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

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.83.026403· OSTI ID:21560032

Piron, R ^[1]; Blenski, T ^[2]

---

1. CEA, DAM, DIF, F-91297 Arpajon (France)
2. CEA, IRAMIS, Service des Photons Atomes et Molecules, F-91191 Gif-sur-Yvette (France)

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.

• OSTI ID: 21560032
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevE.83.026403; (c) 2011 American Institute of Physics; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ALUMINIUM
APPROXIMATIONS
ATOMS
COPPER
ELECTRONS
EQUATIONS OF STATE
EXPERIMENTAL DATA
FREE ENERGY
IONIZATION
IRON
LEAD
MATHEMATICAL SOLUTIONS
PLASMA DENSITY
QUANTUM PLASMA
RELATIVISTIC RANGE
V CODES
VARIATIONAL METHODS
VIRIAL THEOREM
WIGNER-SEITZ METHOD
CALCULATION METHODS
COMPUTER CODES
DATA
ELEMENTARY PARTICLES
ELEMENTS
ENERGY
ENERGY RANGE
EQUATIONS
FERMIONS
INFORMATION
LEPTONS
METALS
NUMERICAL DATA
PHYSICAL PROPERTIES
PLASMA
THERMODYNAMIC PROPERTIES
TRANSITION ELEMENTS