WDM: Universal Hugoniot of Fluid Metals and Thomas-Fermi Theory

An equation of state at extreme conditions in Warm Dense Matter (WDM) is needed for exoplanets and Inertial Confinement Fusion. Development of theory for WDM is problematical because of the need for experimental data for verification. At shock pressures 0.5 - 20 TPa (200 Mbar) measured Hugoniot data of fluid metals [1] are essentially co-linear in U_S (U_P), where U_S and U_P are shock and particle velocity, respectively, essentially independent of material. Calculated shock temperatures of those data range from a few thousand K up to a million K. Those shock-compressed fluids are WDM with Minimum Metallic Conductivity (MMC) [2]. The linear fit to 40 measured data points is known as the Universal Hugoniot of Fluid Metals (UHFM), which is possible verification data for WDM theory. TFD is Thomas Fermi theory for ionized atoms, Fermi-Dirac statistics for electrons, and electron correlation [3]. A possible theory for why that co-linear fit is universal might be a common electron correlation function in TF theory that yields the UHFM for Al, Cu, Fe, Mo, Kr, Gd₃Ga₅O₁₂, etc.
[1] Experimental Data on Shock Compression…, ed. R. F. Trunin (Sarov, VNIIEF, 2001).
[2] N. Ozaki et al, Sci. Reports 6:26000 (2016).
[3] R. P. Feynman, N. Metropolis and E. Teller, Phys. Rev. 75, 1561 (1949).