Sapphire (Al2O3) is a major constituent of the Earth's mantle and has significant contributions to the field of high-pressure physics. Constraining its Hugoniot over a wide pressure range and identifying the location of shock-driven phase transitions allows for development of a multiphase equation of state and enables its use as an impedance-matching standard in shock physics experiments. In this paper we present measurements of the principal Hugoniot and sound velocity from direct impact experiments using magnetically launched flyers on the Z machine at Sandia National Laboratories. The Hugoniot was constrained for pressures from 0.2–2.1 TPa and a four-segment piecewise linear shock-velocity–particle-velocity fit was determined. First-principles molecular dynamics simulations were conducted and agree well with the experimental Hugoniot. Sound-speed measurements identified the onset of melt between 450 and 530 GPa, and the Hugoniot fit refined the onset to 525 ± 13 GPa. A phase diagram which incorporates literature diamond-anvil cell data and melting measurements is presented.
Fully characterizing high energy density (HED) phenomena using pulsed power facilities (Z machine) and coherent light sources is possible only with complementary numerical modeling for design, diagnostic development, and data interpretation. The exercise of creating numerical tests, that match experimental conditions, builds critical insight that is crucial for the development of a strong fundamental understanding of the physics behind HED phenomena and for the design of next generation pulsed power facilities. The persistence of electron correlation in HED materials arising from Coulomb interactions and the Pauli exclusion principle is one of the greatest challenges for accurate numerical modeling and has hitherto impeded our ability to model HED phenomena across multiple length and time scales at sufficient accuracy. An exemplar is a ferromagnetic material like iron, while familiar and widely used, we lack a simulation capability to characterize the interplay of structure and magnetic effects that govern material strength, kinetics of phase transitions and other transport properties. Herein we construct and demonstrate the Molecular-Spin Dynamics (MSD) simulation capability for iron from ambient to earth core conditions, all software advances are open source and presently available for broad usage. These methods are multi-scale in nature, direct comparisons between high fidelity density functional theory (DFT) and linear-scaling MSD simulations is done throughout this work, with advancements made to MSD allowing for electronic structure changes being reflected in classical dynamics. Main takeaways for the project include insight into the role of magnetic spins on mechanical properties and thermal conductivity, development of accurate interatomic potentials paired with spin Hamiltonians, and characterization of the high pressure melt boundary that is of critical importance to planetary modeling efforts.
Two-dimensional electromagnetic (EM) particle-in-cell (PIC) simulations of a radial magnetically-insulated-transmission-line are presented and compared to the model of E. M. Waisman, M. P. Desjarlais, and M. E. Cuneo [Phys. Rev. Accel. Beams 22, 030402 (2019) in the “high-enhancement” (WDC-HE) limit. The simulations use quasi-equilibrium current and voltage values based on the Sandia National Laboratories Z accelerator, with prescribed injection of an electron sheath that gives electron density profiles qualitatively similar to those used in the WDC-HE model. We find that the WDC-HE model accurately predicts the quasiequilibrium ion current losses in the EM PIC simulations for a wide range of current and voltage values. For the case of two ion species where one is magnetically insulated by the ambient magnetic field and the other is not, the charge of the lighter insulated species in the anode-cathode gap can modify the electric field profile, reducing the ion current density enhancement for the heavier ion species. On the other hand, for multiple ion species, when the lighter ions are not magnetically insulated and are a significant fraction of the anode plasma, they dominate the current loss, producing loss currents which are a significant fraction of the lighter ion WDC values. The observation of this effect in the present work is new to the field and may significantly impact the analysis of ion current losses in the Z machine inner MITL and convolute.
Compression-induced solidification has been observed in cerium on nanosecond timescales. A series of experiments was conducted in Sandia National Laboratories' Z Facility in which cerium was shock melted and subsequently shocklessly, or ramp, loaded across the melt line inducing solidification. The signature of solidification manifested in the recovery of material strength and the propagation of waves at the local elastic sound velocity. Density functional theory simulations of cerium along the experimental phase-space path exhibit spontaneous freezing to a tetragonal phase at the same pressure and closely predict the observed physical properties of solid and liquid cerium near melt.
Recent dynamic compression experiments [M. D. Knudson et al., Science 348, 1455 (2015); P. M. Celliers et al., Science 361, 677 (2018)] have observed the insulator-metal transition in dense liquid deuterium, but with an approximately 95-GPa difference in the quoted pressures for the transition at comparable estimated temperatures. It was claimed in the latter of these two papers that a very large latent heat effect on the temperature was overlooked in the first, requiring correction of those temperatures downward by a factor of 2, thereby putting both experiments on the same theoretical phase boundary and reconciling the pressure discrepancy. We have performed extensive path-integral molecular dynamics calculations with density functional theory to directly calculate the isentropic temperature drop due to latent heat in the insulator-metal transition for dense liquid deuterium and show that this large temperature drop is not consistent with the underlying thermodynamics.
Bailly-Grandvaux, M.; Kim, J.; Krauland, C.M.; Zhang, S.; Dozieres, M.; Wei, M.S.; Theobald, W.; Grabowski, P.E.; Santos, J.J.; Nicolai, Ph; Mckenna, P.; Desjarlais, Michael P.; Beg, F.N.
We report experimental results on relativistic electron beam (REB) transport in a set of cold and shock-heated carbon samples using the high-intensity kilojoule-class OMEGA EP laser. The REB energy distribution and transport were diagnosed using an electron spectrometer and X-ray fluorescence measurements from a Cu tracer buried at the rear side of the samples. The measured rear REB density shows brighter and narrower signals when the targets were shock-heated. Hybrid PIC simulations using advanced resistivity models in the target warm-dense-matter (WDM) conditions confirm this observation. We show that the resistivity response of the media, which governs the self-generated resistive fields, is of paramount importance to understand and correctly predict the REB transport.
Magnetically launched flyer plates were used to investigate the shock response of beryllium between 90 and 300 GPa. Solid aluminum flyer plates drove steady shocks into polycrystalline beryllium to constrain the Hugoniot from 90 to 190 GPa. Multilayered copper/aluminum flyer plates generated a shock followed by an overtaking rarefaction which was used to determine the sound velocity in both solid and liquid beryllium between 130 and 300 GPa. Disappearance of the longitudinal wave was used to identify the onset of melt along the Hugoniot and measurements were compared to density functional theory calculations to explore the proposed hcp-bcc transition at high pressure. The onset of melt along the Hugoniot was identified at ∼205GPa, which is in good agreement with theoretical predictions. These results show no clear indication of an hcp-bcc transition prior to melt along the beryllium Hugoniot. Rather, the shear stress, determined from the release wave profiles, was found to gradually decrease with stress and eventually vanish at the onset of melt.
Outstanding problems in the high-pressure phase diagram of hydrogen have demonstrated the need for more accurate ab initio methods for thermodynamic sampling. One promising method that has been deployed extensively above 100 GPa is coupled electron-ion Monte Carlo (CEIMC), which treats the electronic structure with quantum Monte Carlo (QMC). However, CEIMC predictions of the deuterium principal Hugoniot disagree significantly with experiment, overshooting the experimentally determined peak compression density by 7% and lower temperature gas-gun data by well over 20%. By deriving an equation relating the predicted Hugoniot density to underlying equation of state errors, we show that QMC and many-body methods can easily spoil the error cancellation properties inherent in the Rankine-Hugoniot relation, and very likely suffer from error addition. By cross validating QMC based on systematically improvable trial functions against post-Hartree-Fock many-body methods, we find that these methods introduce errors of the right sign and magnitude to account for much of the observed discrepancy between CEIMC and experiment. We stress that this is not just a CEIMC problem, but that thermodynamic sampling based on other many-body methods is likely to experience similar difficulties.
Celliers et al. (Reports, 17 August 2018, p. 677), in an attempt to reconcile differences in inferred metallization pressures, provide an alternative temperature analysis of the Knudson et al. experiments (Reports, 26 June 2015, p. 1455). We show here that this reanalysis implies an anomalously low specific heat for the metallic fluid that is clearly inconsistent with first-principles calculations.
We introduce a 1D planar static model to elucidate the underlying mechanism of large ion current losses in the vacuum convolute and the inner magnetically insulated transmission line (MITL) of the Z machine. We consider E×B electron flow, parallel to the electrodes, and ion motion across the vacuum gap, for given voltage V, gap distance d, anode magnetic field Ba, and vacuum electron current ΔI. This model has been introduced and solved before by Desjarlais [Phys. Rev. Lett. 59, 2295 (1987)PRLTAO0031-900710.1103/PhysRevLett.59.2295] for the applied magnetic field ion diode. Here we apply it to convolute and inner MITL ion losses of Z, relaxing the fix magnetic flux condition of that reference. In the absence of ions we show that the electron vacuum flow must be close to the anode if its current exceeds the value given by the local flow impedance, implying high electric fields there. We then introduce space charge limited ion emission from the anode, neglecting the magnetic force on ions. We obtain the solution of the steady state equations for two special cases: (a) when both the electric potential and the electric field are zero inside the gap, and there is a layer of electrons not carrying current that neutralizes the ion charge between the virtual and the electrode cathode, making that region electric field free, and (b) when the electric field is zero inside the gap, but the potential is not, and zero electron charge between that point and the physical cathode. For case (a) we obtain an ion current density which we conjecture is the maximum attainable for any electron charge distribution in the electron current carrying layer, given V,d,Ba,ΔI an ion species. We obtain the enhancement factor for both cases with respect to the ion-only Child-Langmuir ion current density, and show that it can be significantly larger than that of the electron saturated flow case. Furthermore, imposing electron current conservation as the flow enters the inner MITL from the four outer MITLs, we recover the well-known dependence jion∼V3/2/d2, where voltage and gap are taken near the joining point of those outer MITLs. The implications and limitations of the proposed model are discussed.