Virial coefficients of the uniform electron gas from path-integral Monte Carlo simulations.

The properties of plasmas in the low-density limit are described by virial expansions. Analytical expressions are known from Green's function approaches only for the first three virial coefficients. Accurate path-integral Monte Carlo (PIMC) simulations have recently been performed for the uniform electron gas, allowing the virial expansions to be analyzed and interpolation formulas to be derived. The exact expression for the second virial coefficient is used to test the accuracy of the PIMC simulations and the range of validity of the interpolation formula of Groth et al. [Phys. Rev. Lett. 119, 135001 (2017)0031-900710.1103/PhysRevLett.119.135001], and we discuss the fourth virial coefficient, which is not exactly known yet. Combining PIMC simulations with benchmarks from exact virial expansion results would allow us to obtain more accurate representations of the equation of state for parameter ranges of conditions which are of interest, e.g., for helioseismology.

Observing the onset of pressure-driven K-shell delocalization.

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.

Proton stopping measurements at low velocity in warm dense carbon.

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

Erratum: Using Diffuse Scattering to Observe X-Ray-Driven Nonthermal Melting [Phys. Rev. Lett. 126, 015703 (2021)].

This corrects the article DOI: 10.1103/PhysRevLett.126.015703.

Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures.

We present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, [Formula: see text], also called mylar) shock-compressed to ([Formula: see text]) GPa and ([Formula: see text]) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

Using Diffuse Scattering to Observe X-Ray-Driven Nonthermal Melting.

We present results from the SPring-8 Angstrom Compact free electron LAser facility, where we used a high intensity (∼10^{20} W/cm^{2}) x-ray pump x-ray probe scheme to observe changes in the ionic structure of silicon induced by x-ray heating of the electrons. By avoiding Laue spots in the scattering signal from a single crystalline sample, we observe a rapid rise in diffuse scattering and a transition to a disordered, liquidlike state with a structure significantly different from liquid silicon. The disordering occurs within 100 fs of irradiation, a timescale that agrees well with first principles simulations, and is faster than that predicted by purely inertial behavior, suggesting that both the phase change and disordered state reached are dominated by Coulomb forces. This method is capable of observing liquid scattering without masking signal from the ambient solid, allowing the liquid structure to be measured throughout and beyond the phase change.

Demonstration of X-ray Thomson scattering as diagnostics for miscibility in warm dense matter.

The gas and ice giants in our solar system can be seen as a natural laboratory for the physics of highly compressed matter at temperatures up to thousands of kelvins. In turn, our understanding of their structure and evolution depends critically on our ability to model such matter. One key aspect is the miscibility of the elements in their interiors. Here, we demonstrate the feasibility of X-ray Thomson scattering to quantify the degree of species separation in a 1:1 carbon-hydrogen mixture at a pressure of ~150 GPa and a temperature of ~5000 K. Our measurements provide absolute values of the structure factor that encodes the microscopic arrangement of the particles. From these data, we find a lower limit of [Formula: see text]% of the carbon atoms forming isolated carbon clusters. In principle, this procedure can be employed for investigating the miscibility behaviour of any binary mixture at the high-pressure environment of planetary interiors, in particular, for non-crystalline samples where it is difficult to obtain conclusive results from X-ray diffraction. Moreover, this method will enable unprecedented measurements of mixing/demixing kinetics in dense plasma environments, e.g., induced by chemistry or hydrodynamic instabilities.

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation.

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.

Evidence for Crystalline Structure in Dynamically-Compressed Polyethylene up to 200 GPa.

We investigated the high-pressure behavior of polyethylene (CH2) by probing dynamically-compressed samples with X-ray diffraction. At pressures up to 200 GPa, comparable to those present inside icy giant planets (Uranus, Neptune), shock-compressed polyethylene retains a polymer crystal structure, from which we infer the presence of significant covalent bonding. The A2/m structure which we observe has previously been seen at significantly lower pressures, and the equation of state measured agrees with our findings. This result appears to contrast with recent data from shock-compressed polystyrene (CH) at higher temperatures, which demonstrated demixing and recrystallization into a diamond lattice, implying the breaking of the original chemical bonds. As such chemical processes have significant implications for the structure and energy transfer within ice giants, our results highlight the need for a deeper understanding of the chemistry of high pressure hydrocarbons, and the importance of better constraining planetary temperature profiles.

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering.

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.

Liquid Structure of Shock-Compressed Hydrocarbons at Megabar Pressures.

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.

Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter.

The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor S(q,ω) constitutes a key quantity as it is directly measured in x-ray Thomson scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first ab initio results for S(q,ω) by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction G(q,ω). In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for S(q,ω) over substantial parts of the warm dense matter regime.

Experimental discrimination of ion stopping models near the Bragg peak in highly ionized matter.

The energy deposition of ions in dense plasmas is a key process in inertial confinement fusion that determines the α-particle heating expected to trigger a burn wave in the hydrogen pellet and resulting in high thermonuclear gain. However, measurements of ion stopping in plasmas are scarce and mostly restricted to high ion velocities where theory agrees with the data. Here, we report experimental data at low projectile velocities near the Bragg peak, where the stopping force reaches its maximum. This parameter range features the largest theoretical uncertainties and conclusive data are missing until today. The precision of our measurements, combined with a reliable knowledge of the plasma parameters, allows to disprove several standard models for the stopping power for beam velocities typically encountered in inertial fusion. On the other hand, our data support theories that include a detailed treatment of strong ion-electron collisions.

A strong diffusive ion mode in dense ionized matter predicted by Langevin dynamics.

The state and evolution of planets, brown dwarfs and neutron star crusts is determined by the properties of dense and compressed matter. Due to the inherent difficulties in modelling strongly coupled plasmas, however, current predictions of transport coefficients differ by orders of magnitude. Collective modes are a prominent feature, whose spectra may serve as an important tool to validate theoretical predictions for dense matter. With recent advances in free electron laser technology, X-rays with small enough bandwidth have become available, allowing the investigation of the low-frequency ion modes in dense matter. Here, we present numerical predictions for these ion modes and demonstrate significant changes to their strength and dispersion if dissipative processes are included by Langevin dynamics. Notably, a strong diffusive mode around zero frequency arises, which is not present, or much weaker, in standard simulations. Our results have profound consequences in the interpretation of transport coefficients in dense plasmas.

Nanosecond formation of diamond and lonsdaleite by shock compression of graphite.

The shock-induced transition from graphite to diamond has been of great scientific and technological interest since the discovery of microscopic diamonds in remnants of explosively driven graphite. Furthermore, shock synthesis of diamond and lonsdaleite, a speculative hexagonal carbon polymorph with unique hardness, is expected to happen during violent meteor impacts. Here, we show unprecedented in situ X-ray diffraction measurements of diamond formation on nanosecond timescales by shock compression of pyrolytic as well as polycrystalline graphite to pressures from 19 GPa up to 228 GPa. While we observe the transition to diamond starting at 50 GPa for both pyrolytic and polycrystalline graphite, we also record the direct formation of lonsdaleite above 170 GPa for pyrolytic samples only. Our experiment provides new insights into the processes of the shock-induced transition from graphite to diamond and uniquely resolves the dynamics that explain the main natural occurrence of the lonsdaleite crystal structure being close to meteor impact sites.

Predictions for the energy loss of light ions in laser-generated plasmas at low and medium velocities.

The energy loss of light ions in dense plasmas is investigated with special focus on low to medium projectile energies, i.e., at velocities where the maximum of the stopping power occurs. In this region, exceptionally large theoretical uncertainties remain and no conclusive experimental data are available. We perform simulations of beam-plasma configurations well suited for an experimental test of ion energy loss in highly ionized, laser-generated carbon plasmas. The plasma parameters are extracted from two-dimensional hydrodynamic simulations, and a Monte Carlo calculation of the charge-state distribution of the projectile ion beam determines the dynamics of the ion charge state over the whole plasma profile. We show that the discrepancies in the energy loss predicted by different theoretical models are as high as 20-30%, making these theories well distinguishable in suitable experiments.

Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperature.

The uniform electron gas at finite temperature is of key relevance for many applications in dense plasmas, warm dense matter, laser excited solids, and much more. Accurate thermodynamic data for the uniform electron gas are an essential ingredient for many-body theories, in particular, density-functional theory. Recently, first-principles restricted path integral Monte Carlo results became available, which, however, had to be restricted to moderate degeneracy, i.e., low to moderate densities with r_{s}=r[over ¯]/a_{B}≳1. Here we present novel first-principles configuration path integral Monte Carlo results for electrons for r_{s}≤4. We also present quantum statistical data within the e^{4} approximation that are in good agreement with the simulations at small to moderate r_{s}.

Ab initio approach to model x-ray diffraction in warm dense matter.

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 ab 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.

Observation of finite-wavelength screening in high-energy-density matter.

A key component for the description of charged particle systems is the screening of the Coulomb interaction between charge carriers. First investigated in the 1920s by Debye and Hückel for electrolytes, charge screening is important for determining the structural and transport properties of matter as diverse as astrophysical and laboratory plasmas, nuclear matter such as quark-gluon plasmas, electrons in solids, planetary cores and charged macromolecules. For systems with negligible dynamics, screening is still mostly described using a Debye-Hückel-type approach. Here, we report the novel observation of a significant departure from the Debye-Hückel-type model in high-energy-density matter by probing laser-driven, shock-compressed plastic with high-energy X-rays. We use spectrally resolved X-ray scattering in a geometry that enables direct investigation of the screening cloud, and demonstrate that the observed elastic scattering amplitude is only well described within a more general approach.

Evidence for a glassy state in strongly driven carbon.

Here, we report results of an experiment creating a transient, highly correlated carbon state using a combination of optical and x-ray lasers. Scattered x-rays reveal a highly ordered state with an electrostatic energy significantly exceeding the thermal energy of the ions. Strong Coulomb forces are predicted to induce nucleation into a crystalline ion structure within a few picoseconds. However, we observe no evidence of such phase transition after several tens of picoseconds but strong indications for an over-correlated fluid state. The experiment suggests a much slower nucleation and points to an intermediate glassy state where the ions are frozen close to their original positions in the fluid.