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Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data. rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange-correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principle PIMC and DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions.

We present results from X-ray imaging of high-aspect-ratio magnetic reconnection experiments driven at the National Ignition Facility. Two parallel, self-magnetized, elongated laser-driven plumes are produced by tiling 40 laser beams. A magnetic reconnection layer is formed by the collision of the plumes. A gated X-ray framing pinhole camera with micro-channel plate (MCP) detector produces multiple images through various filters of the formation and evolution of both the plumes and current sheet. As the diagnostic integrates plasma self-emission along the line of sight, 2-dimensional electron temperature maps $\langle T_e \rangle_Y$ are constructed by taking the ratio of intensity of these images obtained with different filters. The plumes have a characteristic temperature $\langle T_e \rangle_Y = 240 \pm 20$ eV at 2 ns after the initial laser irradiation and exhibit a slow cooling up to 4 ns. The reconnection layer forms at 3 ns with a temperature $\langle T_e \rangle_Y = 280 \pm 50$ eV as the result of the collision of the plumes. The error bars of the plumes and current sheet temperatures separate at $4$ ns, showing the heating of the current sheet from colder inflows. Using a semi-analytical model, we find that the observed heating of the current sheet is consistent with being produced by electron-ion drag, rather than the conversion of magnetic to kinetic energy., Comment: Submitted to Physics of Plasmas. 19 pages (total), 14 figures, 2 tables

Ionic structure of high pressure, high temperature fluids is a challenging theoretical problem with applications to planetary interiors and fusion capsules. Here we report a multi-messenger platform using velocimetry and \textit{in situ} angularly and spectrally resolved X-ray scattering to measure the thermodynamic conditions and ion structure factor of materials at extreme pressures. We document the pressure, density, and temperature of shocked silicon near 100 GPa with uncertainties of 6%, 2%, and 20%, respectively. The measurements are sufficient to distinguish between and rule out some ion screening models., Comment: Main Paper: 5 pages, 4 figures. Supplementary Material: 9 pages, 8 figures

By applying auxiliary-field quantum Monte Carlo, we calculate the equation of state (EOS) and B1-B2 phase transition of magnesium oxide (MgO) up to 1 TPa. The results agree with available experimental data at low pressures and are used to benchmark the performance of various exchange-correlation functionals in density functional theory calculations. We determine PBEsol is an optimal choice for the exchange-correlation functional and perform extensive phonon and quantum molecular-dynamics calculations to obtain the thermal EOS. Our results provide a preliminary reference for the EOS and B1-B2 phase boundary of MgO from zero up to 10,500 K., Comment: 41 pages (single column), 16 figures, 4 tables

First-principles calculations and analysis of the thermodynamic, structural, and electronic properties of liquid SiO$_2$ characterize the bonded-to-atomic transition at 0.1--1.6 TPa and 10$^4$--10$^5$ K (1--7 eV), the high-energy-density regime relevant to understanding planetary interiors. We find strong ionic bonds that become short-lived due to high kinetics during the transition, with sensitivity of the transition temperature to pressure, and our calculated Hugoniots agree with past experimental data. These results reconcile previous experimental and theoretical findings by clarifying the nature of the bond dissociation process in early Earth and "rocky" (oxide) constituents of large planets., Comment: 11 pages, 11 figures

Magnetic reconnection can explosively release magnetic energy when opposing magnetic fields merge and annihilate through a current sheet, driving plasma jets and accelerating non-thermal particle populations to high energy, in plasmas ranging from space and astrophysical to laboratory scales. Through laboratory experiments and spacecraft observations, significant experimental progress has been made in demonstrating how fast dissipation and reconnection occurs in narrow, kinetic-scale current sheets. However, a challenge has been to demonstrate what triggers reconnection and how it proceeds rapidly and efficiently as part of a global system much larger than these kinetic scales. Here we show experimentally the full development of a process where the current sheet forms and then breaks up into multiple current-carrying structures at the ion kinetic scale. The results are consistent with tearing of the current sheet, however modified by collisionless kinetic ion effects, which leads to a larger growth rate and number of plasmoids than observed in previous experiments or compared to predictions from standard tearing instability theory and previous non-linear kinetic reconnection simulations. This effect will increase the role of plasmoid instabilities in many natural reconnection systems and should be considered in triggering rapid reconnection in a broad range of natural plasmas with collisionless, compressible flows, including at the Earth's magnetosheath and magnetotail and at the heliopause, in accretion disks, and in turbulent high-Mach-number collisionless shocks., Comment: 18 pages, 4 figures, with Supplementary materials

Warm dense matter (WMD) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM needs to be created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. Time-Dependent Density Functional Theory (TD-DFT), often intractable. We have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping acr

The design of inertial confinement fusion (ICF) ignition targets requires radiation-hydrodynamics simulations with accurate models of the fundamental material properties (i.e., equation of state, opacity, and conductivity). Validation of these models are required via experimentation. A feasibility study of using spatially-integrated, spectrally-resolved, X-ray Thomson scattering (XRTS) measurements to diagnose the temperature, density, and ionization of the compressed DT shell and hot spot of a laser direct-drive implosion at two-thirds convergence was conducted. Synthetic scattering spectra were generated using 1-D implosion simulations from the LILAC code that were post processed with the X-ray Scattering (XRS) model which is incorporated within SPECT3D. Analysis of two extreme adiabat capsule conditions showed that the plasma conditions for both compressed DT shells could be resolved., Comment: 11 pages, 8 figures

The liquid-liquid phase transition in high-pressure Hydrogen is a problem of longstanding and controversy. The recent Nature paper by Cheng et al. [vol. 585, p. 217] makes a set of strong claims to the effect that all the previous density functional theory molecular dynamics (MD-DFT) and quantum Monte Carlo calculations of that transition are incorrect because of finite size effects and, in the MD-DFT case, short run times. The basis of those claims is their use of large systems and long durations for classical MD driven by a machine-learnt potential (MLP) which they developed. The straightforward test of their claims is to do MD-DFT on systems as large or larger than Cheng et al. used and for significantly longer durations than in the previous MD-DFT simulations. We have done so and find that neither diagnosis of theirs (size effects, duration limits) is correct. Instead, we find that the MLP does not drive MD in fidelity with the underlying DFT electronic structure that it is supposed to replicate. The result is that the MLP-driven MD results are artifactual, not systematically connected to the theoretical underpinning on which the MLP was trained.

To understand the most-recent experiment on room-temperature superconductivity in carbonaceous sulfur hydride (CSH) systems under high pressure, we have performed extensive stoichiometry and structure searches of ternary CSH compounds using generic evolutionary algorithms. Judged from the formation enthalpy of different CSH compounds, our studies conclude that certain levels of carbon doping (~5%-6%) in sulfur hydride (H$_3$S) in its R3m and phases gives rise to the most-stable structure (second to the H$_3$S itself) among the various CSH systems found. The replacement of a small amount of sulfur atoms by carbon in compounds like C$_1$S$_{15}$H$_{48}$ and C$_1$S$_{17}$H$_{54}$ results in a stronger electron-phonon coupling and a higher averaged phonon frequency that increases with pressure, thereby leading to room-temperature superconductivity at ~270 GPa. The calculated superconducting transition temperature T$_c$ of C$_1$S$_{15}$H$_{48}$ and C$_1$S$_{17}$H$_{54}$ as a function of pressure shows reasonably good agreement with experimental measurements. Before transition to superconducting states at ~80 GPa, the CSH system is predicted to have a stoichiometry of C$_2$S$_2$H$_{10}$ with a stable structure of P1 symmetry, which is supported by the direct comparison of its Raman spectrum with experiment., Comment: 23 pages with 8 figures (with Supplementary Material)

We present the results of the first Charged-Particle Transport Coefficient Code Comparison Workshop, which was held in Albuquerque, NM October 4-6, 2016. In this first workshop, scientists from eight institutions and four countries gathered to compare calculations of transport coefficients including thermal and electrical conduction, electron-ion coupling, inter-ion diffusion, ion viscosity, and charged particle stopping powers. Here, we give general background on Coulomb coupling and computational expense, review where some transport coefficients appear in hydrodynamic equations, and present the submitted data. Large variations are found when either the relevant Coulomb coupling parameter is large or computational expense causes difficulties. Understanding the general accuracy and uncertainty associated with such transport coefficients is important for quantifying errors in hydrodynamic simulations of inertial confinement fusion and high-energy density experiments., Comment: 45 pages, 17 figures

A microphysics model to describe the photoionization and impact ionization processes in dielectric ablator materials like plastic has been implemented into the one-dimensional hydrodynamic code LILAC for planar and spherical targets. At present, the initial plasma formation during the early stages of a laser drive is modeled in an ad hoc manner, until the formation of a critical surface. Implementation of the physics-based models predicts higher values of electron temperature and pressure than the ad hoc model. Moreover, the numerical predictions are consistent with previous experimental observations of the shine-through mechanism in plastic ablators. For planar targets, a decompression of the rear end of the target was observed that is similar to recent experiments. An application of this model is to understand the laser-imprint mechanism that is caused by nonuniform laser irradiation due to a single beam speckle.

Fast magnetic reconnection was observed between magnetized laser-produced plasmas at the National Ignition Facility. Two highly-elongated plasma plumes were produced by tiling two rows of lasers, with magnetic fields generated in each plume by the Biermann battery effect. Detailed magnetic field observations, obtained from proton radiography using a D$^3$He capsule implosion, reveal reconnection occurring in an extended, quasi-1D current sheet with large aspect ratio $\sim 100$. The 1-D geometry allowed a rigorous and unique reconstruction of the magnetic field, which showed a reconnection current sheet that thinned down to a half-width close to the electron gyro-scale. Despite the large aspect ratio, a large fraction of the magnetic flux reconnected, suggesting fast reconnection supported by the non-gyrotropic electron pressure tensor., Comment: 5 pages, 5 Figures, Supplementary Info

Using conceptually and procedurally consistent density functional theory (DFT) calculations with an advanced meta-GGA exchange-correlation functional in ab initio molecular dynamics simulations, we determine the insulator-metal transition (IMT) of warm dense fluid hydrogen over the pressure range 50 to 300 GPa. Inclusion of nuclear quantum effects via path-integral molecular dynamics (PIMD) sharpens the metallic transition and lowers the transition temperature relative to results from Born-Oppenheimer (BO) MD. BOMD itself gives improved agreement with experimental results compared to previous DFT predictions. Examination of the ionic pair correlation function in the context of the abrupt conductivity increase at the transition confirms a metallic transition due to the dissociation of molecular hydrogen that coincides with an abrupt band gap closure. Direct comparison of the PIMD and BOMD results clearly demonstrates an isotope effect on the IMT. Distinct from stochastic simulations, these results do not depend upon any ad hoc combination of ground-state and finite-T methodologies.

Perturbations in the velocity profile of a laser-ablation-driven shock wave seeded by speckle in the spatial beam intensity (i.e., laser imprint) have been measured. Direct measurements of these velocity perturbations were recorded using a two-dimensional high-resolution velocimeter probing plastic material shocked by a 100-ps picket laser pulse from the OMEGA laser system. The measured results for experiments with one, two, and five overlapping beams incident on the target clearly demonstrate a reduction in long-wavelength ($>$25 um) perturbations with an increasing number of overlapping laser beams, consistent with theoretical expectations. These experimental measurements are crucial to validate radiation-hydrodynamics simulations of laser imprint for laser direct drive inertial confinement fusion research since they highlight the significant (factor of 3) underestimation of the level of seeded perturbation when the microphysics processes for initial plasma formation, such as multiphoton ionization are neglected., Comment: 6 pages, 5 figures

Refraction-enhanced x-ray radiography (REXR) is used to infer shock-wave positions of more than one shock wave, launched by a multiple-picket pulse in a planar plastic foil. This includes locating shock waves before the shocks merge, during the early time and the main drive of the laser pulse that is not possible with the velocity interferometer system for any reflector. Simulations presented in this paper of REXR show that it is necessary to incorporate refraction and attenuation of x rays along with the appropriate opacity and refractive-index tables to interpret experimental images. Simulated REXR shows good agreement with an experiment done on the OMEGA laser facility to image a shock wave. REXR can be applied to design multiple-picket pulses with a better understanding of the shock locations. This will be beneficial to obtain the required adiabats for inertial confinement fusion implosions.

We are reporting the observation of the breakdown of electrons degeneracy and emergence of classical statistics in the simplest element: metallic deuterium. We have studied the optical reflectance, shock velocity and temperature of dynamically compressed liquid deuterium up to its Fermi temperature, TF. Above the insulator-metal transition, the optical reflectance shows the distinctive temperature-independent resistivity saturation, which is prescribed by Mott minimum metallic limit, in agreement with previous experiments. At T > 0.4 TF, however, the reflectance of metallic deuterium starts to rise with a temperature-dependent slope, consistent with the breakdown of the Fermi surface. The experimentally inferred collisional time in this region exhibits the characteristic temperature dependence expected for classical Landau-Spitzer plasma. Our observation of electron degeneracy lifting extends studies of degeneracy to new fermionic species, electron Fermi systems and offers an invaluable benchmark for quantum statistical models of Coulomb systems over a wide range of temperatures relevant to dense astrophysical objects and ignition physics., Comment: 16 pages, 4 figures Accepted in PRL

A theoretical model based on the method of super transition arrays (STA) is used to compute the emissivities, opacities and average ionization states of carbon (C) and polystyrene (CH) plasmas in the warm-dense matter regime in which the coupling constant varies between 0.02 to 2.0. The accuracy of results of STA calculations is assessed by benchmarking against the available experimental data and results obtained using other theoretical methods, assuming that a state of local thermodynamic equilibrium exists in the plasma. In the case of a carbon plasma, the STA method yields spectral features that are in reasonably-good agreement with Dirac-Fock and Hartree-Fock-Slater theories; in the case of CH, we find that STA-derived opacities are very similar to those derived using quantum-molecular-dynamics density-functional theory and Hartree-Fock method down to plasma temperature of about 20 eV. Our calculations also compare favorably with available experimental measurements of Gamboa {\it et al} [High Energy Density Phys. {\bf 11}, 75 (2014)] of the plasma temperature and average ionization state behind a blast wave in a pure carbon foam. Although the STA-computed average-ionization charge state in the rarefaction region appears to be lower than the experimental data, it is within the experimental uncertainty and the discrepancy is nevertheless consistent with results reported using an atomic kinetic model. In addition, we further predict the temperature dependence of average ionization states of CH plasma in the same temperature range as for the carbon plasma., Comment: 17 pages, 9 figures. Typos have been corrected

Recent laboratory experiments with laser-produced plasmas have observed and studied a number of fundamental physical processes relevant to magnetized astrophysical plasmas, including magnetic reconnection, collisionless shocks, and magnetic field generation by Weibel instability, opening up new experimental platforms for laboratory astrophysics. We develop a fully kinetic simulation model for first-principles simulation of these systems including the dynamics of magnetic fields---magnetic field generation by the Biermann battery effect or Weibel instability; advection by the ion flow, Hall effect, and Nernst effect; and destruction of the field by dissipative mechanisms. Key dimensionless parameters describing the system are derived for scaling between kinetic simulation, recent experiments, and astrophysical plasmas. First, simulations are presented which model Biermann battery magnetic field generation in plasmas expanding from a thin target. Ablation of two neighboring plumes leads to the formation of a current sheet as the opposing Biermann-generated fields collide, modeling recent laser-driven magnetic reconnection experiments. Second, we simulate recent experiments on collisionless magnetized shock generation, by expanding a piston plasma into a pre-magnetized ambient plasma. For parameters considered, the Biermann effect generates additional magnetic fields in the curved shock front and thereby increases shock particle reflection. Both cases show the importance of kinetic processes in the interaction of plasmas with magnetic fields, and open opportunities to benchmark these important processes through comparison of theory and experiments., Comment: 17 pages, 6 figures

The molecular dynamics of solid benzene are extremely complex; especially below 77 K, its inner mechanics remain mostly unexplored. Benzene is also a prototypical molecular crystal that becomes energetically frustrated at low temperatures and usually unusual phenomena accompanies such scenarios. We performed dielectric constant measurements on solid benzene down to 5 K and observed a previously unidentified minimum in the imaginary part of the dielectric constant at Tm=17.9 K. Results obtained on deuterated solid benzene (C6D6, where D is deuterium) show an isotope effect in the form of a shift of the critical temperature to Tm'=18.9 K. Our findings indicate that at Tm, only the protons without the carbon atoms continue again to undergo rotational tunneling about the hexad axes. The deuterons appear to do the same accounting for an indirect observation of a continued and sustained 12-body tunneling event. We discuss how similar experiments performed on hydrogen-based molecular crystals can be exploited to help us obtain more insight on the quantum mechanics of many-body tunneling., Comment: 8 pages (12 font, single spaced), 4 figures

Shock compression of silicon (Si) under extremely high pressures (>100 Mbar) was investigated by using two first-principles methods of orbital-free molecular dynamics (OFMD) and path integral Monte Carlo (PIMC). While pressures from the two methods agree very well, PIMC predicts a second compression maximum because of 1s electron ionization that is absent in OFMD calculations since Thomas-Fermi-based theories lack shell structure. The Kohn-Sham density functional theory is used to calculate the equation of state (EOS) of warm dense silicon for low-pressure loadings (P < 100 Mbar). Combining these first-principles EOS results, the principal shock Hugoniot curve of silicon for pressures varying from 1 Mbar to above 10 Gbar was derived. We find that silicon is 20% or more softer than what was predicted by widely-used EOS models. Existing high-pressure experimental data (P = 1 - 2 Mbar) seem to indicate this softening behavior of Si, which calls for future strong-shock experiments (P > 10 Mbar) to benchmark our results., Comment: 30 pages, 6 figures

Filamentation due to the growth of a Weibel-type instability was observed in the interaction of a pair of counter-streaming, ablatively-driven plasma flows, in a supersonic, collisionless regime relevant to astrophysical collisionless shocks. The flows were created by irradiating a pair of opposing plastic (CH) foils with 1.8 kJ, 2-ns laser pulses on the OMEGA EP laser system. Ultrafast laser-driven proton radiography was used to image the Weibel-generated electromagnetic fields. The experimental observations are in good agreement with the analytical theory of the Weibel instability and with particle-in-cell simulations., Comment: Submitted to PRL

Understanding and designing inertial confinement fusion (ICF) implosions through radiation-hydrodynamics simulations rely on the accurate knowledge of the equation of state (EOS) of the deuterium and tritium fuels. To minimize the drive energy for ignition, the imploding shell of DT fuel must be kept as cold as possible. Such low-adiabat ICF implosions can access to coupled and degenerate plasma conditions, in which the analytical or chemical EOS models become inaccurate. Using the path-integral Monte Carlo (PIMC) simulations we have derived a first-principles EOS (FPEOS) table of deuterium that covers typical ICF fuel conditions at densities ranging from 0.002 to 1596 g/cm3 and temperatures of 1.35 eV to 5.5 keV. We report the internal energy and the pressure, and discuss the structure of the plasma in terms of pair-correlation functions. When compared with the widely used SESAME table and the revised Kerley03 table, discrepancies in the internal energy and in the pressure are identified for moderately coupled and degenerate plasma conditions. In contrast to the SESAME table, the revised Kerley03 table is in better agreement with our FPEOS results over a wide range of densities and temperatures. Although subtle differences still exist for lower temperatures (T < 10 eV) and moderate densities (1 to 10 g/cc), hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table and the Kerley03 table have resulted in similar results for the peak density, areal density ({\rho}R), and neutron yield, which are significantly different from the SESAME simulations., Comment: 15 pages, 18 figures, 1 long table

Full, three dimensional, time-dependent simulations are presented demonstrating the quantized transfer of angular momentum to a Bose-Einstein condensate from a laser carrying orbital angular momentum in a Laguerre-Gaussian mode. The process is described in terms of coherent Bragg scattering of atoms from a chiral optical lattice. The transfer efficiency and the angular momentum content of the output coupled vortex state are analyzed and compared with a recent experiment., Comment: 4 pages, 4 figures

We study the density modulation that appears in a Bose-Einstein condensate flowing with supersonic velocity against an obstacle. The experimental density profiles observed at JILA are reproduced by a numerical integration of the Gross-Pitaevskii equation and then interpreted in terms of Cerenkov emission of Bogoliubov excitations by the defect. The phonon and the single-particle regions of the Bogoliubov spectrum are respectively responsible for a conical wavefront and a fan-shaped series of precursors.