Variational-average-atom-in-quantum-plasmas (VAAQP) code and virial theorem: Equation-of-state and shock-Hugoniot calculations for warm dense Al, Fe, Cu, and Pb

Abstract

The numerical code VAAQP (variational average atom in quantum plasmas), which is based on a fully variational model of equilibrium dense plasmas, is applied to equation-of-state calculations for aluminum, iron, copper, and lead in the warm-dense-matter regime. VAAQP does not impose the neutrality of the Wigner-Seitz ion sphere; it provides the average-atom structure and the mean ionization self-consistently from the solution of the variational equations. The formula used for the electronic pressure is simple and does not require any numerical differentiation. In this paper, the virial theorem is derived in both nonrelativistic and relativistic versions of the model. This theorem allows one to express the electron pressure as a combination of the electron kinetic and interaction energies. It is shown that the model fulfills automatically the virial theorem in the case of local-density approximations to the exchange-correlation free-energy. Applications of the model to the equation-of-state and Hugoniot shock adiabat of aluminum, iron, copper, and lead in the warm-dense-matter regime are presented. Comparisons with other approaches, including the inferno model, and with available experimental data are given. This work allows one to understand the thermodynamic consistency issues in the existing average-atom models. Starting from the case of aluminum, a comparative study of the thermodynamic consistency of the models is proposed. A preliminary study of the validity domain of the inferno model is also included.

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

“…On the other hand, using the DH equations (9),(10) and (11) we can also calculate the value of the excess freeenergy density at the equilibrium from Eq. (17). We obtain:…”

“…As stems from Eqs. (17) and (24), βA ξ /V is a functional of {h ij (r)}, {̺ i }, and of the functions {βξu ij (r)}. As a consequence, we can write:…”

Wide ranging equation of state with Tartarus: A hybrid Green’s function/orbital based average atom code

“…On applying spherical symmetry to the Dirac equation, n e (r) can be written in terms of orbitals [7,24]…”

Linear response of a variational average atom in plasma: Semi-classical model

“…It stems from the TFAA model that a finite electron density n (0) 0 = n(r W S ) related to the chemical potential µ 0 is obtained at the WS boundary. One may then consider as in [10] that beyond the WS sphere is a jellium of electron density n This picture of one ion in a jellium with a cavity was used in the framework of a cluster expansion (see [17]) in previous works leading to the Variational Average-Atom in Quantum Plasma (VAAQP) model (see [1,2,5]). It was proved that the TFAA model can also be considered as resulting from the VAAQP approach, if the electron free-energy is taken in the TF approximation.…”