X-ray scattering measurements of strong ion-ion correlations in shock-compressed aluminum

Superradiant Thomson scattering from graphite in the extreme ultraviolet

We study the Thomson scattering from highly oriented pyrolitic graphite excited by the extreme ultraviolet, coherent pulses of FERMI free electron laser (FEL). An apparent nonlinear behavior is observed and fully described in terms of the coherent nature of both exciting FEL beam and scattered radiation, producing an intensity-dependent enhancement of the Thomson scattering cross-section. The process resembles Dicke's superradiant phenomenon and is thus interpreted as the observation of superradiant Thomson scattering. The process also triggers the creation of coherent, low-q ([Formula: see text] 0.3 Å[Formula: see text]), low energy phonons. The experimental data and analysis provide quantitative information on the sample characteristics, absorption, scattering factor, and coherent phonon energies and populations and open the route for the investigation of the deep nature of complex materials.

Quantifying the partial ionization effect of gold in the transition region between condensed matter and warm dense matter

It is now well known that solids under ultra-high-pressure shock compression will enter the warm dense matter (WDM) regime which connects condensed matter and hot plasma. How condensed matter turns into the WDM, however, remains largely unexplored due to the lack of data in the transition pressure range. In this letter, by employing the unique high-Z three-stage gas gun launcher technique developed recently, we compress gold into TPa shock pressure to fill the gap inaccessible by the two-stage gas gun and laser shock experiments. With the aid of high-precision Hugoniot data obtained experimentally, we observe a clear softening behavior beyond ~560 GPa. The state-of-the-art ab-initio molecular dynamics calculations reveal that the softening is caused by the ionization of 5d electrons in gold. This work quantifies the partial ionization effect of electrons under extreme conditions, which is critical to model the transition region between condensed matter and WDM.

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics

Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm^{3} to 16 g/cm^{3} and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

Thermal excitation signals in the inhomogeneous warm dense electron gas

We investigate the emergence of electronic excitations from the inhomogeneous electronic structure at warm dense matter parameters based on first-principles calculations. The emerging modes are controlled by the imposed perturbation amplitude. They include satellite signals around the standard plasmon feature, transformation of plasmons to optical modes, and double-plasmon modes. These modes exhibit a pronounced dependence on the temperature. This makes them potentially invaluable for the diagnostics of plasma parameters in the warm dense matter regime. We demonstrate that these modes can be probed with present experimental techniques.

Bound electron screening effect on ion-ion potential of warm and hot dense matter

The effects of bound electron screening in warm and hot dense matter are investigated analytically and a theoretical description of screened short-range repulsion is given meanwhile. An empirical ion-ion potential including the classic charge screening and chemical bond attraction at various temperatures and densities is proposed. By solving hypernetted chain equations and comparing the obtained radial distribution function (RDF) with ab initio simulations, the proposed ion-ion potential is found to be promising over a wide range of temperatures and densities for warm dense aluminum and iron. The elastic scattering amplitude and the x-ray absorption near the edge structure of warm dense aluminum calculated from the obtained RDF are in good agreement with experiment results.

Structure and dynamics of warm dense aluminum: a molecular dynamics study with density functional theory and deep potential

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.

Dynamical structure factor of strongly coupled ions in a dense quantum plasma

The dynamical structure factor (DSF) of strongly coupled ions in dense plasmas with partially and strongly degenerate electrons is investigated. The main focus is on the impact of electronic correlations (nonideality) on the ionic DSF. The latter is computed by carrying out molecular dynamics (MD) simulations with a screened ion-ion interaction potential. The electronic screening is taken into account by invoking the Singwi-Tosi-Land-Sjölander approximation, and it is compared to the MD simulation data obtained considering the electronic screening in the random phase approximation and using the Yukawa potential. We find that electronic correlations lead to lower values of the ion-acoustic mode frequencies and to an extension of the applicability limit with respect to the wave-number of a hydrodynamic description. Moreover, we show that even in the limit of weak electronic coupling, electronic correlations have a nonnegligible impact on the ionic longitudinal sound speed. Additionally, the applicability of the Yukawa potential with an adjustable screening parameter is discussed, which will be of interest, e.g., for the interpretation of experimental results for the ionic DSF of dense plasmas.

Structural characteristics of strongly coupled ions in a dense quantum plasma

The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential. Special focus is put on the description of the electronic screening in the Singwi-Tosi-Land-Sjölander (STLS) approximation. Different cross-checks and analyses using ion potentials obtained from ground-state quantum Monte Carlo data, the random phase approximation (RPA), and existing analytical models are presented for the computation of the structural properties, such as the pair distribution and the static structure factor, of strongly coupled ions. The results are highly sensitive to the features of the screened pair interaction potential. This effect is particularly visible in the static structure factor. The applicability range of the screened potential computed from STLS is identified in terms of density and temperature of the electrons. It is demonstrated that at r_{s}>1, where r_{s} is the ratio of the mean interelectronic distance to the Bohr radius, electronic correlations beyond RPA have a nonnegligible effect on the structural properties. Additionally, the applicability of the hypernetted chain approximation for the calculation of the structural properties using the screened pair interaction potential is analyzed employing the effective coupling parameter approach.

Path integral Monte Carlo simulations of warm dense aluminum

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of 0.1-32.4gcm^{-3} and 10^{4}-10^{8} K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and 〈Z〉 to reveal the evolution of the plasma structure and ionization behavior.

Measurement of temperature and density using non-collective X-ray Thomson scattering in pulsed power produced warm dense plasmas

We present the first experimental measurement of temperature and density of a warm dense plasma produced by a pulsed power driver at the Nevada Terawatt Facility (NTF). In the early phases of discharge, most of the mass remains in the core, and it has been challenging to diagnose with traditional methods, e.g. optical probing, because of the high density and low temperature. Accurate knowledge of the transport coefficients as well as the thermodynamic state of the plasma is important to precisely test or develop theoretical models. Here, we have used spectrally resolved non-collective X-ray Thomson scattering to characterize the dense core region. We used a graphite load driven by the Zebra current generator (0.6 MA in 200 ns rise time) and the Ti He-α line produced by irradiating a Ti target with the Leopard laser (30 J, 0.8 ns) as an X-ray probing source. Using this configuration, we obtained a signal-to-noise ratio ~2.5 for the scattered signal. By fitting the experimental data with predicted spectra, we measured T = 2±1.9 eV, ρ = 0.6±0.5 gr/cc, 70 ns into the current pulse. The complexity of the dense core is revealed by the electrons in the dense core that are found to be degenerate and weakly coupled, while the ions remain highly coupled.

Ion-ion dynamic structure factor, acoustic modes, and equation of state of two-temperature warm dense aluminum

The ion-ion dynamical structure factor and the equation of state of warm dense aluminum in a two-temperature quasiequilibrium state, with the electron temperature higher than the ion temperature, are investigated using molecular-dynamics simulations based on ion-ion pair potentials constructed from a neutral pseudoatom model. Such pair potentials based on density functional theory are parameter-free and depend directly on the electron temperature and indirectly on the ion temperature, enabling efficient computation of two-temperature properties. Comparison with ab initio simulations and with other average-atom calculations for equilibrium aluminum shows good agreement, justifying a study of quasiequilibrium situations. Analyzing the van Hove function, we find that ion-ion correlations vanish in a time significantly smaller than the electron-ion relaxation time so that dynamical properties have a physical meaning for the quasiequilibrium state. A significant increase in the speed of sound is predicted from the modification of the dispersion relation of the ion acoustic mode as the electron temperature is increased. The two-temperature equation of state including the free energy, internal energy, and pressure is also presented.

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.

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.

Bayesian inference of x-ray diffraction spectra from warm dense matter with the one-component-plasma model

We show that the Bayesian inference of recently measured x-ray diffraction spectra from laser-shocked aluminum [L. B. Fletcher et al., Nat. Photon. 9, 274 (2015)10.1038/nphoton.2015.41] with the one-component-plasma (OCP) model performs remarkably well at estimating the ionic density and temperature. This statistical approach requires many evaluations of the OCP static structure factor, which were done using a recently derived analytic fit. The atomic form factor is approximated by an exponential function in the diffraction window of the first peak. The electronic temperature is then estimated from a comparison of this approximated form factor with the electronic structure of an average atom model. Out-of-equilibrium states, with electrons hotter than ions, are diagnosed for the spectra obtained early after the pump, whereas at a late time delay the plasma is at thermal equilibrium. Apart from the present findings, this OCP-based modeling of warm dense matter has an important role to play in the interpretation of x-ray Thomson scattering measurements currently performed at large laser facilities.

Pair potentials for warm dense matter and their application to x-ray Thomson scattering in aluminum and beryllium

Ultrafast laser experiments yield increasingly reliable data on warm dense matter, but their interpretation requires theoretical models. We employ an efficient density functional neutral-pseudoatom hypernetted-chain (NPA-HNC) model with accuracy comparable to ab initio simulations and which provides first-principles pseudopotentials and pair potentials for warm-dense matter. It avoids the use of (i) ad hoc core-repulsion models and (ii) "Yukawa screening" and (iii) need not assume ion-electron thermal equilibrium. Computations of the x-ray Thomson scattering (XRTS) spectra of aluminum and beryllium are compared with recent experiments and with density-functional-theory molecular-dynamics (DFT-MD) simulations. The NPA-HNC structure factors, compressibilities, phonons, and conductivities agree closely with DFT-MD results, while Yukawa screening gives misleading results. The analysis of the XRTS data for two of the experiments, using two-temperature quasi-equilibrium models, is supported by calculations of their temperature relaxation times.

X-ray scattering measurements on imploding CH spheres at the National Ignition Facility

We have performed spectrally resolved x-ray scattering measurements on highly compressed polystyrene at pressures of several tens of TPa (100 Mbar) created by spherically convergent shocks at the National Ignition Facility. Scattering data of line radiation at 9.0 keV were recorded from the dense plasma shortly after shock coalescence. Accounting for spatial gradients, opacity effects, and source broadening, we demonstrate the sensitivity of the elastic scattering component to carbon K-shell ionization while at the same time constraining the temperature of the dense plasma. For six times compressed polystyrene, we find an average temperature of 86 eV and carbon ionization state of 4.9, indicating that widely used ionization models need revision in order to be suitable for the extreme states of matter tested in our experiment.

X-ray Thomson Scattering in Warm Dense Matter without the Chihara Decomposition

X-ray Thomson scattering is an important experimental technique used to measure the temperature, ionization state, structure, and density of warm dense matter (WDM). The fundamental property probed in these experiments is the electronic dynamic structure factor. In most models, this is decomposed into three terms [J. Chihara, J. Phys. F 17, 295 (1987)] representing the response of tightly bound, loosely bound, and free electrons. Accompanying this decomposition is the classification of electrons as either bound or free, which is useful for gapped and cold systems but becomes increasingly questionable as temperatures and pressures increase into the WDM regime. In this work we provide unambiguous first principles calculations of the dynamic structure factor of warm dense beryllium, independent of the Chihara form, by treating bound and free states under a single formalism. The computational approach is real-time finite-temperature time-dependent density functional theory (TDDFT) being applied here for the first time to WDM. We compare results from TDDFT to Chihara-based calculations for experimentally relevant conditions in shock-compressed beryllium.

Ionic Transport Coefficients of Dense Plasmas without Molecular Dynamics

We present a theoretical model that allows a fast and accurate evaluation of ionic transport properties of realistic plasmas spanning from warm and dense to hot and dilute conditions, including mixtures. This is achieved by combining a recent kinetic theory based on effective interaction potentials with a model for the equilibrium radial density distribution based on an average atom model and the integral equations theory of fluids. The model should find broad use in applications where nonideal plasma conditions are traversed, including inertial confinement fusion, compact astrophysical objects, solar and extrasolar planets, and numerous present-day high energy density laboratory experiments.

Scaling relationships for nonadiabatic energy relaxation times in warm dense matter: toward understanding the equation of state

The dependence of nonadiabatic ion-electron energy transfer rates in warm dense aluminum on the mass density and temperature with decoherence changing this relationship qualitatively.

Models of the elastic x-ray scattering feature for warm dense aluminum

The elastic feature of x-ray scattering from warm dense aluminum has recently been measured by Fletcher et al. [Nature Photonics 9, 274 (2015)]10.1038/nphoton.2015.41 with much higher accuracy than had hitherto been possible. This measurement is a direct test of the ionic structure predicted by models of warm dense matter. We use the method of pseudoatom molecular dynamics to predict this elastic feature for warm dense aluminum with temperatures of 1-100 eV and densities of 2.7-8.1g/cm^{3}. We compare these predictions to experiments, finding good agreement with Fletcher et al. and corroborating the discrepancy found in analyses of an earlier experiment of Ma et al. [Phys. Rev. Lett. 110, 065001 (2013)]PRLTAO0031-900710.1103/PhysRevLett.110.065001. We also evaluate the validity of the Thomas-Fermi model of the electrons and of the hypernetted chain approximation in computing the elastic feature and find them both wanting in the regime currently probed by experiments.

Out-of-equilibrium conditions in x-ray Thomson scattering experiments

We study out-of-equilibrium conditions in recent x-ray Thomson scattering experiments performed in warm dense matter. We use an effective one-component plasma model to characterize the states in which electron and ion temperatures are different. An estimation of the ion temperature is obtained. This method is tested against two recent experiments. Strong out-of-equilibrium conditions are found.

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.

Analysis and implementation of a space resolving spherical crystal spectrometer for x-ray Thomson scattering experiments

The application of a space-resolving spectrometer to X-ray Thomson Scattering (XRTS) experiments has the potential to advance the study of warm dense matter. This has motivated the design of a spherical crystal spectrometer, which is a doubly focusing geometry with an overall high sensitivity and the capability of providing high-resolution, space-resolved spectra. A detailed analysis of the image fluence and crystal throughput in this geometry is carried out and analytical estimates of these quantities are presented. This analysis informed the design of a new spectrometer intended for future XRTS experiments on the Z-machine. The new spectrometer collects 6 keV x-rays with a spherically bent Ge (422) crystal and focuses the collected x-rays onto the Rowland circle. The spectrometer was built and then tested with a foam target. The resulting high-quality spectra prove that a spherical spectrometer is a viable diagnostic for XRTS experiments.

Average-atom model combined with the hypernetted chain approximation applied to warm dense matter

We have combined the average-atom model with the hypernetted chain approximation (AAHNC) to describe the electronic and ionic structure in the warm dense matter regime. On the basis of the electronic and ionic structures, the x-ray Thomson scattering (XRTS) spectrum is calculated using the random-phase approximation. While the electronic structure is described within the average-atom model, the effects of other ions on the electronic structure are considered using an integral equation method of the theory of liquids, namely the hypernetted chain approximation. The ion-ion pair potential is calculated using the modified Gordon-Kim model based on the electronic density distribution. Finally, the electronic and ionic structures are determined self-consistently. The XRTS spectrum is calculated according to the Chihara formula, where the scattering contributions are divided into three components: elastic, bound-free, and free-free. Comparison of the present AAHNC results with other theoretical models and experimental data shows very good agreement. Thus the AAHNC model can give a reasonable description of the electronic and ionic structure in warm dense matter.

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.

Evidence for out-of-equilibrium states in warm dense matter probed by x-ray Thomson scattering

A recent and unexpected discrepancy between ab initio simulations and the interpretation of a laser shock experiment on aluminum, probed by x-ray Thomson scattering (XRTS), is addressed. The ion-ion structure factor deduced from the XRTS elastic peak (ion feature) is only compatible with a strongly coupled out-of-equilibrium state. Orbital free molecular dynamics simulations with ions colder than the electrons are employed to interpret the experiment. The relevance of decoupled temperatures for ions and electrons is discussed. The possibility that it mimics a transient, or metastable, out-of-equilibrium state after melting is also suggested.

Qualification of a high-efficiency, gated spectrometer for x-ray Thomson scattering on the National Ignition Facility

We have designed, built, and successfully fielded a highly efficient and gated Bragg crystal spectrometer for x-ray Thomson scattering measurements on the National Ignition Facility (NIF). It utilizes a cylindrically curved Highly Oriented Pyrolytic Graphite crystal. Its spectral range of 7.4-10 keV is optimized for scattering experiments using a Zn He-α x-ray probe at 9.0 keV or Mo K-shell line emission around 18 keV in second diffraction order. The spectrometer has been designed as a diagnostic instrument manipulator-based instrument for the NIF target chamber at the Lawrence Livermore National Laboratory, USA. Here, we report on details of the spectrometer snout, its novel debris shield configuration and an in situ spectral calibration experiment with a Brass foil target, which demonstrated a spectral resolution of E/ΔE = 220 at 9.8 keV.

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.

Properties of warm dense polystyrene plasmas along the principal Hugoniot

Polystyrene (CH) is often chosen as the ablator material for inertial confinement fusion (ICF) targets. Its static, dynamical, and optical properties in warm, dense conditions (due to shock compression) are important for ICF designs. Using the first-principles quantum molecular dynamics (QMD) method, we have investigated the equation of state (EOS) and optical reflectivity of shock-compressed CH up to an unprecedentedly high pressure of 62 Mbar along the principal Hugoniot. The QMD results are compared with existing experimental measurements as well as the SESAME EOS model. Although the Hugoniot pressure and/or temperature from QMD calculations agrees with experiments and the SESAME EOS model at low pressures below 10 Mbar, we have identified for the first time a stiffer behavior of shocked CH at higher pressures (>10 Mbar). Such a stiffer behavior of warm, dense CH can affect the ablation pressure (shock strength), shock coalescence dynamics, and nonuniformity growth in ICF implosions. In addition, we corrected the mistake made in literature for calculating the reflectivity of shocked CH and obtained good agreements with experimental measurements, which should lend credence to future opacity calculations in a first-principles fashion.

Ab initio simulations for the ion-ion structure factor of warm dense aluminum

We perform ab initio simulations based on finite-temperature density functional theory in order to determine the static and dynamic ion-ion structure factor in aluminum. We calculate the dynamic structure factor via the intermediate scattering function and extract the dispersion relation for the collective excitations. The results are compared with available experimental x-ray scattering data. Very good agreement is obtained for the liquid metal domain. In addition we perform simulations for warm dense aluminum in order to obtain the ion dynamics in this strongly correlated quantum regime. We determine the sound velocity for both liquid and warm dense aluminum which can be checked experimentally using narrow-bandwidth free electron laser radiation.

Observations of continuum depression in warm dense matter with x-ray Thomson scattering

Detailed measurements of the electron densities, temperatures, and ionization states of compressed CH shells approaching pressures of 50 Mbar are achieved with spectrally resolved x-ray scattering. Laser-produced 9 keV x-rays probe the plasma during the transient state of three-shock coalescence. High signal-to-noise x-ray scattering spectra show direct evidence of continuum depression in highly degenerate warm dense matter states with electron densities ne>1024  cm-3. The measured densities and temperatures agree well with radiation-hydrodynamic modeling when accounting for continuum lowering in calculations that employ detailed configuration accounting.

Predictions of x-ray scattering spectra for warm dense matter

We present calculations of x-ray scattering spectra based on ionic and electronic structure factors that are computed from a new model for warm dense matter. In this model, which has no free parameters, the ionic structure is determined consistently with the electronic structure of the bound and free states. The x-ray scattering spectrum is thus fully determined by the plasma temperature, density and nuclear charge, and the experimental parameters. The combined model of warm dense matter and of the x-ray scattering theory is validated against an experiment on room-temperature, solid beryllium. It is then applied to experiments on warm dense beryllium and aluminum. Generally good agreement is found with the experiments. However, some significant discrepancies are revealed and appraised. Based on the strength of our model, we discuss the current state of x-ray scattering experiments on warm dense matter and their potential to determine plasma parameters, to discriminate among models, and to reveal interesting and difficult to model physics in dense plasmas.

Probing the complex ion structure in liquid carbon at 100 GPa

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.

Orbital-free density-functional theory simulations of the dynamic structure factor of warm dense aluminum

Here, we report orbital-free density-functional theory (OF DFT) molecular dynamics simulations of the dynamic ion structure factor of warm solid density aluminum at T=0.5 eV and T=5 eV. We validate the OF DFT method in the warm dense matter regime through comparison of the static and thermodynamic properties with the more complete Kohn-Sham DFT. This extension of OF DFT to dynamic properties indicates that previously used models based on classical molecular dynamics may be inadequate to capture fully the low frequency dynamics of the response function.

Reduced coupled-mode approach to electron-ion energy relaxation

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.