A Robust Algorithm for Orbital-Free Average Atom Models of Dense Plasmas

Average atom models are the primary method for predicting equation of state (EOS) properties in plasmas. While the most high-fidelity models rely on orbital-based density functional theory (DFT) [1], orbital-free models are still in wide use due to both their computational efficiency as well well their ability to continuously exhaust the temperature-density space. The most popular orbital-free DFT is the Thomas-Fermi model [2]; however, this simplistic model can be systematically improved through gradient corrections, exchange-correlation effects, etc. While these more sophisticated models have been explored in the past [3], they are often poorly formulated due to ambiguity in the boundary conditions. Here, we derive the proper boundary conditions necessary in orbital-free average atom models and present a numerical investigation of the governing equations. EOS calculations are compared with data from both orbital-based methods and experiments.

[1] B. Wilson, V. Sonnad, P. Sterne and W. Isaacs. "PURGATORIO—a new implementation of the INFERNO algorithm." Journal of Quantitative Spectroscopy and Radiative Transfer 99, 658 (2006).

[2] R. P. Feynman, N. Metropolis and E. Teller. "Equations of state of elements based on the generalized Fermi-Thomas theory." Physical Review 75, 1561 (1949).

[3] K. Yonei, J. Ozaki and Y. Tomishima. "Solution of the temperature-dependent Thomas-Fermi-Dirac-Weizsacker equation with a correlation correction." Journal of the Physical Society of Japan 56, 2697 (1987).