Predictive design of REHEDS experiments with radiation-hydrodynamic simulations requires knowledge of material properties (e.g. equations of state (EOS), transport coefficients, and radiation physics). Interpreting experimental results requires accurate models of diagnostic observables (e.g. detailed emission, absorption, and scattering spectra). In conditions of Local Thermodynamic Equilibrium (LTE), these material properties and observables can be pre-computed with relatively high accuracy and subsequently tabulated on simple temperature-density grids for fast look-up by simulations. When radiation and electron temperatures fall out of equilibrium, however, non-LTE effects can profoundly change material properties and diagnostic signatures. Accurately and efficiently incorporating these non-LTE effects has been a longstanding challenge for simulations. At present, most simulations include non-LTE effects by invoking highly simplified inline models. These inline non-LTE models are both much slower than table look-up and significantly less accurate than the detailed models used to populate LTE tables and diagnose experimental data through post-processing or inversion. Because inline non-LTE models are slow, designers avoid them whenever possible, which leads to known inaccuracies from using tabular LTE. Because inline models are simple, they are inconsistent with tabular data from detailed models, leading to ill-known inaccuracies, and they cannot generate detailed synthetic diagnostics suitable for direct comparisons with experimental data. This project addresses the challenge of generating and utilizing efficient, accurate, and consistent non-equilibrium material data along three complementary but relatively independent research lines. First, we have developed a relatively fast and accurate non-LTE average-atom model based on density functional theory (DFT) that provides a complete set of EOS, transport, and radiative data, and have rigorously tested it against more sophisticated first-principles multi-atom DFT models, including time-dependent DFT. Next, we have developed a tabular scheme and interpolation methods that compactly capture non-LTE effects for use in simulations and have implemented these tables in the GORGON magneto-hydrodynamic (MHD) code. Finally, we have developed post-processing tools that use detailed tabulated non-LTE data to directly predict experimental observables from simulation output.
We present the development of a pulsed power experimental technique to infer the electrical conductivity of metals from ambient to high energy density conditions. The method is implemented on Thor, a moderate scale (1-2 MA) pulsed power driver. The electrical conductivity of copper at elevated temperature (>4000 K) and pressure (>10 GPa) is determined, and a new tabular material model is developed, guided by density functional theory, which preserves agreement with existing experimental data. Minor modifications (<10%) are found to be necessary to the previous Lee-More-Desjarlais model isotherms in the vicinity of the melt transition in order to account for observed discrepancies with the new experimental data. An analytical model for magnetic direct drive flyer acceleration and Joule heating induced vaporization based on the Tsiolkovsky "rocket equation"is presented to assess sensitivity of the method to minor changes in electrical conductivity.
The outer core of the Earth is composed primarily of liquid iron, and the inner core boundary is governed by the intersection of the melt line and the geotherm. While there are many studies on the thermodynamic equation of state for solid iron, the equation of state of liquid iron is relatively unexplored. We use dynamic compression to diagnose the high-pressure liquid equation of state of iron by utilizing the shock-ramp capability at Sandia National Laboratories’ Z-Machine. This technique enables measurements of material states off the Hugoniot by initially shocking samples and subsequently driving a further, shockless compression. Planetary studies benefit greatly from isentropic, off-Hugoniot experiments since they can cover pressure-temperature (P-T) conditions that are close to adiabatic profiles found in planetary interiors. We used this method to drive iron to P-T conditions similar to those of the Earth’s outer-inner core boundary, along an elevated-temperature isentrope in the liquid from 275 GPa to 400 GPa. We derive the equation of state using a hybrid backward integration – forward Lagrangian technique on particle velocity traces to determine the pressure-density history of the sample. Our results are in excellent agreement with SESAME 92141, a previously published equation of state table. With our data and previous experimental data on liquid iron we provide new information on the iron melting line and derive new parameters for a Vinet-based equation of state. The table and our parameterized equation of state are applied to provide an updated means of modeling the pressure, mass, and density of liquid iron cores in exoplanetary interiors.
Elucidating the mechanisms responsible for sub-microsecond desorption of water and other impurities from electrode surfaces at high heating rates is crucial for understanding pulsed power behavior. Ionization of desorbed impurities in the vacuum regions causes power or current loss; devising methods to limit such desorption during the short time scale of pulsed power is needed to improve corresponding applications. Previous molecular modeling studies have strongly suggested that, under high vacuum conditions, the amount of water impurity desorbing from oxide surfaces on metal electrodes is at a sub-monolayer level at room temperature, which appears insufficient to explain observed pulsed power energy losses at high current densities. In this work, we apply Density Functional Theory (DFT) techniques to show that hydrogen trapped inside iron metal can diffuse into hematite (α-Fe2O3) on the metal surface, ultimately reacting with the oxide to form Fe(II) and H2O. The latter desorbs at elevated temperature and may explain the anomalous amount of desorbed impurity inferred from pulsed-power experiments. We also apply a suite of characterization techniques to demonstrate that when iron metal is heated to 650 °C, the dominant surface oxide component becomes α-Fe2O3. The oxide facets exposed are found to be a mixture of (0001), (10-10), and others, in agreement with the DFT models used.
This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.
Hypervelocity impact-driven vaporization is characteristic of late-stage planet formation. Yet the behavior and properties of liquid-vapor mixtures of planetary materials of interest are typically unknown. Multiphase equations of state used in hydrodynamic simulations of planet impacts therefore lack reliable data for this important phenomenon. Here, we present the first constraints on the liquid-vapor critical point and coexistence phase boundary of Mg2SiO4 computed from ab initio molecular dynamics simulations. We found that the vapor is depleted in magnesium and enriched in silica and oxygen, while the coexisting liquid is enriched in magnesium and depleted in oxygen, from which we infer vaporization is incongruent. The critical point was estimated from an equation of state fit to the data. The results are in line with recent calculations of MgSiO3 and together confirm that extant multiphase equation of state (EOS) models used in planetary accretion modeling significantly underestimate the amount of supercritical material postimpact.
Mixing of cold, higher-Z elements into the fuel region of an inertial confinement fusion target spoils the fusion burn efficiency. This mixing process is driven by both "turbulent" and "atomic" mixing processes, the latter being modeled through transport corrections to the basic hydrodynamic models. Recently, there has been a surge in the development of dense plasma transport modeling and the associated transport coefficients; however, experimental validation remains in its infancy. To address this gap in our knowledge of interfacial mixing, Sandia National Laboratories is developing a new experimental platform at the Z-facility to investigate plasma transport in dense plasmas that span the entire warm dense matter regime. Specifically, this platform is being developed to measure species transport across a V/CH interface, using an x-ray driven hohlraum to drive the sample to [?] 190eV over 5ns. The heated sample is diagnosed using radiography optimized to measure the distribution of Vanadium perpendicular the interface. In order to interpret measurements made using this experimental platform, modeling tools that incorporate transport effects in strongly coupled plasmas are required. To this end, we utilize new advances in multi-species kinetic theory, collision models applicable to strongly coupled plasmas and modeling of degenerate electron plasmas to develop such a capability. The resulting kinetic transport code has been applied, along with state-of-the-art radiation hydrodynamic codes, to model the experiments. Results from this modeling effort highlight the importance of strong electric fields, which are present in the kinetic transport code, but absent in the radiation hydrodynamics code, in driving interfacial mixing. Synthetic radiography generated from all of these models reveals the ability of experimental diagnostics to distinguish interfacial mixing driven by a range of transport effects. We demonstrate that the spatial and temporal resolution of radiography diagnostics currently available at the Z-facility can distinguish between these different transport effects when multiple (3 [?] 4) radiographs, separated in time ( [?] 2 ns ) with accurate timing are captured per experiment.
The shock Hugoniot for full-density and porous CeO2 was investigated in the liquid regime using ab initio molecular dynamics (AIMD) simulations with Erpenbeck's approach based on the Rankine-Hugoniot jump conditions. The phase space was sampled by carrying out NVT simulations for isotherms between 6000 and 100 000 K and densities ranging from ρ=2.5 to 20g/cm3. The impact of on-site Coulomb interaction corrections +U on the equation of state (EOS) obtained from AIMD simulations was assessed by direct comparison with results from standard density functional theory simulations. Classical molecular dynamics (CMD) simulations were also performed to model atomic-scale shock compression of larger porous CeO2 models. Results from AIMD and CMD compression simulations compare favorably with Z-machine shock data to 525 GPa and gas-gun data to 109 GPa for porous CeO2 samples. Using results from AIMD simulations, an accurate liquid-regime Mie-Grüneisen EOS was built for CeO2. In addition, a revised multiphase SESAME-Type EOS was constrained using AIMD results and experimental data generated in this work. This study demonstrates the necessity of acquiring data in the porous regime to increase the reliability of existing analytical EOS models.
Aglitskiy, Y.; Velikovich, A.L.; Karasik, M.; Schmitt, A.J.; Serlin, V.; Weaver, J.L.; Oh, J.; Obenschain, S.P.; Cochrane, Kyle C.
Absolute Hugoniot measurements for empty plastic foams at ∼10% of solid polystyrene density and supporting rad-hydro simulation results are reported. Planar foam slabs, ∼400 μm thick and ∼500 μm wide, some of which were covered with a 10 μm solid plastic ablator, were directly driven by 4 ns long Nike krypton-fluoride 248 nm wavelength laser pulses that produced strong shock waves in the foam. The shock and mass velocities in our experiments were up to 104 km/s and 84 km/s, respectively, and the shock pressures up to ∼9 Mbar. The motion of the shock and ablation fronts was recorded using side-on monochromatic x-ray imaging radiography. The steadiness of the observed shock and ablation fronts within ∼1% has been verified. The Hugoniot data inferred from our velocity measurements agree with the predictions of the SESAME and CALEOS equation-of-state models near the highest pressure ∼9 Mbar and density compression ratio ∼5. In the lower pressure range 2-5 Mbar, a lower shock density compression is observed than that predicted by the models. Possible causes for this discrepancy are discussed.
Presented are the results from the liner ablation experiments conducted at 550 kA on the Michigan Accelerator for Inductive Z-Pinch Experiments. These experiments were performed to evaluate a hypothesis that the electrothermal instability (ETI) is responsible for the seeding of magnetohydrodynamic instabilities and that the cumulative growth of ETI is primarily dependent on the material-specific ratio of critical temperature to melting temperature. This ratio is lower in refractory metals (e.g., tantalum) than in non-refractory metals (e.g., aluminum or titanium). The experimental observations presented herein reveal that the plasma-vacuum interface is remarkably stable in tantalum liner ablations. This stability is particularly evident when contrasted with the observations from aluminum and titanium experiments. These results are important to various programs in pulsed-power-driven plasma physics that depend on liner implosion stability. Examples include the magnetized liner inertial fusion (MagLIF) program and the cylindrical dynamic material properties program at Sandia National Laboratories, where liner experiments are conducted on the 27-MA Z facility.
In recent years, α-quartz has been used prolifically as an impedance matching standard in shock wave experiments in the multi-Mbar regime (1 Mbar = 100 GPa = 0.1 TPa). This is due to the fact that above ∼90-100 GPa along the principal Hugoniot α-quartz becomes reflective, and thus, shock velocities can be measured to high precision using velocity interferometry. The Hugoniot and release of α-quartz have been studied extensively, enabling the development of an analytical release model for use in impedance matching. However, this analytical release model has only been validated over a range of 300-1200 GPa (0.3-1.2 TPa). Here, we extend this analytical model to 200-3000 GPa (0.2-3 TPa) through additional α-quartz Hugoniot and release measurements, as well as first-principles molecular dynamics calculations.
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%.
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.
Eighty years ago, it was proposed that solid hydrogen would become metallic at sufficiently high density. Despite numerous investigations, this transition has not yet been experimentally observed. More recently, there has been much interest in the analog of this predicted metallic transition in the dense liquid, due to its relevance to planetary science. Here, we show direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Experimental determination of the location of this transition provides a much-needed benchmark for theory and may constrain the region of hydrogen-helium immiscibility and the boundary-layer pressure in standard models of the internal structure of gas-giant planets.
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.
Recyclable transmission lines (RTL)s are being studied as a means to repetitively drive z pinches to generate fusion energy. We have shown previously that the RTL mass can be quite modest. Minimizing the RTL mass reduces recycling costs and the impulse delivered to the first wall of a fusion chamber. Despite this reduction in mass, a few seconds will be needed to reload an RTL after each subsequent shot. This is in comparison to other inertial fusion approaches that expect to fire up to ten capsules per second. Thus a larger fusion yield is needed to compensate for the slower repetition rate in a z-pinch driven fusion reactor. We present preliminary designs of z-pinch driven fusion capsules that provide an adequate yield of 1-4 GJ. We also present numerical simulations of the effect of these fairly large fusion yields on the RTL and the first wall of the reactor chamber. These simulations were performed with and without a neutron absorbing blanket surrounding the fusion explosion. We find that the RTL will be fully vaporized out to a radius of about 3 meters assuming normal incidence. However, at large enough radius the RTL will remain in either the liquid or solid state and this portion of the RTL could fragment and become shrapnel. We show that a dynamic fragmentation theory can be used to estimate the size of these fragmented particles. We discuss how proper design of the RTL can allow this shrapnel to be directed away from the sensitive mechanical parts of the reactor chamber.
A new method for measuring the wavelength dependence of the transit time, material dispersion, and attenuation of an optical fiber is described. The authors inject light from a 4-ns risetime pulsed broad-band flashlamp into various length fibers and record the transmitted signals with a time-resolved spectrograph. Segments of data spanning an approximately 3,000 {angstrom} range are recorded from a single flashlamp pulse. Comparison of data acquired with short and long fibers enables the determination of the transit time and the material dispersion as functions of wavelength dependence for the entire recorded spectrum simultaneously. The wavelength dependent attenuation is also determined from the signal intensities. The method is demonstrated with experiments using a step index 200-{micro}m-diameter SiO{sub 2} fiber. The results agree with the transit time determined from the bulk glass refractive index to within {+-} 0.035% for the visible (4,000--7,200 {angstrom}) spectrum and 0.12% for the ultraviolet (2,650--4,000 {angstrom}) spectrum, and with the attenuation specified by the fiber manufacturer to within {+-} 10%.