Equation of state and transport properties of an interacting multispecies plasma: Application to a multiply ionized Al plasma

We present a first principles theory of the ionization equilibrium, thermodynamics, and linear transport properties of an interacting mixture of electrons and several species of ions and neutrals, which are typical of a hot plasma. The thermodynamic functions are self-consistently calculated using the density functional theory (DFT). The inputs are the nuclear charge Z, the average electron density n¯, the temperature T, and the configurations of the ions and neutrals atoms to be considered. Ion-electron pseudopotentials and ion-ion pair potentials (including repulsive core contributions) are derived from the DFT. The ionic structure factors are determined using the multicomponent hypernetted chain theory. The ion-species concentrations ${\mathit{x}}_{\mathit{i}}$ are obtained through a minimization of the total free-energy F at constant volume and temperature. The average ionization ${\mathit{Z}}^{\mathrm{*}}$, the internal energy, the pressure, and the resistivity are computed. The method is illustrated by applications to aluminum plasma. In the calculations for expanded Al at T=1.5 eV we find a low-electron-density range where two solutions are obtained for a given average atomic volume; the most stable has the highest ionization. The unstable solution has an excitation energy that can reach 2.5 eV. At a higher density, the results imply a plasma phase transition from a state with average ionization ${\mathit{Z}}^{\mathrm{*}}$=1.2 to a state with ${\mathit{Z}}^{\mathrm{*}}$=3. We also provide calculations for a variety of expanded, compressed, and shocked plasmas, which are of current theoretical and experimental interest.