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The study of matter at extreme densities and temperatures as they occur in astrophysical objects and state-of-the-art experiments with high-intensity lasers is of high current interest for many applications. While no overarching theory for this regime exists, accurate data for the density response of correlated electrons to an external perturbation are of paramount importance. In this context, the key quantity is given by the local field correction (LFC), which provides a wave-vector resolved description of exchange-correlation effects. In this work, we present extensive new path integral Monte Carlo (PIMC) results for the static LFC of the uniform electron gas, which are subsequently used to train a fully connected deep neural network. This allows us to present a representation of the LFC with respect to continuous wave-vectors, densities, and temperatures covering the entire warm dense matter regime. Both the PIMC data and neural-net results are available online. Moreover, we expect the presented combination of ab initio calculations with machine-learning methods to be a promising strategy for many applications. [ABSTRACT FROM AUTHOR]

The gravitational pressure in many astrophysical objects exceeds one gigabar (one billion atmospheres)1–3, creating extreme conditions where the distance between nuclei approaches the size of the K shell. This close proximity modifies these tightly bound states and, above a certain pressure, drives them into a delocalized state4. Both processes substantially affect the equation of state and radiation transport and, therefore, the structure and evolution of these objects. Still, our understanding of this transition is far from satisfactory and experimental data are sparse. Here we report on experiments that create and diagnose matter at pressures exceeding three gigabars at the National Ignition Facility5 where 184 laser beams imploded a beryllium shell. Bright X-ray flashes enable precision radiography and X-ray Thomson scattering that reveal both the macroscopic conditions and the microscopic states. The data show clear signs of quantum-degenerate electrons in states reaching 30 times compression, and a temperature of around two million kelvins. At the most extreme conditions, we observe strongly reduced elastic scattering, which mainly originates from K-shell electrons. We attribute this reduction to the onset of delocalization of the remaining K-shell electron. With this interpretation, the ion charge inferred from the scattering data agrees well with ab initio simulations, but it is significantly higher than widely used analytical models predict6.Experiments at the National Ignition Facility show how delocalization of K-shell electrons is driven by extreme pressure and temperature. [ABSTRACT FROM AUTHOR]

Calculations of Debye-Scherrer diffraction patterns from polycrystalline materials have typically been done in the limit of small deviatoric stresses. Although these methods are well suited for experiments conducted near hydrostatic conditions, more robust models are required to diagnose the large strain anisotropies present in dynamic compression experiments. A method to predict Debye-Scherrer diffraction patterns for arbitrary strains has been presented in the Voigt (iso-strain) limit [Higginbotham, J. Appl. Phys. 115, 174906 (2014)]. Here, we present a method to calculate Debye-Scherrer diffraction patterns from highly stressed polycrystalline samples in the Reuss (iso-stress) limit. This analysis uses elastic constants to calculate lattice strains for all initial crystallite orientations, enabling elastic anisotropy and sample texture effects to be modeled directly. The effects of probing geometry, deviatoric stresses, and sample texture are demonstrated and compared to Voigt limit predictions. An example of shock-compressed polycrystalline diamond is presented to illustrate how this model can be applied and demonstrates the importance of including material strength when interpreting diffraction in dynamic compression experiments. [ABSTRACT FROM AUTHOR]

We compare calculations for the energy loss of α-particles and the electron-ion energy transfer rate in high-density hydrogen plasmas at conditions similar to the compressed main fuel in ICF targets. Different models, which do and do not account for collective effects and electron degeneracy, are considered. It is shown that quantum degeneracy in the cold fuel significantly lowers the energy deposition of the α-particles at the high densities of ICF targets. Electron degeneracy is also important for the electron-ion energy transfer where collective modes can play an important role as well.

We investigate the influence of various ionic structure models on the interpretation of the X-ray Thomson scattering signal. For the calculation of the ion structure, classical hypernetted chain equations are used applying different effective inter-particle potentials. It is shown that the different models lead to significant discrepancies in the theoretically predicted weight of the Rayleigh peak, in particular for small k-values where correlation effects are important. Here, we propose conditions which might allow for an experimental verification of the theories under consideration of experimental constraints of k-vector blurring.

We investigate the effect of non-equilibrium electron distributions in the analysis of Thomson scattering for a range of conditions of interest to inertial confinement fusion experiments. Firstly, a generalised one-component model based on quantum statistical theory is given in the random phase approximation (RPA). The Chihara expression for electron-ion plasmas is then adapted to include the new non-equilibrium electron physics. The theoretical scattering spectra for both diffuse and dense plasmas in which non-equilibrium electron distributions are expected to arise are considered. We find that such distributions strongly influence the spectra and are hence an important consideration for accurately determining the plasma conditions.

We determine the strength of laser shock-compressed polycrystalline diamond at stresses above the Hugoniot elastic limit using a technique combining x-ray diffraction from the Linac Coherent Light Source with velocity interferometry. X-ray diffraction is used to measure lattice strains, and velocity interferometry is used to infer shock and particle velocities. These measurements, combined with density-dependent elastic constants calculated using density functional theory, enable determination of material strength above the Hugoniot elastic limit. Our results indicate that diamond retains approximately 20 GPa of strength at longitudinal stresses of 150–300 GPa under shock compression. [ABSTRACT FROM AUTHOR]

Warm dense matter (WDM)—an exotic state of highly compressed matter—has attracted increased interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations, and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first ab initio data for the exchange–correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations; for recent reviews, see Dornheim et al., Phys. Plasmas 24, 056303 (2017) and Phys. Rep. 744, 1–86 (2018). In the present article, we review recent further progress in QMC simulations of the warm dense UEG: namely, ab initio results for the static local field correction G(q) and for the dynamic structure factor S (q , ω). These data are of key relevance for comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models. In the second part of this paper, we discuss the simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, time-dependent DFT, and hydrodynamics. Here, we analyze the strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method. [ABSTRACT FROM AUTHOR]

We present measurements of the complex ion structure of warm dense carbon close to the melting line at pressures around 100GPa. High-pressure samples were created by laser-driven shock compression of graphite and probed by intense laser-generated x-ray sources with photon energies of 4.75 keV and 4.95 keV. High-efficiency crystal spectrometers allow for spectrally resolving the scattered radiation. Comparing the ratio of elastically and inelastically scattered radiation, we find evidence for a complex bonded liquid that is predicted by ab-initio quantum simulations showing the influence of chemical bonds under these conditions. Using graphite samples of different initial densities we demonstrate the capability of spectrally resolved x-ray scattering to monitor the carbon solid-liquid transition at relatively constant pressure of 150 GPa. Showing first single-pulse scattering spectra from cold graphite of unprecedented quality recorded at the Linac Coherent Light Source, we demonstrate the outstanding possibilities for future high-precision measurements at 4th Generation Light Sources. [ABSTRACT FROM AUTHOR]

Strong plasmon resonances characteristics of electron density fluctuations have recently been observed in dynamically compressed diamond for the first time at the Linac Coherent Light Source. These experiments observe the forward scattering spectra from 8 keV x-ray pulses at record peak brightness to probe laser-compressed diamond foils at the Matter in Extreme Conditions instrument. We demonstrate single-shot measurements of the x-ray scattering spectrum, which are sensitive to the temperatures and densities of the compressed samples. The inferred values from the inelastic scattering are compared to simulations, finding good agreement with the temperature and demonstrating the need to include solid state effects in the modeling of the plasmon oscillation. [ABSTRACT FROM AUTHOR]

In megabar shock waves, materials compress and undergo a phase transition to a dense charged-particle system that is dominated by strong correlations and quantum effects. This complex state, known as warm dense matter, exists in planetary interiors and many laboratory experiments (for example, during high-power laser interactions with solids or the compression phase of inertial confinement fusion implosions). Here, we apply record peak brightness X-rays at the Linac Coherent Light Source to resolve ionic interactions at atomic (ångström) scale lengths and to determine their physical properties. Our in situ measurements characterize the compressed lattice and resolve the transition to warm dense matter, demonstrating that short-range repulsion between ions must be accounted for to obtain accurate structure factor and equation of state data. In addition, the unique properties of the X-ray laser provide plasmon spectra that yield the temperature and density with unprecedented precision at micrometre-scale resolution in dynamic compression experiments. [ABSTRACT FROM AUTHOR]

It is demonstrated how the static electron-electron structure factor in warm dense matter can be obtained from density functional theory in combination with quantum Monte Carlo data. In contrast to theories assuming well-separated bound and free states, this ah initio approach yields also valid results for systems close to the Mott transition (pressure ionization), where bound states are strongly modified and merge with the continuum. The approach is applied to x-ray Thomson scattering and compared to predictions of the Chihara formula whereby we use the ion-ion and electron-ion structure from the same simulations. The results show significant deviations of the screening cloud from the often applied Debye-like form. [ABSTRACT FROM AUTHOR]

We have developed a model for analysing x-ray Thomson scattering data from high-density, millimetre- scale inhomogeneous plasmas created during ultra-high pressure implosions at the National Ignition Facility in a spherically convergent geometry. The density weighting of the scattered signal and attenuation of the incident and scattered x-rays throughout the target are included using radial profiles of the density, opacity, ionization state, and temperature provided by radiationhydrodynamics simulations. These simulations show that the scattered signal is strongly weighted toward the bulk of the shocked plasma and the Fermi degenerate material near the ablation front. We show that the scattered signal provides a good representation of the temperature of this highly nonuniform bulk plasma and can be determined to an accuracy of ca. 15% using typical data analysis techniques with simple 0D calculations. On the other hand, the mean ionization of the carbon in the bulk is underestimated. We suggest that this discrepancy is due to the convolution of scattering profiles from different regions of the target. Subsequently, we discuss modifications to the current platform to minimise the impact of inhomogeneities, as well as opacity, and also to enable probing of conditions more strongly weighted toward the compressed core. [ABSTRACT FROM AUTHOR]

Using simultaneous spectrally, angularly, and temporally resolved x-ray scattering, we measure the pronounced ion-ion correlation peak in a strongly coupled plasma. Laser-driven shock-compressed aluminum at ~3× solid density is probed with high-energy photons at 17.9 keV created by molybdenum He-α emission in a laser-driven plasma source. The measured elastic scattering feature shows a well-pronounced correlation peak at a wave vector of k = 4Å -1. The magnitude of this correlation peak cannot be described by standard plasma theories employing a linear screened Coulomb potential. Advanced models, including a strong short-range repulsion due to the inner structure of the aluminum ions are however in good agreement with the scattering data. These studies have demonstrated a new highly accurate diagnostic technique to directly measure the state of compression and the ion-ion correlations. We have since applied this new method in single-shot wave-number resolved S(k) measurements to characterize the physical properties of dense plasmas. [ABSTRACT FROM AUTHOR]

We present the first direct experimental test of the complex ion structure in liquid carbon at pressures around 100 GPa, using spectrally resolved x-ray scattering from shock-compressed graphite samples. Our results confirm the structure predicted by ab initio quantum simulations and demonstrate the importance of chemical bonds at extreme conditions similar to those found in the interiors of giant planets. The evidence presented here thus provides a firmer ground for modeling the evolution and current structure of carbon-bearing icy giants like Neptune, Uranus, and a number of extrasolar planets. [ABSTRACT FROM AUTHOR]

We present a reduced model for the energy transfer via coupled collective modes in two-temperature plasmas based on quantum statistical theory. The model is compared with exact numerical evaluations of the coupled-mode (CM) energy transfer rate and with alternative reduced approaches over a range of conditions in the warm dense matter (WDM) and inertial confinement fusion (ICF) regimes. Our approach shows excellent agreement with an exact treatment of the CM rate and supports the importance of the coupled-mode effect for the temperature and energy relaxation in WDM and ICF plasmas. We find that electronic damping of collective ion density fluctuations is crucial for correctly describing the mode spectrum and, thus, the energy exchange. The reduced CM approach is studied over a wide parameter space, enabling us to establish its limits of applicability. [ABSTRACT FROM AUTHOR]

Proof-of-principle measurements of the electron densities, temperatures, and ionization states of spherically compressed multi-shocked CH (polystyrene) capsules have been achieved using spectrally resolved x-ray Thomson scattering. A total energy of 13.5 kJ incident on target is used to compress a 70 μm thick CH shell above solid-mass density using three coalescing shocks. Separately, a laser-produced zinc He-α x-ray source at 9 keV delayed 200 ps-800 ps after maximum compression is used to probe the plasma in the non-collective scattering regime. The data show that x-ray Thomson scattering enables a complete description of the time-dependent hydrodynamic evolution of shock-compressed CH capsules, with a maximum measured density of ρ > 6 g cm-3. In addition, the results demonstrate that accurate measurements of x-ray scattering from bound-free transitions in the CH plasma demonstrate strong evidence that continuum lowering is the primary ionization mechanism of carbon L-shell electrons. [ABSTRACT FROM AUTHOR]

The dynamics of the ion structure in warm dense matter is determined by molecular dynamics simulations using an effective ion-ion potential. This potential is obtained from ab initio simulations and has a strong short-range repulsion added to a screened Coulomb potential. Models based on static or dynamic local field corrections are found to be insufficient to describe the data. An extended Mermin approach, a hydrodynamic model, and the method of moments with local constraints are capable of reproducing the numerical results but have rather limited predictive powers as they all need some numerical data as input. The method of moments is found to be the most promising. [ABSTRACT FROM AUTHOR]

Abstract: We combine experiments and theoretical models to characterize warm dense deuterium. A shockwave was driven in a planar target by the OMEGA laser without a standard pusher making the analysis independent of a quartz or aluminium pressure standard. The conditions of the shocked material were diagnosed with VISAR and optical pyrometry which yields the shock velocity (16.9 ± 0.9 km/s) and the temperature (0.57 ± 0.05 eV). We find a self-consistent description of the data when using ab initio simulations (DFT-MD), but not for other equation of state (EOS) models tested. [Copyright &y& Elsevier]

The effects of collective modes on the temperature relaxation in fully ionized, weakly coupled plasmas are investigated. A coupled mode (CM) formula for the electron-ion energy transfer is derived within the random phase approximation and it is shown how it can be evaluated using standard methods. The CM rates are considerably smaller than rates based on Fermi’s golden rule for some parameters and identical for others. It is shown how the CM effects are connected to the occurrence of ion acoustic modes and when they occur. Interestingly, CM effects occur also for plasmas with very high electron temperatures; a regime, where the Landau–Spitzer approach is believed to be accurate. [ABSTRACT FROM AUTHOR]

One of the grand challenges of contemporary physics is understanding strongly interacting quantum systems comprising such diverse examples as ultracold atoms in traps, electrons in high-temperature superconductors and nuclear matter. Warm dense matter, defined by temperatures of a few electron volts and densities comparable with solids, is a complex state of such interacting matter. Moreover, the study of warm dense matter states has practical applications for controlled thermonuclear fusion, where it is encountered during the implosion phase, and it also represents laboratory analogues of astrophysical environments found in the core of planets and the crusts of old stars. Here we demonstrate how warm dense matter states can be diagnosed and structural properties can be obtained by inelastic X-ray scattering measurements on a compressed lithium sample. Combining experiments and ab initio simulations enables us to determine its microscopic state and to evaluate more approximate theoretical models for the ionic structure. [ABSTRACT FROM AUTHOR]

We present results for the ionic structure in hydrocarbons (polystyrene, polyethylene) that were shock compressed to pressures of up to 190 GPa, inducing rapid melting of the samples. The structure of the resulting liquid is then probed using in situ diffraction by an x-ray free electron laser beam, demonstrating the capability to obtain reliable diffraction data in a single shot, even for low-Z samples without long range order. The data agree well with ab initio simulations, validating the ability of such approaches to model mixed samples in states where complex interparticle bonds remain, and showing that simpler models are not necessarily valid. While the results clearly exclude the possibility of complete carbon-hydrogen demixing at the conditions probed, they also, in contrast to previous predictions, indicate that diffraction is not always a sufficient diagnostic for this phenomenon. [ABSTRACT FROM AUTHOR]

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems. [ABSTRACT FROM AUTHOR]