Publications

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Included in this memo are the final values for the BSE and SiO₂ critical points. VASP 5.3.3 was used to calculate the values in each table. Standard methodology is to continue equilibrating the simulation until the block averaged standard deviation is less than 1%. However, due to the simulation sizes in these simulations, the average standard deviation of the BSE pressure is 5% (ranging between 2% and 7%, which is much higher than the usual under 1% considered acceptable) and the SiO₂ pressure is 6% with the lower density error bars being significantly larger than the highest density. The critical point is chosen where the dP/dρ >= 0 for an entire isotherm but is often difficult to distinguish because of the noise along each isotherm. As such, the actual values of the critical points are found by “best guess”. Further computer simulations creating a more pressure values along each isotherm would help but time constraints preclude this. Similarly, the ability to calculate pressures at lower densities that are currently feasible with VASP would also make determination of the critical point easier.

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The electrical conductivity of materials under extremes of temperature and pressure is of crucial importance for a wide variety of phenomena, including planetary modeling, inertial confinement fusion, and pulsed power based dynamic materials experiments. There is a dearth of experimental techniques and data for highly compressed materials, even at known states such as along the principal isentrope and Hugoniot, where many pulsed power experiments occur. We present a method for developing, calibrating, and validating material conductivity models as used in magnetohydrodynamic (MHD) simulations. The difficulty in calibrating a conductivity model is in knowing where the model should be modified. Our method isolates those regions that will have an impact. It also quantitatively prioritizes which regions will have the most beneficial impact. Finally, it tracks the quantitative improvements to the conductivity model during each incremental adjustment. In this paper, we use an experiment on Sandia National Laboratories Z-machine to isentropically launch multiple flyer plates and, with the MHD code ALEGRA and the optimization code DAKOTA, calibrated the conductivity such that we matched an experimental figure of merit to +/-1%.

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We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as it implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ∼1000 GPa is achieved in all cases. These experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.

In this study, we explore magnetized liner inertial fusion (MagLIF) [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] using a semi-analytic model [R. D. McBride and S. A. Slutz, Phys. Plasmas 22, 052708 (2015)]. Specifically, we present simulation results from this model that: (a) illustrate the parameter space, energetics, and overall system efficiencies of MagLIF; (b) demonstrate the dependence of radiative loss rates on the radial fraction of the fuel that is preheated; (c) explore some of the recent experimental results of the MagLIF program at Sandia National Laboratories [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)]; (d) highlight the experimental challenges presently facing the MagLIF program; and (e) demonstrate how increases to the preheat energy, fuel density, axial magnetic field, and drive current could affect future MagLIF performance.

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We report on experiments where cylindrical beryllium liners filled with liquid deuterium were compressed to extreme pressure and density with current pulse shaping. In one set of experiments the pressure at stagnation is inferred to be & 100 Mbar using penetrating radiography. A peak liner convergence ratio (initial radius over final radius) of 7.6 was measured resulting in an average deuterium density of 10 g=cm³ and areal density of 0.45 g=cm². The stagnation shock propagating radially outward through the liner wall was directly measured with a strength of ≈ 120 Mbar. In a second set of experiments the liner was imploded to a peak convergence of 19 resulting in a density of 55 g=cm³ and areal density of 0.5 g=cm². The pressure at stagnation in this experiment is estimated to be 2 Gbar. This platform enables the study of high-pressure, high-density, implosion deceleration and stagnation dynamics at spatial scales that are readily diagnosable (R ~ 0.1 -- 0.4 mm). Thus, these experiments are directly relevant to both Inertial Con nement Fusion and the study of material properties under extreme conditions.

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Mixtures of light elements with heavy elements are important in inertial confinement fusion. We explore the physics of molecular scale mixing through a validation study of equation of state (EOS) properties. Density functional theory molecular dynamics (DFT-MD) at elevated temperature and pressure is used to obtain the thermodynamic state properties of pure xenon, ethane, and various compressed mixture compositions along their principal Hugoniots. To validate these simulations, we have performed shock compression experiments using the Sandia Z-Machine. A bond tracking analysis correlates the sharp rise in the Hugoniot curve with the completion of dissociation in ethane. The DFT-based simulation results compare well with the experimental data along the principal Hugoniots and are used to provide insight into the dissociation and temperature along the Hugoniots as a function of mixture composition. Interestingly, we find that the compression ratio for complete dissociation is similar for several compositions suggesting a limiting compression for C-C bonded systems.

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