Density-Functional-Theory--Based Equation-of-State Table of Beryllium for Inertial Confinement Fusion Applications

Beryllium has been considered a superior ablator material for inertial confinement fusion target designs. Based on density-functional-theory calculations, we have established a wide-range beryllium equation-of-state (EOS) table of density $\rho =$ 0.001 to $\rho =$ 500 g/cm$^{\mathrm{3}}$ and temperature $T =$ 2000 to $10^{8}$ K. Our first-principles equation-of-state (FPEOS) table\footnote{Y. H. Ding and S. X. Hu, Phys. Plasmas \textbf{24}, 062702 (2017).} is in better agreement with widely used \textit{SESAME }EOS table (\textit{SESAME }2023) than the average-atom \textit{INFERNO }model and the \textit{Purgatorio }model. For the principal Hugoniot, our FPEOS prediction shows $\sim $10{\%} stiffer behavior than the last two models at maximum compression. Comparisons between FPEOS and \textit{SESAME }for off-Hugoniot conditions show that both the pressure and internal energy differences are within $\sim $20{\%} between two EOS tables. By implementing the FPEOS table into the 1-D radiation--hydrodynamics code \textit{LILAC}, we studied the EOS effects on beryllium target-shell implosions. The FPEOS simulation predicts up to an $\sim $15{\%} higher neutron yield compared to the simulation using the \textit{SESAME }2023 EOS table. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.