Variational Average-Atom in Quantum Plasmas (VAAQP) – Recent progress, virial theorem and applications to the equation-of-state of warm dense Be

The Variational Average-Atom in Quantum Plasmas (VAAQP) code is based on a fully variational theory of dense plasmas in equilibrium in which the neutrality of the Wigner-Seitz ion sphere is not required, contrary to the Inferno model. We report on some recent progress in the VAAQP model and numerical code. Three important points of the virial theorem derivation are emphasized and explained. The virial theorem is also used as an important tool allowing us to check the formulas and numerical methods used in the code. Applications of the VAAQP code are shown using as an example the equation-of-state of beryllium in the warm dense matter regime. Comparisons with the Inferno model, and with available experimental data on the principal Hugoniot are also presented.