Publications

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Shock compression experiments in the few hundred GPa (multi-Mbar) regime were performed on Lithium Deuteride single crystals. This study utilized the high velocity flyer plate capability of the Sandia Z Machine to perform impact experiments at flyer plate velocities in the range of 17-32 km/s. Measurements included pressure, density, and temperature between ∼190 and 570 GPa along the Principal Hugoniot - the locus of end states achievable through compression by large amplitude shock waves - as well as pressure and density of reshock states up to ∼920 GPa. The experimental measurements are compared with density functional theory calculations, tabular equation of state models, and legacy nuclear driven results that have been reanalyzed using modern equations of state for the shock wave standards used in the experiments.

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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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Experiments on the Sandia Z pulsed-power accelerator have demonstrated the ability to produce warm dense matter (WDM) states with unprecedented uniformity, duration, and size, which are ideal for investigations of fundamental WDM properties. For the first time, space-resolved x-ray Thomson scattering (XRTS) spectra from shocked carbon foams were recorded on Z. The large (>20 MA) electrical current produced by Z was used to launch Al flyer plates up to 25 km/s. The impact of the flyer plate on a CH2 foam target produced a shocked state with an estimated pressure of 0.75 Mbar, density of 0.52 g/cm3, and temperature of 4.3 eV. Both unshocked and shocked portions of the foam target were probed with 6.2 keV x-rays produced by focusing the Z-Beamlet laser onto a nearby Mn foil. The data are composed of three spatially distinct spectra that were simultaneously captured with a single spectrometer with high spectral (4.8 eV) and spatial (190 μm) resolutions. Detailed spectral information from three target locations is provided simultaneously: the incident x-ray source, the scattered signal from unshocked foam, and the scattered signal from shocked foam.

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.

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We report on the progress made to date for a Laboratory Directed Research and Development (LDRD) project aimed at diagnosing magnetic flux compression on the Z pulsed-power accelerator (0-20 MA in 100 ns). Each experiment consisted of an initially solid Be or Al liner (cylindrical tube), which was imploded using the Z accelerator's drive current (0-20 MA in 100 ns). The imploding liner compresses a 10-T axial seed field, B z ( 0 ) , supplied by an independently driven Helmholtz coil pair. Assuming perfect flux conservation, the axial field amplification should be well described by B z ( t ) = B z ( 0 ) x [ R ( 0 ) / R ( t )] 2 , where R is the liner's inner surface radius. With perfect flux conservation, B z ( t ) and dB z / dt values exceeding 10 4 T and 10 12 T/s, respectively, are expected. These large values, the diminishing liner volume, and the harsh environment on Z, make it particularly challenging to measure these fields. We report on our latest efforts to do so using three primary techniques: (1) micro B-dot probes to measure the fringe fields associated with flux compression, (2) streaked visible Zeeman absorption spectroscopy, and (3) fiber-based Faraday rotation. We also mention two new techniques that make use of the neutron diagnostics suite on Z. These techniques were not developed under this LDRD, but they could influence how we prioritize our efforts to diagnose magnetic flux compression on Z in the future. The first technique is based on the yield ratio of secondary DT to primary DD reactions. The second technique makes use of the secondary DT neutron time-of-flight energy spectra. Both of these techniques have been used successfully to infer the degree of magnetization at stagnation in fully integrated Magnetized Liner Inertial Fusion (MagLIF) experiments on Z [P. F. Schmit et al. , Phys. Rev. Lett. 113 , 155004 (2014); P. F. Knapp et al. , Phys. Plasmas, 22 , 056312 (2015)]. Finally, we present some recent developments for designing and fabricating novel micro B-dot probes to measure B z ( t ) inside of an imploding liner. In one approach, the micro B-dot loops were fabricated on a printed circuit board (PCB). The PCB was then soldered to off-the-shelf 0.020- inch-diameter semi-rigid coaxial cables, which were terminated with standard SMA connectors. These probes were recently tested using the COBRA pulsed power generator (0-1 MA in 100 ns) at Cornell University. In another approach, we are planning to use new multi-material 3D printing capabilities to fabricate novel micro B-dot packages. In the near future, we plan to 3D print these probes and then test them on the COBRA generator. With successful operation demonstrated at 1-MA, we will then make plans to use these probes on a 20-MA Z experiment.

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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.

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Presented are voltage measurements taken near the load region on the Z pulsed-power accelerator using an inductive voltage monitor (IVM). Specifically, the IVM was connected to, and thus monitored the voltage at, the bottom level of the accelerator's vacuum double post-hole convolute. Additional voltage and current measurements were taken at the accelerator's vacuum-insulator stack (at a radius of 1.6 m) by using standard D-dot and B-dot probes, respectively. During postprocessing, the measurements taken at the stack were translated to the location of the IVM measurements by using a lossless propagation model of the Z accelerator's magnetically insulated transmission lines (MITLs) and a lumped inductor model of the vacuum post-hole convolute. Across a wide variety of experiments conducted on the Z accelerator, the voltage histories obtained from the IVM and the lossless propagation technique agree well in overall shape and magnitude. However, large-amplitude, high-frequency oscillations are more pronounced in the IVM records. It is unclear whether these larger oscillations represent true voltage oscillations at the convolute or if they are due to noise pickup and/or transit-time effects and other resonant modes in the IVM. Results using a transit-time-correction technique and Fourier analysis support the latter. Regardless of which interpretation is correct, both true voltage oscillations and the excitement of resonant modes could be the result of transient electrical breakdowns in the post-hole convolute, though more information is required to determine definitively if such breakdowns occurred. Despite the larger oscillations in the IVM records, the general agreement found between the lossless propagation results and the results of the IVM shows that large voltages are transmitted efficiently through the MITLs on Z. These results are complementary to previous studies [R.D. McBride et al., Phys. Rev. ST Accel. Beams 13, 120401 (2010)] that showed efficient transmission of large currents through the MITLs on Z. Taken together, the two studies demonstrate the overall efficient delivery of very large electrical powers through the MITLs on Z.

Magnetically-driven, planar shockless-compression experiments to multi-megabar pressures were performed on tantalum samples using a stripline target geometry. Free-surface velocity waveforms were measured in 15 cases; nine of these in a dual-sample configuration with two samples of different thicknesses on opposing electrodes, and six in a single-sample configuration with a bare electrode opposite the sample. Details are given on the application of inverse Lagrangian analysis (ILA) to these data, including potential sources of error. The most significant source of systematic error, particularly for single-sample experiments, was found to arise from the pulse-shape dependent free-surface reflected wave interactions with the deviatoric-stress response of tantalum. This could cause local, possibly temporary, unloading of material from a ramp compressed state, and thus multi-value response in wave speed that invalidates the free-surface to in-material velocity mapping step of ILA. By averaging all 15 data sets, a final result for the principal quasi-isentrope of tantalum in stress-strain was obtained to a peak longitudinal stress of 330GPa with conservative uncertainty bounds of ±4.5% in stress. The result agrees well with a tabular equation of state developed at Los Alamos National Laboratory.

S hock compression exper iments in the few hundred GPa (multi - Mabr) regime were performed on Lithium Deuteride (LiD) single crystals . This study utilized the high velocity flyer plate capability of the Sandia Z Machine to perform impact experiments at flyer plate velocities in the range of 17 - 32 km/s. Measurements included pressure, density, and temperature between %7E200 - 600 GPa along the Principal Hugoniot - the locus of end states achievable through compression by large amplitude shock waves - as well as pressure and density of re - shock states up to %7E900 GPa . The experimental measurements are compared with recent density functional theory calculations as well as a new tabular equation of state developed at Los Alamos National Labs.

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In this article we discuss scaling the magnetically accelerated flyer plate technique to currents greater than is available on the Z accelerator. Peak flyer plate speeds in the range 7-46 km/s are achieved in pulsed power driven, hyper-velocity impact experiments on Z for peak currents in the range 8-20 MA. The highest (lowest) speeds are produced using aluminum (aluminum-copper) flyer plates. In either case, the ≈1 mm thick flyer plate is shocklessly accelerated by magnetic pressure to ballistic speed in ≈400 ns; it arrives at the target with a fraction of material at standard density. During acceleration a melt front, due to resistive heating, moves from the drive-side toward the target-side of the flyer plate; the speed of the melt front increases with increasing current. Peak flyer speeds on Z scale quadratically (linearly) with current at the low (high) end of the range. Magnetohydrodynamic simulation shows that the change in scaling is due to geometric deformation, and that linear scaling continues as current increases. However, the combined effects of shockless acceleration and resistive heating lead to an upper bound on the magnetic field feasible for pulsed power driven flyer plate experiments, which limits the maximum possible speed of a useful flyer plate to < 100 km/s. © Published under licence by IOP Publishing Ltd.

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Current pulse shaping techniques, originally developed for planar dynamic material experiments on the Z-machine [M. K. Matzen, Phys. Plasmas 12, 055503 (2005)], are adapted to the design of controlled cylindrical liner implosions. By driving these targets with a current pulse shape that prevents shock formation inside the liner, shock heating is avoided along with the corresponding decrease in electrical conductivity ahead of the magnetic diffusion wave penetrating the liner. This results in an imploding liner with a significant amount of its mass in the solid phase and at multi-megabar pressures. Pressures in the solid region of a shaped pulse driven beryllium liner fielded on the Z-machine are inferred to 5.5 Mbar, while simulations suggest implosion velocities greater than 50 kms-1. These solid liner experiments are diagnosed with multi-frame monochromatic x-ray backlighting which is used to infer the material density and pressure. This work has led to a new platform on the Z-machine that can be used to perform off-Hugoniot measurements at higher pressures than are accessible through magnetically driven planar geometries. © 2012 American Institute of Physics.

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The success of dynamic materials properties research at Sandia National Laboratories has led to research into ultra-low impedance, compact pulsed power systems capable of multi-MA shaped current pulses with rise times ranging from 220-500 ns. The Genesis design consists of two hundred and forty 200 kV, 80 kA modules connected in parallel to a solid dielectric disk transmission line and is capable of producing 280 kbar of magnetic pressure (>500 kbar pressure in high Z materials) in a 1.75 nH, 20 mm wide stripline load. Stripline loads operating under these conditions expand during the experiment resulting in a time-varying load that can impact the performance and lifetime of the system. This paper provides analysis of time-varying stripline loads and the impact of these loads on system performance. Further, an approach to reduce dielectric stress levels through active damping is presented as a means to increase system reliability and lifetime. © 2011 IEEE.

Genesis is a compact pulsed power platform designed by Sandia National Laboratories to generate precision shaped multi-MA current waves with a rise time of 200-500 ns. In this system, two hundred and forty, 200 kV, 80 kA modules are selectively triggered to produce 280 kbar of magnetic pressure (>500 kbar pressure in high Z materials) in a stripline load for dynamic materials properties research. This new capability incorporates the use of solid dielectrics to reduce system inductance and size, programmable current shaping, and gas switches that must perform over a large range of operating conditions. Research has continued on this technology base with a focus on demonstrating the integrated performance of key concepts into a Genesis-like prototype called Protogen. Protogen measures approximately 1.4 m by 1.4 m and is designed to hold twelve Genesis modules. A fixed inductance load will allow rep-rate operation for component reliability and system lifetime experiments at the extreme electric field operating conditions expected in Genesis. © 2011 IEEE.

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Magnetic Liner Inertial Fusion (MagLIF) [S. A. Slutz, et al., Phys. Plasmas 17 056303 (2010)] is a promising new concept for achieving >100 kJ of fusion yield on Z. The greatest threat to this concept is the Magneto-Rayleigh-Taylor (MRT) instability. Thus an experimental campaign has been initiated to study MRT growth in fast-imploding (<100 ns) cylindrical liners. The first sets of experiments studied aluminum liner implosions with prescribed sinusoidal perturbations (see talk by D. Sinars). By contrast, this poster presents results from the latest sets of experiments that used unperturbed beryllium (Be) liners. The purpose for using Be is that we are able to radiograph 'through' the liner using the 6-keV photons produced by the Z-Beamlet backlighting system. This has enabled us to obtain time-resolved measurements of the imploding liner's density as a function of both axial and radial location throughout the field of view. This data is allowing us to evaluate the integrity of the inside (fuel-confining) surface of the imploding liner as it approaches stagnation.

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In addressing the issue of the determining the hazard categorization of the Z Accelerator of doing Special Nuclear Material (SNM) experiments the question arose as to whether the machine could be fired with its central vacuum chamber open, thus providing a path for airborne release of SNM materials. In this report we summarize calculations that show that we could only expect a maximum current of 460 kA into such a load in a long-pulse mode, which will be used for the SNM experiments, and 750 kA in a short-pulse mode, which is not useful for these experiments. We also investigated the effect of the current for both cases and found that for neither case is the current high enough to either melt or vaporize these loads, with a melt threshold of 1.6 MA. Therefore, a necessary condition to melt, vaporize, or otherwise disperse SNM material is that a vacuum must exist in the Z vacuum chamber. Thus the vacuum chamber serves as a passive feature that prevents any airborne release during the shot, regardless of whatever containment may be in place.

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The implosion phase of a wire-array Z pinch is investigated using three-dimensional (3D) simulations, which model the mass ablation phase and its associated axial instability using a mass injection boundary condition. The physical mechanisms driving the trailing mass network are explored, and it is found that in 3D the current paths though the trailing mass can reduce bubble growth on the imploding plasma sheath, relative to the 2D (r,z) equivalent. Comparison between the simulations and a high quality set of experimental radiographs is presented. © 2008 American Institute of Physics.

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Approximate lower bounds for the kinetic energy and magnetic flux dissipation for tungsten wire arrays on the Z pulsed-power accelerator at Sandia National Laboratories [R. B. Spielman, Phys. Plasmas 5, 2105 (1998)] are obtained. A procedure, extending previous work determining pinch inductance as a function of time [E. M. Waisman, Phys. Plasmas 11, 2009 (2004)], is introduced and applied to electrical and x-ray energy measurements. It employs the pinch energy balance to determine lower bounds for the plasma kinetic energy just before the main pinch reaches the axis and for the magnetic flux dissipation during stagnation. From the lower bound for the dissipated flux, a lower bound for pinch resistance after x-ray peak power is estimated. The results of applying the introduced energy balance procedure to selected tungsten wire array implosions on Z are given. It is believed that this is the first time that a measure of wire array Z-pinch resistance at stagnation is obtained purely from data analysis without recourse to specific assumptions on the plasma motion. © 2008 American Institute of Physics.

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Using two-dimensional (2D), radiation magnetohydrodynamics (RMHD) numerical simulations, we have designed a feasible z-pinch radiation source that ignites a high yield fuel capsule in a z-pinch driven, double ended hohlraum concept. The z-pinch is composed of nested beryllium (Be) shells and a coaxial, cylindrical foam converter. The z-pinch is designed to produce a shaped radiation pulse that compresses a capsule by a sequence of three shocks without significant entropy increase. We present results of simulations pertaining to the z-pinch design, and discuss conditions that must be achieved in the z-pinch to ensure production of the required radiation pulse. © 2008 IEEE.

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The intense magnetic field generated in the 20 MA Z-machine is used to accelerate metallic flyer plates to high velocity for the purpose of generating strong shocks in equation of state experiments. We present results pertaining to experiments in which a 0.085 cm thick Al flyer plate is magnetically accelerated across a vacuum gap into a quartz target. Peak magnetic drive pressures up to 4.9 Mbar were produced, which yielded a record 34 km/s flyer velocity without destroying it by shock formation or Joule heating. Two-dimensional MHD simulation was used to optimize the magnetic drive pressure on the flyer surface, shape the current pulse to accelerate the flyer without shock formation (i.e., quasi-isentropically), and predict the flyer velocity. Shock pressures up to 11.5 Mbar were produced in quartz. Accurate measurements of the shock velocity indicate that a fraction of the flyer is at solid density when it arrives at the target. Comparison of measurements and simulation results yields a consistent picture of the flyer state at impact with the quartz target.

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The intense magnetic field produced by the 20 MA Z accelerator is used as an impulsive pressure source to accelerate metal flyer plates to high velocity for the purpose of performing plate impact, shock wave experiments. This capability has been significantly enhanced by the recently developed pulse shaping capability of Z, which enables tailoring the rise time to peak current for a specific material and drive pressure to avoid shock formation within the flyer plate during acceleration. Consequently, full advantage can be taken of the available current to achieve the maximum possible magnetic drive pressure. In this way, peak magnetic drive pressures up to 490 GPa have been produced, which shocklessly accelerated 850 {micro}m aluminum (6061-T6) flyer plates to peak velocities of 34 km/s. We discuss magnetohydrodynamic (MHD) simulations that are used to optimize the magnetic pressure for a given flyer load and to determine the shape of the current rise time that precludes shock formation within the flyer during acceleration to peak velocity. In addition, we present results pertaining to plate impact, shock wave experiments in which the aluminum flyer plates were magnetically accelerated across a vacuum gap and impacted z-cut, {alpha}-quartz targets. Accurate measurements of resulting quartz shock velocities are presented and analyzed through high-fidelity MHD simulations enhanced using optimization techniques. Results show that a fraction of the flyer remains at solid density at impact, that the fraction of material at solid density decreases with increasing magnetic pressure, and that the observed abrupt decrease in the quartz shock velocity is well correlated with the melt transition in the aluminum flyer.

A dynamic hohlraum is created when an annular z-pinch plasma implodes onto a cylindrical 0.014 g/cc 6-mm-diameter CH{sub 2} foam. The impact launches a radiating shock that propagates toward the axis at {approx}350 {micro}m/ns. The radiation trapped by the tungsten z-pinch plasma forms a {approx}200 eV hohlraum that provides X-rays for indirect drive inertial confinement fusion capsule implosion experiments. We are developing the ability to diagnose the hohlraum interior using emission and absorption spectroscopy of Si atoms added as a tracer to the central portion of the foam. Time- and space-resolved Si spectra are recorded with an elliptical crystal spectrometer viewing the cylindrical hohlraum end-on. A rectangular aperture at the end of the hohlraum restricts the field of view so that the 1D spectrometer resolution corresponds approximately to the hohlraum radial direction. This enables distinguishing between spectra from the unshocked radiation-heated foam and from the shocked foam. Typical spectral lines observed include the Si Ly{alpha} with its He-like satellites and the He-like resonance sequence including He{alpha}, He{beta}, and He{gamma}, along with some of their associated Li-like satellites. Work is in progress to infer the hohlraum conditions using collisional-radiative modeling that accounts for the radiation environment and includes both opacity effects and detailed Stark broadening calculations. These 6-mm-scale radiation-heated plasmas might eventually also prove suitable for testing Stark broadening line profile calculations or for opacity measurements.

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Z-pinch plasmas are susceptible to the magnetic Rayleigh-Taylor (MRT) instability. The Z-pinch dynamic hohlraum (ZPDH), as implemented on the Z machine at Sandia National Laboratories, is composed of an annular tungsten plasma that implodes onto a coaxial foam convertor. The collision between tungsten Z pinch and convertor launches a strong shock in the foam. Shock heating generates radiation that is trapped by the tungsten Z pinch. The radiation can be used to implode a fuel-filled, inertial confinement fusion capsule. Hence, it is important to understand the influence that the MRT instability has on shock generation. This paper presents results of an investigation to determine the affect that the MRT instability has on characteristics of the radiating shock in a ZPDH. Experiments on Z were conducted in which a 1.5 cm tall, nested array (two arrays with initial diameters of 2.0 and 4.0 cm), tungsten wire plasma implodes onto a 5 mg/cc, CH{sub 2} foam convertor to create a {approx}135 eV dynamic hohlraum. X-ray pinhole cameras viewing along the ZPDH axis recorded time and space resolved images of emission produced by the radiating shock. These measurements showed that the shock remained circular to within +/-30-60 {micro}m as it propagated towards the axis, and that it was highly uniform along its height. The measured emission intensities are compared with synthetic x-ray images obtained by postprocessing two-dimensional, radiation magnetohydrodynamic simulations in which the amplitude of MRT perturbations is varied. These simulations accurately reproduce the measured shock trajectory and spatial profiles of the dynamic hohlraum interior emission as a function of time, even for large MRT amplitudes. Furthermore, the radiating shock remains relatively uniform in the axial direction regardless of the MRT amplitude because nonuniformities are tamped by the interaction of the tungsten Z-pinch plasma with the foam. These results suggest that inertial confinement fusion implosions driven by a ZPDH should be relatively free from random radiation symmetry variations produced by Z-pinch instabilities.

Progress in understanding the physics of dynamic-hohlraums is reviewed for a system capable of generating 13 TW of axial radiation for high temperature (>200 eV) radiation-flow experiments and ICF capsule implosions.

Trends in radiation production from dynamic-hohlraums driven by single and nested wire arrays were studied. The axial radiation developed from the interior of an imploding dynamic hohlraum target was compared with that generated using a standard nested array on Z. Measurements over a range of single-array masses showed a decrease in radiation power for masses above 3.5 mg.

The intense magnetic field generated in the 20 MA Z-machine is used to accelerate metallic flyer plates to high velocity (peak velocity {approx}20-30 km/s) for the purpose of generating strong shocks (peak pressure {approx}5-10 Mb) in equation of state experiments. We have used the Sandia developed, 2D magneto-hydrodynamic (MHD) simulation code ALEGRA to investigate the physics of accelerating flyer plates using multi-megabar magnetic drive pressures. Through detailed analysis of experimental data using ALEGRA, we developed a 2D, predictive MHD model for simulating material science experiments on Z. The ALEGRA MHD model accurately produces measured time dependent flyer velocities. Details of the ALEGRA model are presented. Simulation and experimental results are compared and contrasted for shots using standard and shaped current pulses whose peak drive pressure is {approx}2 Mb. Isentropic compression of Al to 1.7 Mb is achieved by shaping the current pulse.

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Using intense magnetic pressure, a method was developed to launch flyer plates to velocities in excess of 20 km s{sup -1}. This technique was used to perform plate-impact, shock wave experiments on cryogenic liquid deuterium (LD{sub 2}) to examine its high-pressure equation of state (EOS). Using an impedance matching method, Hugoniot measurements were obtained in the pressure range of 22--100 GPa. The results of these experiments disagree with the previously reported Hugoniot measurements of LD2 in the pressure range above {approx}40 GPa, but are in good agreement with first principles, ab initio models for hydrogen and its isotopes.

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