Laser-driven ramp-compression experiments on the national ignition facility.

This report details the analyses and related uncertainties in measuring longitudinal-stress-density paths in indirect laser-driven ramp equation-of-state (EOS) experiments [Smith et al., Nat. Astron. 2(6), 452-458 (2018); Smith et al., Nature 511(7509), 330-333 (2014); Fratanduono et al., Science 372(6546), 1063-1068 (2021); and Fratanduono et al., Phys. Rev. Lett. 124(1), 015701 (2020)]. Experiments were conducted at the National Ignition Facility (NIF) located at the Lawrence Livermore National Laboratory. The NIF can deliver up to 2 MJ of laser energy over 30 ns and provide the necessary laser power and control to ramp compress materials to TPa pressures (1 TPa = 10 × 106 atmospheres). These data provide low-temperature solid-state EOS data relevant to the extreme conditions found in the deep interiors of giant planets. In these experiments, multi-stepped samples with thicknesses in the range of 40-120 µm experience an initial shock compression followed by a time-dependent ramp compression to peak pressure. Interface velocity measurements from each thickness combine to place a constraint on the Lagrangian sound speed as a function of particle velocity, which in turn allows for the determination of a continuous stress-density path to high levels of compressibility. In this report, we present a detailed description of the experimental techniques and measurement uncertainties and describe how these uncertainties combine to place a final uncertainty in both stress and density. We address the effects of time-dependent deformation and the sensitivity of ramp EOS techniques to the onset of phase transformations.

Benchmarking boron carbide equation of state using computation and experiment.

Boron carbide (B_{4}C) is of both fundamental scientific and practical interest due to its structural complexity and how it changes upon compression, as well as its many industrial uses and potential for use in inertial confinement fusion (ICF) and high-energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of B_{4}C in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of B_{4}C over a broad range of temperatures (∼6×10^{3}-5×10^{8} K) and densities (0.025-50 g/cm^{3}). We assess that the largest discrepancies between theoretical predictions are ≲5% near the compression maximum at 1-2×10^{6} K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are ∼18% and occur at temperatures between 6×10^{3}-2×10^{5} K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. To account for potential differences in the ion thermal term, we have developed three new equation-of-state models that are consistent with theoretical calculations and experiment. We apply these new models to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.