Session JO6: EOS and Material Dynamics

Inferring the equation of state of shocked liquid deuterium

The equation of state of light elements is essential to understanding the structure of Jovian planets. Here we present a combination of experimental techniques used to characterize warm dense deuterium. The OMEGA laser was used to directly drive a shock wave in a planar liquid-deuterium target. The shocked D2 conditions were diagnosed using VISAR and pyrometry to obtain the shock velocity and temperature. Two shock waves were launched with velocities of 17$\pm$0.9 and 23$\pm$1.0 km/s, as a result of intensity variations in the staggered laser beam drive. Using a blackbody approximation, a temperature of 0.4 to 0.8 eV range was inferred. Various equation of state models including SESAME, PROPACEOS, DFT-MD and Saumon \& Chabrier EOS were used to obtain a range pressures (0.4-0.5 Mbar) and densities (0.65-0.88 g/cc). Differences between models will be discussed. Preliminary data from X-ray scattering, providing a direct measurement of microscopic state of the deuterium for extreme conditions not accessible with VISAR, will also be presented.   

The Refractive Index and Transparency of Lithium Fluoride Compressed to 800~GPa

Lithium fluoride, ramp compressed by direct laser ablation, is observed to remain transparent up to 800 GPa. Simultaneous measurements of the free-surface and interface (particle) velocities in a two-section diamond-LiF target determine the velocity-correction factor and the refractive index of compressed LiF. The refractive index is observed to increase linearly with density over pressures of 30 to 800 GPa. An effective single-oscillator model shows that the refractive index is linear in density as a result of the optical gap closing monotonically with increasing density. Extrapolation of these results indicate that metallization of LiF should occur at pressures significantly higher than the Goldhammer--Herzfeld criterion ($\sim $2750 GPa), suggesting that LiF will remain transparent at extremely high pressures. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302.   

Precision Measurements of the Equation of State (EOS) of GDP Ablator Materials at $\sim $1 to 10 Mbar Using Laser-Driven Shock Waves

The behavior of polymer materials at high-pressure ($>$1 Mbar) is essential for understanding ignition target ablators. We report on EOS measurements on glow-discharge-polymer (GDP) (C$_{43}$H$_{56}$O) and germanium-doped GDP at shock pressures of $\sim $1 to 10 Mbar. This represents the only available high-pressure EOS measurements on these materials to date. These experiments use laser-driven shocks to drive impedance-match measurements using alpha quartz as a standard material. Shock velocities in these transparent samples \textit{and} the standard can be measured to $\sim $1{\%} precision. This allows the impedance-match technique for laser-driven shock experiments to produce precise data at extreme pressures. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302.   

Solid phase of aluminum at high energy densities

Recently, there is a growing interest in using isochoric heating of solids induced by an intense, ultrafast energy source to produce gradient-free, high-energy-density matter in the laboratory. Of central importance in such an approach is the persistence of the heated material in its solid phase. In previous experiments a solid phase of gold was found to last from $\sim $20 ps after being heated by a 400 nm, 150 fs laser pulse to an energy density of 10$^{10}$ J/m$^{3}$ to $\sim $2 ps for an energy density of $\sim $4x10$^{11}$ J/m$^{3}$ [T. Ao \textit{et. al}, PRL \underline {96}, 055001 (2006); Y. Ping \textit{et. al}, PRL \underline {96}, 255003 (2006)]. In this paper, we report on observations made on aluminum isochorically heated by a 400 nm, 40 fs laser pulse. The experiment was performed at the Advanced Laser Light Source (ALLS) in Quebec. Aluminum was chosen for its free-electron like density of states in contrary to the hybridized 5d-6s/p states in gold. Interestingly, under such ultrafast laser excitation, aluminum also appeared to remain solid on a ps time scale at an energy density of $\sim $10$^{11}$ J/m$^{3}$.   

K-edge shift and XANES investigation of laser driven reshock-compressed Aluminum

The physical properties of warm dense matter, specially their structural properties, are still poorly known. In this work, K-edge shift and X-ray Absorption Near Edge Spectroscopy (XANES) of reshocked Aluminum have been investigated with the aim of bringing information on the evolution of its electronic structure. The experiment was performed at LULI where we used one long pulse (500 ps, I$_{L}$~$\approx $~8~10$^{13}$~W/cm$^{2})$ to create the shock and a second picosecond beam (I$_{L}$~$\approx $~10$^{17}$~W/cm$^{2})$ to generate an ultra-short broadband X-ray source near the Al K-edge. The spectra were registered by using two conical KAP Bragg crystals. By changing the delay between the two beams, we have been able to observe the modification of absorption spectra for different and extreme Al conditions, up to now unexplored ($\rho \quad \le $ 3 $\rho _{0}$ and T $\le $ 8 eV). The hydrodynamical Al conditions were measured by using VISARs interferometers and self-emission diagnostic. Experimental data are compared to various calculations.   

Rayleigh-Taylor experimental results of dynamic Ta material strength at $>$1 Mbar pressure

We have measured the Rayleigh-Taylor (RT) instability growth rate in Ta using Omega and EP joint laser shots. The Ta sample is maintained in the solid state by a ramped drive using a reservoir-gap-sample configuration, reaching peak pressures $>$ 1 Mbar at strain rates of 10$^{6}$-10$^{8}$ s$^{-1}$. The Ta sample RT growth factors were measured using a 22 keV backlighter driven by the EP petawatt laser. The material strength can greatly suppress the RT instability growth rate via an effective lattice viscosity [1]. In 2D simulations of these experiments, we find that the various analytic constitutive (material strength) models overpredict the Ta growth by factors of $\sim $2 or more, whereas a newly developed multiscale model matches the experimental measurements to within $\sim $30{\%}. This paper will present the details on the experimental results and comparisons with the multi-scale model. Designs that extend this experiment to 5 Mbar on NIF will also be shown [1] J. D. Colvin et al., JAP, 93, 5287 (2003); H.S. Park et al., PRL. 104, 135504 (2010).   

Material deformation dynamics at ultrahigh pressures and strain rates

Solid-state dynamics experiments at extreme pressures, up to 10 Mbar, and strain rates (1.e6 -1.e8 1/s) are being developed for the NIF laser. The experimental methods are being developed on the Omega laser facility. VISAR measurements establish the ramped, high-pressure conditions. Recovery experiments offer a look at the residual microstructure. Dynamic diffraction measurements allow phase, shear stress (strength), and possibly twin volume fraction and dislocation density to be inferred. Constitutive models for material strength at these conditions by comparing 2D simulations with experiments measuring the Rayleigh-Taylor instability evolution in solid-state samples of vanadium and tantalum. The material deformation likely falls into the phonon drag regime. We estimate of the (microscopic) phonon drag coefficient, by relating to the (macroscopic) effective lattice viscosity.   

High pressure, quasi-isentropic drive designs for material dynamics experiments on the NIF

We have developed a series of novel designs for reaching high pressures in planar samples along a quasi-isentropic loading path, based on a ``plasma drive'' concept. The goal is to be able to study fundamental material properties and material dynamics in the solid state at very high pressures and strain rates. These designs use a target layering approach for generating the required pulse shaping to keep the samples under study at low temperatures, well below the melt temperature. The critical design components and criteria will be discussed, as will tests of aspects of these drive designs done with experiments at the Omega laser.   

Error Budget Analysis for Tantalum Rayleigh-Taylor Experiment

We analyze the expected experimental errors in a 5 Mbar peak pressure, Rayleigh-Taylor (RT) strength measurement in solid-state Ta to be performed on the National Ignition Facility in FY 2011. We also analyze the experimental errors for experiments on 1 Mbar Ta strength already being carried out at the Omega-EP laser facility. The strength is inferred by measuring its strong stabilizing effect on the RT instability growth rate of solid-state Ta samples. We will show a detailed design and a thorough error analysis, based on a suite of 2D simulations, used to optimize the experiment and minimize the predicted uncertainty in the deduced Ta material strength from these solid-state RT experiments.   

Off-Hugoniot measurements for diamond to TPa regime using reflected shock compression

Carbon is one of the most important materials for several areas of modern science. We have performed shock compression experiments for diamond to 1.6 TPa pressure. Diamond off-Hugoniot states have been measured using reflected shock compression technique with shock anvil materials. The reshoked diamond temperature is significantly suppressed compared with single shocked diamond temperature at the same pressure.   

High pressure property of MgO under shock compression to 1 TPa

Optical property of highly compressed MgO has been investigated using laser-driven smoothly decaying shock wave. Shock Hugoniot and temperature measurements for MgO were performed for the first time in TPa pressure regime. Shock compressed MgO is transparent near 300 GPa, meanwhile it is not highly reflecting up to 1 TPa. This wide range opaque property is not comparable with other crystalline dielectrics.   

PIMC Validation of Effective Quantum Potentials for MD Simulations of Dense Plasmas

Molecular dynamics (MD) simulations of dense plasmas, such as those found in non-equilibrium laser fusion experiments, are challenging due to the importance of several quantum mechanical effects. We currently employ approximate statistical potentials, obtained exactly in the pair approximation from a numerical solution of the Bloch equation for the Coulomb density matrix. The fermionic character of the electrons is handled via an effective Pauli potential. We first study the accuracy of existing pair potentials and their extension to lower temperature and high Z ions by examining the exact pair density matrix. We then perform classical hypernetted chain and MD simulations using those effective potentials to study equilibrium thermodynamics of dense plasmas. Fully quantum path integral Monte Carlo (PIMC) simulations are used to gauge the accuracy of the classical calculations for dense hydrogen. Using feedback from the PIMC, we can further refine the effective Coulomb and Pauli potentials. Prepared by LLNL under Contract DE-AC52-07NA27344.   

Extended Thomas-Fermi Molecular Dynamics for Dense, Strongly-Coupled Plasmas

The primary challenge in simulating dense plasmas is the self-consistent treatment of partial ionization. We present an orbital-free density-functional theory (OF-DFT) that includes, self-consistently, the physics of partially degenerate electrons, strongly coupled ions, and arbitrary degrees of ionization. The ions are treated dynamically according to the forces derived from the all-electron density calculation thereby allowing the computation of various transport quantities. Our variant of OF-DFT is based on extending the Thomas-Fermi functional to include gradient corrections and the exact, non-local, ideal-Fermi-gas response for weak coupling. We will describe our method and discuss various applications, such as equations of state and viscous transport in heterogeneous mixtures. Finally, we will give an outlook on extending this method to a fully dynamical model that describes the electron dynamics as well.