Search

The advent of high-power lasers has provided insights into laboratory high energy density (>1011 J/m3) physics. In particular, the properties of warm dense matter (WDM) with temperatures of 104–106 K and near-solid densities is a research area that has garnered significant interest recently. However, owing to the high temperatures and pressures associated with WDM, the measurement of fundamental properties is difficult, and insufficient data has been a significant setback in WDM research. Herein, we review recent developments in time-resolved X-ray absorption spectroscopy with synchrotron and X-ray free electron lasers for WDM research. Various physical properties, such as atomic bonding, electronic structures, electron–phonon coupling, and thermal conductivity of various elements in WDM conditions are investigated via this noble X-ray technique at various time scales from 100 ps to 100 fs.

Nature Communications 12(1), 1638 (2021). doi:10.1038/s41467-021-21756-6, Key insights in materials at extreme temperatures and pressures can be gained by accurate measurements that determine the electrical conductivity. Free-electron laser pulses can ionize and excite matter out of equilibrium on femtosecond time scales, modifying the electronic and ionic structures and enhancing electronic scattering properties. The transient evolution of the conductivity manifests the energy coupling from high temperature electrons to low temperature ions. Here we combine accelerator-based, high-brightness multi-cycle terahertz radiation with a single-shot electro-optic sampling technique to probe the evolution of DC electrical conductivity using terahertz transmission measurements on sub-picosecond time scales with a multi-undulator free electron laser. Our results allow the direct determination of the electron-electron and electron-ion scattering frequencies that are the major contributors of the electrical resistivity., Published by Nature Publishing Group UK, [London]

A comparison study of various models in investigating the Coulomb logarithm (CL) for a wide range of densities and temperatures is carried out. Using two known reference parameters, the ion coupling $$ \varGamma $$ and the electron degeneracy $$ \varTheta $$ , the capability of a recently proposed coupled Gericke–Murillo–Schlanges (CGMS) model in evaluating the CL is compared with other previous models—the Gericke–Murillo–Schlanges (GMS) model, the Landau–Spitzer (LS), the Brown–Preston–Singleton (BPS), the classical molecular dynamics (MD), and Khrapak (KH) model. It is observed that the CGMS model shows reliable results in both weakly and strongly coupled regimes. Moreover, the effects of using these models on studying electron heat transfer and conductivity coefficient within the weakly coupled and strongly coupled plasmas are examined.

Materials at high pressures and temperatures are of great interest for planetary science and astrophysics, warm dense-matter physics and inertial confinement fusion research. Planetary structure models rely on an understanding of the behaviour of elements and their mixtures under conditions that do not exist on Earth; at the same time, planets serve as natural laboratories for studying materials at extreme conditions. The topic of dense hydrogen is timely given the recent accurate measurements of the gravitational fields of Jupiter and Saturn, the current and upcoming progress in shock experiments, and the advances in numerical simulations of materials at high pressure. In this Review we discuss the connection between modelling planetary interiors and the high-pressure physics of hydrogen and helium. We summarize key experiments and theoretical approaches for determining the equation of state and phase diagram of hydrogen and helium. We relate this to current knowledge of the internal structures of Jupiter and Saturn, and discuss the importance of high-pressure physics to their characterization. Understanding the behaviour of materials at high pressures and temperatures is of great importance to planetary science and the physics of warm dense matter. This Review addresses the close connection between modelling the interiors of gaseous planets and the high-pressure physics of hydrogen and helium.

High-intensity short-pulse lasers have made possible the generation of energetic proton beams, unlocking numerous applications in high energy density science. One such application is uniform and isochoric heating of materials to the warm dense matter (WDM) state. We have developed a new experimental platform to simultaneously create and probe WDM at the matter in extreme conditions (MEC) end station at the Linac Coherent Light Source (LCLS). The short pulse optical laser (delivering up to 1 J in 45 fs) and the ultrabright LCLS X-ray laser with tunable frequency, respectively, deliver high power required to heat materials to WDM and precision-timed high-resolution X-rays to probe them. The laser-accelerated proton beam driven from a flat 1.5- $\mu \text{m}$ Cu foil was first measured then directed to a secondary sample of Al or polypropylene (PP), typically 300– $400~\mu \text{m}$ away. The time evolution of the sample electron temperature was measured using streaked optical pyrometry, where we observed a peak temperature of 0.9 ± 0.15 eV on the rear surface of an Al sample heated by the proton beam. Simulations using the hybrid-PIC code LSP and the rad-hydro code HELIOS show that a measured proton beam can heat Al to approximately 4 eV and PP to 1 eV if instead focused by a hemispherical Cu target. Through additional LSP simulations, we anticipate creating hotter WDM states (~20 eV) by increasing the laser energy to 10 J and keeping the other laser parameters fixed.

Free-electron laser pulse-based X-ray absorption spectroscopy measurements on warm dense copper are presented. The incident X-ray pulse energies were measured with a detector assembly consisting of a photocathode membrane and microchannel plates, and the transmitted energies were measured simultaneously with a photodiode detector. The precision of the absorption measurements was evaluated. For a warm dense copper foil irradiated by an intense femtosecond laser pulse, the enhanced X-ray absorption below the L 3-edge, followed by the rapid evolution of highly excited Fermi liquid within a picosecond, were successfully measured. This result demonstrates a unique capability to study femtosecond non-equilibrium electron–hole dynamics in extreme states of matter.

We present a first-principles equation-of-state (EOS) table of deuterium aimed at improving the previously established first-principles equation-of-state table (FPEOS) [S. X. Hu et al., Phys. Rev. B 84, 224109 (2011); S. X. Hu et al., Phys. Plasmas 22, 056304 (2015)]. The EOS table presented here, referred to as iFPEOS, introduces (1) a universal density functional theory (DFT) treatment of all density and temperature conditions, (2) a fully consistent treatment of exchange-correlation (XC) thermal effects across the entire range of temperatures covered, and (3) quantum treatment of ions. Based on ab initio molecular dynamics driven by thermal density functional theory, iFPEOS includes density points in the range $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}1.6\ifmmode\times\else\texttimes\fi{}{10}^{3}$ $\mathrm{g}/{\mathrm{cm}}^{3}$ and temperature points in the range 800 K $\ensuremath{\le}T\ensuremath{\le}256$ MK, thus covering the challenging warm dense matter (WDM) regime. For an improved description of the electronic structure, iFPEOS employs an advanced free-energy XC density functional with explicit temperature dependence, which is at the metageneralized gradient approximation level of DFT. We use the latest orbital-free free-energy density functional for the high-temperature regime where it shows excellent agreement with standard Mermin-Kohn-Sham DFT. For quantum treatment of ions we use path-integral molecular dynamics in order to take into account nuclear quantum effects. Results are compared to other EOS models and most recent experimental measurements of deuterium properties such as the molecular-to-atomic fluid transition, the principal and reshock Hugoniot, and sound speed. We find that iFPEOS provides an improved agreement with experimental data compared to other first-principles EOS models in the WDM regime for pressures up to 200 GPa and temperatures up to $60\phantom{\rule{0.16em}{0ex}}000$ K. For higher pressures and temperatures, however, iFPEOS is in agreement with other models in predicting lower compressibility and higher sound speed along the Hugoniot, compared to experiment.

We report on the study of electron kinetics induced by intense femtosecond (fs) laser excitation of electrons in the $5d$ band of Au. Changes in the electron system are observed from the temporal evolution of ac conductivity and conduction electron density. The results reveal an increase of electron thermalization time with excitation energy density, contrary to the Fermi-liquid behavior of the decrease of thermalization time associated with the heating of conduction electrons. This is attributed to the severe mitigation of photoexcitation by Auger decay. The study also uncovers the shortening of $5d$ hole lifetime with the increase of photoexcitation rates. These unique findings provide valuable insights for understanding electron kinetics under extreme nonequilibrium conditions.

We show with a recently devised extended first-principles molecular dynamics method that calculated Hugoniots of poly-$\ensuremath{\alpha}$-methylstyrene agree well with precision experimental results of Kritcher et al. [Nature (London) 584, 51 (2020)] and D\"oppner et al. [Phys. Rev. Lett. 121, 025001 (2018)]. The deviation is smaller than 0.8%. This agreement does not sensitively rely on the approximations in the employed first-principles methods as long as underlying physics are well described, as illustrated in the calculation of equation of state for polystyrene covering the warm dense regime. These results may stimulate a broad range of quantitative investigations on warm dense matter that were not thought possible before, and may thus afford a new prospect to the field of inertial confinement fusion and high-energy-density physics.

We present a method to investigate the bulk propagation of a shock wave in a thick, opaque metallic plate. The shock wave is generated by laser-loading. An elastic plane probe wave, contra-propagative with respect to the shock, is emitted by means of a phase-array device. Shock propagation monitoring is performed by analyzing on the phase-array detection the acoustic elastic plane wave after its interaction with the shock. The time-space detection of the probe wave allows to evaluate the spatial distribution of the shock wave all along its propagation in the opaque structure, from near to far field. Applications range from fundamental wave science to laser-loading material science.

Small and large amplitude linear and nonlinear ion acoustic and Langmuir waves are investigated for plasma with the generalized equation of state (EoS). This EoS covers a wide range of energy-density conditions from dilute classical regime up to the relativistically degenerate matter. Investigation shows that the linear dispersion and localized excitations of ion acoustic waves are significantly affected by the plasma parameters. It is also found that the criterion for ordinary soliton existence is significantly different for fully degenerate and nondegenerate plasma regimes with given electron temperature. In the nondegenerate regime, bright solitons form only for Mach numbers above a critical value which is only a function of the fluid temperature.

Using ab initio molecular dynamics simulations, detailed ionic structures and transport properties of warm dense nitrogen have been investigated in the density and temperature ranges of 1.5–3.0 g cm−3 and 1000–50,000 K, respectively. The simulations find that the nitrogen molecules primarily dissociate at temperatures above 10,000 K along the isotherms and Hugoniot in the warm dense matter regime, and a few different size-scale clusters form. The dissociations have a dominant effect on the electrical and thermal conductivities, and the contributions of the clusters to the transport properties are not negligible. Additionally, detailed simulations of the behavior of the electrical and thermal conductivities of warm dense nitrogen indicate that nitrogen is metallic at pressures above 60 GPa. This phenomenon has also been explored from the standpoint of the Wiedemann–Franz law, which is consistent with the calculation of the electrical conductivity for metallic pressures. The present simulation results provide a valuable reference for future experimental and theoretical modeling studies.

We have employed an exploding-wire compression method to measure the electrical conductivity of diamond-like carbon (DLC) in a warm dense matter (WDM) state. We generated a DLC in the WDM state using shock compression driven by an exploding-wire discharge within a rigid capillary. To elucidate the generation of DLC in WDM, we performed a 1-D magnetohydrodynamic simulation. Using the numerical results, we estimated the electrical conductivity of the DLC plasma. By comparing the time-evolutions of the voltage and current for gold and gold + DLC samples, we demonstrated that the voltage–current evolution is different in the two cases. From the absorption spectroscopy, we estimated the DLC temperature to be 8000–9000 K. By comparing the results of the experiment with those of the numerical simulation, we determined the electrical conductivity of the DLC plasma to be 106 S/m. This is relatively high compared with the electrical conductivity of the conventional carbon plasma, but the experimental results are similar to the theoretical values for diamond at solid density.

We numerically model the ablation process of a 25- $\mu \text{m}$ -thick aluminum foil driven by a pulsed-power machine that provides a 1-MA peak current in a 100-ns zero-to-peak rise time. The extended magnetohydrodynamics simulation is a discontinuous Galerkin code with Cartesian coordinates in 3-D and with 25- $\mu \text{m}$ spatial resolution. We investigate the influence of an external magnetic field normal to the foil surface, $B_{z}$ . During the foil ablation, $B_{z}=1$ T causes more nonuniform distributions of density and current compared to $B_{z}=0$ T. $B_{z}=4$ T delays the generation of surface plasma relative to the 0- and 1-T cases. The understanding of a material’s ablation as it undergoes transition from the solid to plasma phases requires detailed knowledge of a material’s equation of state and conductivity. This paper of warm dense matter and how instabilities propagate from a solid material to plasma motivates improvements to both numerical simulations and experimental diagnostics.

In the warm dense regime, where the electron temperature is increased to the same order of the Fermi temperature, the dynamical stability of elemental metals depends on its electronic band structure as well as its crystal structure. It has been known that phonon hardening occurs due to an enhanced internal pressure caused by electron excitations as in close-packed simple metals, whereas phonon softening occurs at a specific point in the Brillouin zone as in body-centered cubic metals. Here, we investigate the dynamical stability of binary ordered alloys (Au and Cu) in the L1$_0$ and L1$_2$ structures. By performing first principles calculations on phonon dispersions, we demonstrate that warm dense Au-Cu systems show phonon hardening behavior except the lowest frequency phonon mode at point R of AuCu in the L1$_0$ structure. We show that when a phonon mode is stabilized by long-range interatomic interactions at ambient condition, such a phonon will be destabilized by the short-range nature of the warm dense matters., 8 pages, 6 figures

We present a free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter to cover a wide range of thermodynamic conditions and photon energies including the entire x-ray range. It uses Mermin-Kohn-Sham density functional theory with exchange-correlation (XC) thermal effects taken into account via a fully temperature dependent generalized gradient approximation XC functional. The methodology incorporates a combination of the ab initio molecular dynamics (AIMD) snapshotted Kubo-Greenwood optic data with a single atom in simulation cell calculations to close the photon energy gap between the $L$ and $K$ edges and extend the $K$-edge tail toward many-keV photon energies. This gap arises in the standard scheme due to a prohibitively large number of bands required for the Kubo-Greenwood calculations with AIMD snapshots. Kubo-Greenwood data on snapshots provide an accurate description of optic properties at low photon frequencies slightly beyond the $L$ edge and x-ray absorption near edges structure (XANES) spectra, while data from periodic calculations with single atoms cover the tail regions beyond the edges. To demonstrate its applicability to mid-$Z$ materials where the standard DFT-based approach is not computationally feasible, we have applied it to opacity calculations of warm dense silicon plasmas. These first-principles calculations revealed a very interesting phenomenon of redshift-to-blueshift in $K\ensuremath{-}L$ ($1s\ensuremath{\rightarrow}2p$) and $K$-edge absorptions along both isotherm and isochore, which are absent in most continuum-lowering models of traditional plasma physics. This new physics phenomenon can be attributed to the underlying competition between the screening of deeply bound core electrons and the screening of outer-shell electrons caused by warm-dense-plasma conditions. We further demonstrate that the ratio of $1s\ensuremath{\rightarrow}2p$ to the $K$-edge x-ray absorptions can be used to characterize warm-dense-plasma conditions. Eventually, based on our absorption calculations, we have established a first-principles opacity table (FPOT) for silicon in a wide range of material densities and temperatures.

We present the design and parameters of a compact and mobile high-current pulse generator, which can be applied in the study of warm dense matter in university laboratories. The generator dimensions are 550 × 570 × 590 mm3, the weight is ∼70 kg, and it consists of four “bricks” connected in parallel. Each brick, made up of 2 × 40 nF, 100 kV low-inductance capacitors connected in parallel, has its own multi-gap and multichannel ball gas spark switch, triggered via a capacitively coupled triggering by a positive polarity pulse of ∼80 kV amplitude and ∼15 ns rise time. At a charging voltage of ∼70 kV, the generator produces a ∼155 kA current pulse with a rise time of ∼220 ns on a ∼15 nH inductive short-circuit load and a ∼90 kA amplitude current pulse in the underwater electrical explosion of a copper wire.

We put forward a co-axial pump (optical)-probe (x-rays) experimental concept and show performance of the optical component. A Bessel beam generator with a central 100 µm diameter hole (on the optical axis) was fabricated using femtosecond (fs) laser structuring inside a silica plate. This flat-axicon optical element produces a needle-like axial intensity distribution which can be used for the optical pump pulse. The fs-x-ray free electron laser (X-FEL) beam of sub-1 µm diameter can be introduced through the central hole along the optical axis onto a target as a probe. Different realisations of optical pump are discussed. Such optical elements facilitate alignment of ultra-short fs-pulses in space and time and can be used in light–matter interaction experiments at extreme energy densities on the surface and in the volume of targets. Full advantage of ultra-short 10 fs-X-FEL probe pulses with fs-pump (optical) opens an unexplored temporal dimension of phase transitions and the fastest laser-induced rates of material heating and quenching. A wider field of applications of fs-laser-enabled structuring of materials and design of specific optical elements for astrophotonics is presented.

We present a finite-temperature density functional theory investigation of the nonequilibrium transient electronic structure of warm dense Li, Al, Cu, and Au created by laser excitation. Photons excite electrons either from the inner shell orbitals or from the valence bands according to the photon energy, and give rise to isochoric heating of the sample. Localized states related to the 3d orbital are observed for Cu when the hole lies in the inner shell 3s orbital. The electrical conductivity for these materials at nonequilibrium states is calculated using the Kubo-Greenwood formula. The change of the electrical conductivity, compared to the equilibrium state, is different for the case of holes in inner shell orbitals or the valence band. This is attributed to the competition of two factors: the shift of the orbital energies due to reduced screening of core electrons, and the increase of chemical potential due to the excitation of electrons. The finite temperature effect of both the electrons and the ions on the electrical conductivity is discussed in detail. This work is helpful to better understand the physics of laser excitation experiments of warm dense matter., Comment: 111 pages, 9 figures

Motivated by the poor understanding of the applicability of new exchange-correlation (XC) functionals to warm dense matter (WDM), we designed and performed multiple-shock reverberation compression experiments on dense krypton to evaluate explicitly the implications of recently derived XC functionals. The equation of states of krypton up to 155 GPa and 45 000 K, which ranges from an initial dense gaseous state up to the insulator-metal transition regime, were determined accurately. It is found that the experimental data are better reproduced by the strongly constrained and appropriately normed (SCAN) XC functional compared to the conventional Perdew-Burke-Ernzerhof and Van der Waals (vdW) DF1 functionals, elucidating that the introduction of the kinetic energy density and the intermediate-range vdW interaction is decisive. However, the incorporation of long-range interactions into the SCAN ($\mathrm{SCAN}+\mathrm{rVV}10$ XC functional) results in a noticeably stiffer prediction due to an overestimation of the density and internal energy of the system at low densities and temperatures. Our evaluation of the Karasiev-Sjostrom-Dufty-Trickey free-energy functional experimentally validates the XC thermal effect in the WDM regime, verifies the previous predictions, and sheds light on a direction for future theoretical efforts. Finally, a phase diagram of krypton is given, which provides a clear picture for understanding the thermophysical behavior of krypton in a wider temperature-pressure range.

Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting applications from astrophysics to fusion energy research. Here we explore the real-space Green’s function method as a technique for solving the Kohn–Sham density functional theory equations under warm dense matter conditions. We find the method to be tractable and accurate throughout the density and temperature range of interest, in contrast to other approaches. Good agreement on equation of state is found when comparing to other methods, where they are thought to be accurate.

We present extensive new \textit{ab intio} path integral Monte Carlo results for the momentum distribution function $n(\mathbf{k})$ of the uniform electron gas (UEG) in the warm dense matter (WDM) regime over a broad range of densities and temperatures. This allows us to study the nontrivial exchange--correlation induced increase of low-momentum states around the Fermi temperature, and to investigate its connection to the related lowering of the kinetic energy compared to the ideal Fermi gas. In addition, we investigate the impact of quantum statistics on both $n(\mathbf{k})$ and the off-diagonal density matrix in coordinate space, and find that it cannot be neglected even in the strongly coupled electron liquid regime. Our results were derived without any nodal constraints, and thus constitute a benchmark for other methods and approximations.

The European physical journal / D 75, 224 (2021). doi:10.1140/epjd/s10053-021-00235-z, In this paper, we report on the Boltzmann kinetic equation approach adapted for simulations of warm dense matter created by irradiation of bulk gold with intense ultrashort X-ray pulses. X-rays can excite inner-shell electrons, which triggers creation of deep-lying core holes. Their relaxation, especially in heavier elements such as gold (atomic number Z=79) takes complicated pathways, involving collisional processes, and leading through a large number of active configurations. This number can be so high that solving a set of evolution equations for each configuration becomes computationally inefficient, and another modeling approach should be used instead. Here, we use the earlier introduced ���predominant excitation and relaxation path��� approach. It still uses true atomic configurations but limits their number by restricting material relaxation to a selected set of predominant pathways for material excitation and relaxation. With that, we obtain time-resolved predictions for excitation and relaxation in X-ray irradiated bulk of gold, including the respective change of gold optical properties. We compare the predictions with the available data from high-energy-density experiments. Their good agreement indicates ability of the Boltzmann kinetic equation approach to describe warm dense matter created from high-Z materials after their irradiation with X rays, which can be validated in future experiments., Published by Springer, Heidelberg

International audience; Average atom (AA) models allow one to efficiently compute electronic and optical properties of materials over a wide range of conditions and are often employed to interpret experimental data. However, at high pressure, predictions from AA models have been shown to disagree with results from ab initio computer simulations. Here we reconcile these deviations by developing an innovative type of AA model, AVION, that computes the electronic eigenstates with novel boundary conditions within the ion sphere. Bound and free states are derived consistently. We drop the common AA image that the free-particle spectrum starts at the potential threshold, which we found to be incompatible with ab initio calculations. We perform ab initio simulations of crystalline and liquid carbon and aluminum over a wide range of densities and show that the computed band structure is in very good agreement with predictions from AVION.

The low-density limit of the electrical conductivity $\sigma(n,T)$ of hydrogen as the simplest ionic plasma is presented as function of temperature T and mass density n in form of a virial expansion of the resistivity. Quantum statistical methods yield exact values for the lowest virial coefficients which serve as benchmark for analytical approaches to the electrical conductivity as well as for numerical results obtained from density functional theory based molecular dynamics simulations (DFT-MD) or path-integral Monte Carlo (PIMC) simulations. While these simulations are well suited to calculate $\sigma(n,T)$ in a wide range of density and temperature, in particular for the warm dense matter region, they become computationally expensive in the low-density limit, and virial expansions can be utilized to balance this drawback. We present new results of DFT-MD simulations in that regime and discuss the account of electron-electron collisions by comparing with the virial expansion., Comment: Supplementary Material will be made available upon journal publication

Density functional calculations can fail for want of an accurate exchange-correlation approximation. The energy can instead be extracted from a sequence of density functional calculations of conditional probabilities (CP-DFT). Simple CP approximations yield usefully accurate results for two-electron ions, the hydrogen dimer, and the uniform gas at all temperatures. CP-DFT has no self-interaction error for one electron, and correctly dissociates H2, both major challenges. For warm dense matter, classical CP-DFT calculations can overcome the convergence problems of Kohn-Sham DFT., 6 pages, 3 figures, 2 tables

We show that the entire x-ray Thomson scattering (XRTS) spectrum, including both elastic and inelastic features, can be calculated from first principles in the framework of quantum perturbation theories. Our derivation shows that the elastic scattering feature in a warm dense regime is different from that of condensed matter at low temperature. In addition to the contribution from spatial fluctuations of electronic density, which dominates elastic scattering at low temperature, there is an extra contribution from partially occupied inner-shell states, which is important in the warm dense regime. Calculated XRTS of isochorically heated beryllium agrees well with previous experimental measurements, which may give this method a further edge on interpreting XRTS spectra compared to empirical modeling methods.

We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al and Si as well as the compounds LiF, B4C, BN, CH4, CH2, C2H3, CH, C2H, MgO, and MgSiO3. For all these materials, we provide the pressure and internal energy over a density-temperature range from ~0.5 to 50 g/cc and from ~10^4 to 10^9 K, which are based on ~5000 different first-principles simulations. We compute isobars, adiabats and shock Hugoniot curves in the regime of L and K shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of H2O, H2O2, Al2O3, CO, and CO2 to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their endmembers. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the supplementary material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions., 13 figures, will appear in Phys. Rev. E

A numerical model for laser-matter interactions in the warm dense matter regime is presented with broad applications, e.g., ablation, thermionic emission, and radiation. A unique approach is adopted, in which a complete set of collisional and transport data is calculated using a quantum model and incorporated into the classical two-temperature model for the electron and lattice-ion temperatures. The data set was produced by the average atom model that combines speed, conceptual simplicity, and straightforward numerical development. Such data are suitable for use in the warm dense matter regime, where most of the laser-matter interactions at moderate intensities occur, thus eliminating deficiencies of previous models, e.g., interpolation between solid and ideal plasma regimes. In contrast to other works, we use a more rigorous definition of solid and plasma states of the metal, based on the physical condition of the lattice, crystalline (ordered) versus melted (disordered), rather than a definition based on electron temperature. The synergy between the two-temperature and average atom models has been demonstrated on a problem involving heating and melting of the interior of Al by a short-pulse laser with duration 0.1--1 ps and laser fluences $1\ifmmode\times\else\texttimes\fi{}{10}^{3}\ensuremath{-}3\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.16em}{0ex}}\mathrm{J}/{\mathrm{m}}^{2}(0.1\text{--}3\phantom{\rule{0.16em}{0ex}}\mathrm{J}/\mathrm{c}{\mathrm{m}}^{2})$. The melting line, which separates the solid and plasma regimes, has been tracked in time and space. The maximum melting depth has been determined as a function of laser fluence: ${l}_{\mathrm{melt}}(\ensuremath{\mu}\mathrm{m})\ensuremath{\cong}4\ifmmode\times\else\texttimes\fi{}{10}^{3}F\phantom{\rule{4pt}{0ex}}(\frac{\mathrm{J}}{{\mathrm{m}}^{2}})$.

There is growing interest in warm dense matter (WDM), an exotic state on the border between condensed matter and plasmas. Due to the simultaneous importance of quantum and correlation effects, WDM is complicated to treat theoretically. A key role has been played by ab initio path integral Monte Carlo (PIMC) simulations, and recently extensive results for thermodynamic quantities have been obtained. The first extension of PIMC simulations to the dynamic structure factor of the uniform electron gas was reported by Dornheim et al. [Phys. Rev. Lett. 121, 255001 (2018)]. This was based on an accurate reconstruction of the dynamic local field correction. Here we extend this concept to other dynamical quantities of the warm dense electron gas including the dynamic susceptibility, the dielectric function, and the conductivity.

Plasma flows encountered in high-energy-density experiments display features that differ from those of equilibrium systems. Nonequilibrium approaches such as kinetic theory (KT) capture many, if not all, of these phenomena. However, KT requires closure information, which can be computed from microscale simulations and communicated to KT. We present a concurrent heterogeneous multiscale approach that couples molecular dynamics (MD) with KT in the limit of near-equilibrium flows. To reduce the cost of gathering information from MD, we use active learning to train neural networks on MD data obtained by randomly sampling a small subset of the parameter space. We apply this method to a plasma interfacial mixing problem relevant to warm dense matter, showing considerable computational gains when compared with the full kinetic-MD approach. We find that our approach enables the probing of Coulomb coupling physics across a broad range of temperatures and densities that are inaccessible with current theoretical models.

Warm dense matter (WDM)---an extreme state with high temperatures and densities that occurs e.g. in astrophysical objects---constitutes one of the most active fields in plasma physics and materials science. These conditions can be realized in the lab by shock compression or laser excitation, and the most accurate experimental diagnostics is achieved with lasers and free electron lasers which is theoretically modeled using linear response theory. Here, we present first \textit{ab initio} path integral Monte Carlo results for the nonlinear density response of correlated electrons in WDM and show that for many situations of experimental relevance nonlinear effects cannot be neglected.

We present an effective static approximation (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor S(q,ω), the static structure factor S(q), and the interaction energy v. The ESA combines the recent neural-net representation by T. Dornheim et al., [J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit obtained from quantum Monte Carlo data of the on-top pair distribution function g(0). It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001]. We find that an accurate incorporation of electronic correlations in terms of the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.

Finite-temperature density functional theory has become a standard tool for first-principles calculations of the properties of warm dense matter (WDM) relevant to high-energy-density physics (HEDP) applications. Here we present theoretical grounds of thermal hybrid exchange-correlation (XC) functionals within the generalized Mermin-Kohn-Sham scheme for an improved description of WDM. Building on the previously developed KSDT (Karasiev-Sjostrom-Dufty-Trickey) [Karasiev et al., Phys. Rev. Lett. 112, 076403 (2014)] local density approximation (LDA) and the KDT16 (Karasiev-Dufty-Trickey 2016) [Karasiev et al., Phys. Rev. Lett. 120, 076401 (2018)] generalized-gradient approximation (GGA) XC free-energy density functionals, we construct a novel thermal hybrid XC functional, referred to here as KDT0. The KDT0 model at low temperature reduces to the popular ground-state PBE0 hybrid due to properties of the used KDT16 density functional approximation. Application to static calculations of electronic band gap and band structure at a wide range of temperatures for various systems of interest to HEDP show that KDT0 provides a significant improvement to the lower LDA and GGA rung XC functionals and to the ground-state PBE0 hybrid.

The electron-ion relaxation dynamics in warm dense iron were investigated by time-resolved x-ray absorption near-edge spectroscopy (XANES). A novel analysis, combining ab initio density functional theory (DFT) and two temperature model (TTM) simulations, was developed to calculate the x-ray absorption spectra as a function of delay time. Here we present experimental evidence of changes at the XAS L3 edge of iron that are consistent with the reduction of the electron-phonon coupling under warm dense matter conditions. The experimental results are in agreement with the model that takes both the electron (${T}_{e}$) and the ion temperature (${T}_{i}$) dependence of the thermophysical properties into consideration, while models where either constant electron-phonon coupling factor (G) or only ${T}_{e}$-dependent G are used do not agree with the observed relaxation dynamics of iron.

We present a new model of electron transport in warm and hot dense plasmas which combines the quantum Landau-Fokker-Planck equation with the concept of mean-force scattering. We obtain electrical and thermal conductivities across several orders of magnitude in temperature, from warm dense matter conditions to hot, nondegenerate plasma conditions, including the challenging crossover regime between the two. The small-angle approximation characteristic of Fokker-Planck collision theories is mitigated to good effect by the construction of accurate effective Coulomb logarithms based on mean-force scattering, which allows the theory to remain accurate even at low temperatures, as compared with high-fidelity quantum simulation results. Electron-electron collisions are treated on equal footing as electron-ion collisions. Their accurate treatment is found to be essential for hydrogen, and is expected to be important to other low-Z elements. We find that electron-electron scattering remains influential to the value of the thermal conductivity down to temperatures somewhat below the Fermi energy. The accuracy of the theory seems to falter only for the behavior of the thermal conductivity at very low temperatures due to a subtle interplay between the Pauli exclusion principle and the small-angle approximation as they pertain to electron-electron scattering. Even there, the model is in fair agreement with ab initio simulations., Comment: 17 pages, 7 figures (2 new, 1 updated)

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures ($l50\text{ }\text{ }\mathrm{eV}$). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

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.

The effective one-component plasma (EOCP) model has provided an efficient approach to obtaining many important thermophysical parameters of hot dense matter [J. Cl\'erouin, et al., Phys. Rev. Lett. 116, 115003 (2016)]. In this paper, we perform extensive quantum molecular dynamics (QMD) simulations to determine the equations of state, ionic structures, and ionic transport properties of neon and krypton within the warm dense matter (WDM) regime where the density ( $\ensuremath{\rho}$ ) is up to 12 $\mathrm{g}/{\mathrm{cm}}^{3}$ and the temperature ($T$) is up to 100 kK. The simulated data are then used as a benchmark to explicitly evaluate the EOCP and Yukawa models. It is found that, within present $\ensuremath{\rho}$-T regime, the EOCP model can excellently reproduce the diffusion and viscosity coefficients of neon and krypton due to the fact that this model defines a system which nearly reproduces the actual physical states of WDM. Therefore, the EOCP model may be a promising alternative approach to reasonably predicting the transport behaviors of matter in WDM regime at lower QMD computational cost. The evaluation of Yukawa model shows that the consideration of the energy level broadening effect in the average atom model is necessary. Finally, with the help of EOCP model, the Stokes-Einstein relationships about neon and krypton are discussed, and fruitful plasma parameters as well as a practical $\ensuremath{\rho}$-T-dependent formula of the effective coupling parameter are obtained. These results not only provide valuable information for future theoretical and experimental studies on dense neon and krypton but also reveal the applicability of the EOCP model and the limitation of the Yukawa model in WDM regime and further support the continuing search for a unified description of ionic transport in dense plasma.

We systematically investigate finite-size effects in the dynamic structure factor S(q,ω) of the uniform electron gas obtained via the analytic continuation of ab initio path integral Monte Carlo data for the imaginary-time density-density correlation function F(q,τ). Using the recent scheme by Dornheim et al. [Phys. Rev. Lett. 121, 255001 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.255001], we find that the reconstructed spectra are not afflicted with any finite-size effects for as few as N=14 electrons both at warm dense matter (WDM) conditions and at the margins of the strongly correlated electron liquid regime. Our results further corroborate the high quality of our current description of the dynamic density response of correlated electrons, which is of high importance for many applications in WDM theory and beyond.

We use density functional molecular dynamics (DFT-MD) to study the effect of finite temperature exchange-correlation (xc) in Hydrogen. Using the Kohn-Sham approach, the xc energy of the system, $E_{xc}(r_{s})$ is replaced by the xc free energy $f_{xc}(r_{s},\Theta)$ within the local density approximation (LDA) based on parametrized path integral Monte Carlo (PIMC) data for the uniform electron gas (UEG) at warm dense matter (WDM) conditions. We observe insignificant changes in the equation of state (EOS) at the region of metal-insulator transition compared to the regular LDA form, whereas significant changes are observed for T$>$10000 K, i.e., in the important WDM regime. Thus, our results further corroborate the need for temperature-dependent xc functionals for DFT simulations of WDM systems. Moreover, we present the first finite-temperature DFT results for the EOS of Hydrogen in the electron liquid regime up to $r_{s}=14$ and find a drastic impact (about $20\%$) of thermal xc effects, which manifests at lower temperatures compared to WDM. We expect our results to be important for many applications beyond DFT, like quantum hydrodynamics and astrophysical models., Comment: 14 pages, 12 figures

The free-free opacity in plasmas is fundamental to our understanding of energy transport in stellar interiors and for inertial confinement fusion research. However, theoretical predictions in the challenging dense plasma regime are conflicting and there is a dearth of accurate experimental data to allow for direct model validation. Here we present time-resolved transmission measurements in solid-density Al heated by an XUV free-electron laser. We use a novel functional optimization approach to extract the temperature-dependent absorption coefficient directly from an oversampled pool of single-shot measurements, and find a pronounced enhancement of the opacity as the plasma is heated to temperatures of order of the Fermi energy. Plasma heating and opacity enhancement are observed on ultrafast timescales, within the duration of the femtosecond XUV pulse. We attribute further rises in the opacity on ps timescales to melt and the formation of warm dense matter.

We investigate the energy-loss characteristics of an ion in warm dense matter (WDM) and dense plasmas concentrating on the influence of electronic correlations. The basis for our analysis is a recently developed ab initio quantum Monte Carlo- (QMC) based machine learning representation of the static local field correction (LFC) [Dornheim et al., J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013], which provides an accurate description of the dynamical density response function of the electron gas at the considered parameters. We focus on the polarization-induced stopping power due to free electrons, the friction function, and the straggling rate. In addition, we compute the friction coefficient which constitutes a key quantity for the adequate Langevin dynamics simulation of ions. Considering typical experimental WDM parameters with partially degenerate electrons, we find that the friction coefficient is of the order of γ/ω_{pi}=0.01, where ω_{pi} is the ionic plasma frequency. This analysis is performed by comparing QMC-based data to results from the random-phase approximation (RPA), the Mermin dielectric function, and the Singwi-Tosi-Land-Sjolander (STLS) approximation. It is revealed that the widely used relaxation time approximation (Mermin dielectric function) has severe limitations regarding the description of the energy loss of ions in a correlated partially degenerate electrons gas. Moreover, by comparing QMC-based data with the results obtained using STLS, we find that the ion energy-loss properties are not sensitive to the inaccuracy of the static local field correction (LFC) at large wave numbers, k/k_{F}>2 (with k_{F} being the Fermi wave number), but that a correct description of the static LFC at k/k_{F}≲1.5 is important.

Ultrafast laser pulses spatially shaped as Bessel beams in dielectrics create high aspect ratio plasma channels whose relaxation can lead to the formation of nanochannels. We report a strong enhancement of the nanochannel drilling efficiency with illumination by double pulses separated by a delay between 10 and 500 ps. This enables the formation of nanochannels with diameters down to 100 nm. Experimental absorption measurements demonstrate that the increase of drilling efficiency is due to an increase of the confinement of the energy deposition. Nanochannel formation corresponds to a drastic change in absorption of the second pulse, demonstrating the occurrence of a phase change produced by the first pulse. This creates a highly absorbing, long-living state. Our measurements show that it is compatible with the semi-metallization of warm dense glass which takes place within a timescale of

The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)] and strongly coupled electron liquid [\textit{Phys.~Rev.~B}~\textbf{101}, 045129 (2020)] conditions based on exact \textit{ab initio} path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g., astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of $0.05 \leq r_s \leq 0.5$ and $0.85\leq\theta\leq8$. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sj\"olander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of $0.001-0.01\%$. All PIMC data are available online.

Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, as well as matter produced in strong compression experiments. As of late, x-ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor $S(q,\omega)$ and the plasmon dispersion $\omega(q)$. Recently the first \textit{ab initio} results for $S(q,\omega)$ of the homogeneous warm dense electron gas were obtained from path integral Monte Carlo simulations, [Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. Here, we analyse the effects of correlations and finite temperature on the dynamic dielectric function and the plasmon dispersion. Our results for the plasmon dispersion and damping differ significantly from the random phase approximation and from earlier models of the correlated electron gas. Moreover, we show when commonly used weak damping approximations break down and how the method of complex zeros of the dielectric function can solve this problem for WDM conditions.

Proton beams driven by chirped pulse amplified lasers have multi-picosecond duration and can isochorically and volumetrically heat material samples, potentially providing an approach for creating samples of warm dense matter with conditions not present on Earth. Envisioned on a larger scale, they could heat fusion fuel to achieve ignition. We have shown in an experiment that a kilojoule-class, multi-picosecond short pulse laser is particularly effective for heating materials. The proton beam can be focussed via target design to achieve exceptionally high flux, important for the applications mentioned. The laser irradiated spherically curved diamond-like-carbon targets with intensity 4 × 1018 W/cm2, producing proton beams with 3 MeV slope temperature. A Cu witness foil was positioned behind the curved target, and the gap between was either empty or spanned with a structure. With a structured target, the total emission of Cu Kα fluorescence was increased 18 fold and the emission profile was consistent with a tightly focussed beam. Transverse proton radiography probed the target with ps order temporal and 10 μm spatial resolution, revealing the fast-acting focussing electric field. Complementary particle-in-cell simulations show how the structures funnel protons to the tight focus. The beam of protons and neutralizing electrons induce the bright Kα emission observed and heat the Cu to 100 eV.

We combine two first-principles computer simulation techniques, path integral Monte-Carlo and density functional theory molecular dynamics, to determine the equation of state of magnesium oxide in the regime of warm dense matter, with densities ranging from 0.35 to 71~g$\,$cm$^{-3}$ and temperatures from 10,000 K to $5\times10^8$~K. These conditions are relevant for the interiors of giant planets and stars as well as for shock wave compression measurements and inertial confinement fusion experiments. We study the electronic structure of MgO and the ionization mechanisms as a function of density and temperature. We show that the L-shell orbitals of magnesium and oxygen hybridize at high density. This results into a gradual ionization of the L-shell with increasing density and temperature. In this regard, MgO behaves differently from pure oxygen, which is reflected in the shape of the MgO principal shock Hugoniot curve. The curve of oxygen shows two compression maxima, while that of MgO shows only one. We predict a maximum compression ratio of 4.66 to occur for a temperature of 6.73 $\times 10^7$ K. Finally we study how multiple shocks and ramp waves can be used to cover a large range of densities and temperatures., 12 pages, 9 figures. arXiv admin note: text overlap with arXiv:2001.00985

The rate of photon absorption in warm dense matter induced by free-free electron-ion collisions is derived from Sommerfeld's cross section for nonrelativistic bremsstrahlung emission, making use of detailed balance relations. Warm dense matter is treated as a metal-like state in the approximation of a uniform degenerate electron gas and a uniform ion background. Total absorption rates are averaged over the electron Fermi distribution. A closed expression is obtained for the absorption rate, depending on temperature, density, and photon energy, which scales with ion charge Z. It is evaluated numerically for the full nonrelativistic parameter space, which requires different representations of the hypergeometric functions involved. The results are valid for photon frequencies larger than the plasma frequency of the medium. They are compared with approximate formulas in various asymptotic regions.The rate of photon absorption in warm dense matter induced by free-free electron-ion collisions is derived from Sommerfeld's cross section for nonrelativistic bremsstrahlung emission, making use of detailed balance relations. Warm dense matter is treated as a metal-like state in the approximation of a uniform degenerate electron gas and a uniform ion background. Total absorption rates are averaged over the electron Fermi distribution. A closed expression is obtained for the absorption rate, depending on temperature, density, and photon energy, which scales with ion charge Z. It is evaluated numerically for the full nonrelativistic parameter space, which requires different representations of the hypergeometric functions involved. The results are valid for photon frequencies larger than the plasma frequency of the medium. They are compared with approximate formulas in various asymptotic regions.

We perform a systematic study on the structure and dynamics of warm dense aluminum (Al) at temperatures ranging from 0.5 to 5.0 eV with molecular dynamics utilizing both density functional theory (DFT) and the deep potential (DP) method. On one hand, unlike the Thomas-Fermi kinetic energy density functional (KEDF), we find that the orbital-free DFT method with the Wang-Teter non-local KEDF yields properties of warm dense Al that agree well with the Kohn-Sham DFT method, enabling accurate orbital-free DFT simulations of warm dense Al at relatively low temperatures. On the other hand, the DP method constructs a deep neural network that has a high accuracy in reproducing short- and long-ranged properties of warm dense Al when compared to the DFT methods. The DP method is orders of magnitudes faster than DFT and is well-suited for simulating large systems and long trajectories to yield accurate properties of warm dense Al. Our results suggest that the combination of DFT methods and the DP model is a powerful tool for accurately and efficiently simulating warm dense matter.