plasmas will be given. Comparisons with results from the previous statistical approach using the same WS radius for each ion charge state will also be discussed.