Electronic and ionic structures of warm and hot dense matter

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

Variational atomic model of plasma accounting for ion radial correlations and electronic structure of ions

We propose a model of ion-electron plasma (or nucleus-electron plasma) that accounts for the electronic structure around nuclei (i.e., ion structure) as well as for ion-ion correlations. The model equations are obtained through the minimization of an approximate free-energy functional, and it is shown that the model fulfills the virial theorem. The main hypotheses of this model are (1) nuclei are treated as classical indistinguishable particles, (2) electronic density is seen as a superposition of a uniform background and spherically symmetric distributions around each nucleus (system of ions in a plasma), (3) free energy is approached using a cluster expansion (nonoverlapping ions), and (4) resulting ion fluid is modeled through an approximate integral equation. In the present paper, the model is described only in its average-atom version.

Average-atom model with Siegert states

In plasmas, electronic states can be well-localized bound states or itinerant free states, or something in between. In self-consistent treatments of plasma electronic structure such as the average-atom model, all states must be accurately resolved in order to achieve a converged numerical solution. This is a challenging numerical and algorithmic problem in large part due to the continuum of free states which is relatively expensive and difficult to resolve accurately. Siegert states are an appealing alternative. They form a complete eigenbasis with a purely discrete spectrum while still being equivalent to a representation in terms of the usual bound states and free states. However, many of their properties are unintuitive, and it is not obvious that they are suitable for self-consistent plasma electronic structure calculations. Here it is demonstrated that Siegert states can be used to accurately solve an average-atom model and offer advantages over the traditional finite-difference approach, including a concrete physical picture of pressure ionization and continuum resonances.

Yukawa-Friedel-tail pair potentials for warm dense matter applications

Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many high-energy-density situations. Molecular dynamics (MD) is a simulation method that generates EOS and transport data using an externally provided potential to dynamically evolve the particles without further reference to the electrons. To minimize computational cost, pair potentials needed in MD may be obtained from the neutral-pseudoatom (NPA) approach, a form of single-ion density functional theory (DFT), where many-ion effects are included via ion-ion correlation functionals. Standard N-ion DFT-MD provides pair potentials via the force matching technique but at much greater computational cost. Here we propose a simple analytic model for pair potentials with physically meaningful parameters based on a Yukawa form with a thermally damped Friedel tail (YFT) applicable to systems containing free electrons. The YFT model accurately fits NPA pair potentials or the nonparametric force-matched potentials from N-ion DFT-MD, showing excellent agreement for a wide range of conditions. The YFT form provides accurate extrapolations of the NPA or force-matched potentials for small and large particle separations within a physical model. Our method can be adopted to treat plasma mixtures, allowing for large-scale simulations of multispecies warm dense matter.

Dense plasma opacity via the multiple-scattering method

The calculation of the optical properties of hot dense plasmas with a model that has self-consistent plasma physics is a grand challenge for high energy density science. Here we exploit a recently developed electronic structure model that uses multiple scattering theory to solve the Kohn-Sham density functional theory equations for dense plasmas. We calculate opacities in this regime, validate the method, and apply it to recent experimental measurements of opacity for Cr, Ni, and Fe. Good agreement is found in the quasicontinuum region for Cr and Ni, while the self-consistent plasma physics of the approach cannot explain the observed difference between models and the experiment for Fe.

Kinetic model for electron-ion transport in warm dense matter

We present a model for electron-ion transport in warm dense matter that incorporates Coulomb coupling effects into the quantum Boltzmann equation of Uehling and Uhlenbeck through the use of a statistical potential of mean force. Although the model presented here can be derived rigorously in the classical limit [S. D. Baalrud and J. Daligault, Phys. Plasmas 26, 082106 (2019)PHPAEN1070-664X10.1063/1.5095655], its quantum generalization is complicated by the uncertainty principle. Here we apply an existing model for the potential of mean force based on the quantum Ornstein-Zernike equation coupled with an average-atom model [C. E. Starrett, High Energy Density Phys. 25, 8 (2017)1574-181810.1016/j.hedp.2017.09.003]. This potential contains correlations due to both Coulomb coupling and exchange, and the collision kernel of the kinetic theory enforces Pauli blocking while allowing for electron diffraction and large-angle collisions. We use the Uehling-Uhlenbeck equation to predict the momentum and temperature relaxation times and electrical conductivity of solid density aluminum plasma based on electron-ion collisions. We present results for density and temperature conditions that span the transition from classical weakly-coupled plasma to degenerate moderately-coupled plasma. Our findings agree well with recent quantum molecular dynamics simulations.

Equation of state modeling with pseudoatom molecular dynamics

Using a modified version of the pseudoatom molecular-dynamics approach, the silicon and oxygen equations of state were generated and then employed to construct the equation of state of silicon dioxide. The results are supported by the close agreement with ab initio simulations of the silicon pressure and experimental shock Hugoniot of silicon dioxide. Ion thermal contributions to thermodynamic functions provided by the PAMD simulations are compared to their counterparts obtained with the one-component plasma and charged-hard-sphere approximations.

Modeling of short-pulse laser-metal interactions in the warm dense matter regime using the two-temperature model

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 1×10^{3}-3×10^{4}J/m^{2}(0.1-3J/cm^{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_{melt}(μm)≅4×10^{3}F(J/m^{2}).

Super Transition Arrays: A Tool for Studying Spectral Properties of Hot Plasmas

For the theoretical study of X and extreme-UV spectra of ions in plasmas, quantum mechanics brings more detailed results than statistical physics. However, it is impossible to handle individually the billions of levels that must be taken into account in order to properly describe hot plasmas. Such levels can be gathered into electronic configurations or superconfigurations (groups of configurations) and the corresponding calculations rely on appropriate statistical methods, for local or non-local thermodynamic equilibrium plasmas. In this article we present the basic principles of the Super-Transition-Array approach as well as its practical implementation. During the last decades, calculations performed with the SCO code (Superconfiguration Code for Opacity) have been compared to opacity measurements. The code includes static screening of ions by plasma and is well suited for studying plasma density effects (for example pressure ionization) on opacity and equation of state. The recently developed SCO-RCG code (Superconfiguration Code for Opacity combined with Robert Cowan’s “G” subroutine) combines statistical methods from SCO and fine-structure (detailed-level-accounting) calculations using subroutine RCG from Cowan’s code. SCO-RCG enables us to obtain very detailed spectra and to significantly improve the interpretation of experimental spectra. The Super-Transition-Array formalism is still the cornerstone of several opacity codes, and new ideas are emerging, such as the Configurationally Resolved-Super-Transition-Array approach or the extension of the Partially Resolved-Transition-Array concept to the superconfiguration method.

Multiscale simulation of plasma flows using active learning

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.

Model of electron transport in dense plasmas spanning temperature regimes

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.

Correlations between conduction electrons in dense plasmas

Most treatments of electron-electron correlations in dense plasmas either ignore them entirely (random phase approximation) or neglect the role of ions (jellium approximation). In this work, we go beyond both these approximations to derive a formula for the electron-electron static structure factor which properly accounts for the contributions of both ionic structure and quantum-mechanical dynamic response in the electrons. The result can be viewed as a natural extension of the quantum Ornstein-Zernike theory of ionic and electronic correlations, and it is suitable for dense plasmas in which the ions are classical and the conduction electrons are quantum-mechanical. The corresponding electron-electron pair distribution functions are compared with the results of path integral Monte Carlo simulations, showing good agreement whenever no strong electron resonance states are present. We construct approximate potentials of mean force which describe the effective screened interaction between electrons. Significant deviations from Debye-Hückel screening are present at temperatures and densities relevant to high-energy density experiments involving warm and hot dense plasmas. The presence of correlations between conduction electrons is likely to influence the electron-electron contribution to the electrical and thermal conductivity. It is expected that excitation processes involving the conduction electrons (e.g., free-free absorption) will also be affected.

Testing thermal conductivity models with equilibrium molecular dynamics simulations of the one-component plasma

Equilibrium molecular dynamics simulations are used to calculate the thermal conductivity of the one-component plasma via the Green-Kubo formalism over a broad range of Coulomb coupling strength, 0.1≤Γ≤180. These simulations address previous discrepancies between computations using equilibrium versus nonequilibrium methods. Analysis of heat flux autocorrelation functions show that very long (6×10^{5}ω_{p}^{-1}) time series are needed to reduce the noise level to allow ≲2% accuracy. The simulations provide accurate data for Γ≲1. This enables a test of the traditional Landau-Spitzer theory, which is found to agree with the simulations for Γ≲0.3. It also enables tests of theories to address moderate and strong Coulomb coupling. Two are found to provide accurate extensions to the moderate coupling regime of Γ≲10, but none are accurate in the Γ≳10 regime where potential energy transport and coupling between mass flow and stress dominate thermal conduction.

Theory of the electron-ion temperature relaxation rate spanning the hot solid metals and plasma phases

We present a theory for the rate of energy exchange between electrons and ions-also known as the electron-ion coupling factor-in physical systems ranging from hot solid metals to plasmas, including liquid metals and warm dense matter. The paper provides the theoretical foundations of a recent work [J. Simoni and J. Daligault, Phys. Rev. Lett. 122, 205001 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.205001], where first-principles quantum molecular dynamics calculations based on this theory were presented for representative materials and conditions. We first derive a general expression for the electron-ion coupling factor that includes self-consistently the quantum mechanical and statistical nature of electrons, the thermal and disorder effects, and the correlations between particles. The electron-ion coupling is related to the friction coefficients felt by individual ions due to their nonadiabatic interactions with the electrons. Each coefficient satisfies a Kubo relation given by the time integral of the autocorrelation function of the interaction force of an ion with the electrons. Exact properties and different representations of the general expressions are discussed. We then show that our theory reduces to well-known models in limiting cases. In particular, we show that it simplifies to the standard electron-phonon coupling formula in the limit of hot solids with lattice and electronic temperatures much greater than the Debye temperature, and that it extends the electron-phonon coupling formula beyond the harmonic phonon approximation. For plasmas, we show that the theory readily reduces to the well-known Spitzer formula in the hot plasma limit, to the Fermi "golden rule" formula in the limit of weak electron-ion interactions, and to other models proposed to go beyond the latter approximation. We explain that the electron-ion coupling is particularly well adapted to average atom models, which offer an effective way to include nonideal interaction effects to the standard models and at a much reduced computational cost in comparison to first-principles quantum molecular dynamics simulations.

High-temperature electronic structure with the Korringa-Kohn-Rostoker Green's function method

Modeling high-temperature (tens or hundreds of eV), dense plasmas is challenging due to the multitude of non-negligible physical effects including significant partial ionization and multisite effects. These effects cause the breakdown or intractability of common methods and approximations used at low temperatures, such as pseudopotentials or plane-wave basis sets. Here we explore the Korringa-Kohn-Rostoker Green's function method at these high-temperature conditions. The method is all electron, does not rely on pseudopotentials, and uses a spherical harmonic basis set, and so avoids the aforementioned limitations. It is found to be accurate for solid density aluminum and iron plasmas when compared to a plane-wave method at low temperature, while being able to access high temperatures.

Validating Continuum Lowering Models via Multi-Wavelength Measurements of Integrated X-ray Emission

X-ray emission spectroscopy is a well-established technique used to study continuum lowering in dense plasmas. It relies on accurate atomic physics models to robustly reproduce high-resolution emission spectra, and depends on our ability to identify spectroscopic signatures such as emission lines or ionization edges of individual charge states within the plasma. Here we describe a method that forgoes these requirements, enabling the validation of different continuum lowering models based solely on the total intensity of plasma emission in systems driven by narrow-bandwidth x-ray pulses across a range of wavelengths. The method is tested on published Al spectroscopy data and applied to the new case of solid-density partially-ionized Fe plasmas, where extracting ionization edges directly is precluded by the significant overlap of emission from a wide range of charge states.

Isochoric, isobaric, and ultrafast conductivities of aluminum, lithium, and carbon in the warm dense matter regime

We study the conductivities σ of (i) the equilibrium isochoric state σ_{is}, (ii) the equilibrium isobaric state σ_{ib}, and also the (iii) nonequilibrium ultrafast matter state σ_{uf} with the ion temperature T_{i} less than the electron temperature T_{e}. Aluminum, lithium, and carbon are considered, being increasingly complex warm dense matter systems, with carbon having transient covalent bonds. First-principles calculations, i.e., neutral-pseudoatom (NPA) calculations and density-functional theory (DFT) with molecular-dynamics (MD) simulations, are compared where possible with experimental data to characterize σ_{ic}, σ_{ib}, and σ_{uf}. The NPA σ_{ib} is closest to the available experimental data when compared to results from DFT with MD simulations, where simulations of about 64-125 atoms are typically used. The published conductivities for Li are reviewed and the value at a temperature of 4.5 eV is examined using supporting x-ray Thomson-scattering calculations. A physical picture of the variations of σ with temperature and density applicable to these materials is given. The insensitivity of σ to T_{e} below 10 eV for carbon, compared to Al and Li, is clarified.

Thomas-Fermi simulations of dense plasmas without pseudopotentials

The Thomas-Fermi model for warm and hot dense matter is widely used to predict material properties such as the equation of state. However, for practical reasons current implementations use pseudopotentials for the electron-nucleus interaction instead of the bare Coulomb potential. This complicates the calculation and quantities such as free energy cannot be converged with respect to the pseudopotential parameters. We present a method that retains the bare Coulomb potential for the electron-nucleus interaction and does not use pseudopotentials. We demonstrate that accurate free energies are obtained by checking variational consistency. Examples for aluminum and iron plasmas are presented.

Equation of state, phonons, and lattice stability of ultrafast warm dense matter

Using the two-temperature model for ultrafast matter (UFM), we compare the equation of state, pair-distribution functions g(r), and phonons using the neutral pseudoatom (NPA) model with results from density functional theory (DFT) codes and molecular dynamics (MD) simulations for Al, Li, and Na. The NPA approach uses state-dependent first-principles pseudopotentials from an "all-electron" DFT calculation with finite-T exchange-correlation functional (XCF). It provides pair potentials, structure factors, the "bound" and "free" states, as well as a mean ionization Z[over ¯] unambiguously. These are not easily accessible via DFT+MD calculations which become prohibitive for T/T_{F} exceeding ∼0.6, where T_{F} is the Fermi temperature. Hence, both DFT+MD and NPA methods can be compared up to ∼8eV, while higher T can be addressed via the NPA. The high-T_{e} phonon calculations raise the question of UFM lattice stability and surface ablation in thin UFM samples. The ablation forces in a UFM slab are used to define an "ablation time" competing with phonon formation times in thin UFM samples. Excellent agreement for all properties is found between NPA and standard DFT codes, even for Li where a strongly nonlocal pseudopotential is used in DFT codes. The need to use pseudopotentials appropriate to the ionization state Z[over ¯] is emphasized. The effect of finite-T XCF is illustrated via its effect on the pressure and the electron-density distribution at a nucleus.

Multipole expansion in plasmas: Effective interaction potentials between compound particles

In this paper, the multipole expansion method is used to determine effective interaction potentials between particles in both classical dusty plasma and dense quantum plasma. In particular, formulas for interactions of dipole-dipole and charge-dipole pairs in a classical nondegenerate plasma as well as in degenerate quantum and semiclassical plasmas were derived. The potentials describe interactions between atoms, atoms and charged particles, dust particles in the complex plasma, atoms and electrons in the degenerate plasma, and metals. Correctness of the results obtained from the multipole expansion is confirmed by their agreement with the results based on other methods of statistical physics and dielectric response function. It is shown that the method of multipole expansion can be used to derive effective interaction potentials of compound particles, if the effect of the medium on the potential of individual particles comprising compound particles is known.

Equation of state of dense plasmas with pseudoatom molecular dynamics

We present an approximation for calculating the equation of state (EOS) of warm and hot dense matter that is built on the previously published pseudoatom molecular dynamics (PAMD) model of dense plasmas [Starrett et al., Phys. Rev. E 91, 013104 (2015)PLEEE81539-375510.1103/PhysRevE.91.013104]. While the EOS calculation with PAMD was previously limited to orbital-free density functional theory (DFT), the new approximation presented here allows a Kohn-Sham DFT treatment of the electrons. The resulting EOS thus includes a quantum mechanical treatment of the electrons with a self-consistent model of the ionic structure, while remaining tractable at high temperatures. The method is validated by comparisons with pressures from ab initio simulations of Be, Al, Si, and Fe. The EOS in the Thomas-Fermi approximation shows remarkable thermodynamic consistency over a wide range of temperatures for aluminum. We calculate the principal Hugoniots of aluminum and silicon up to 500 eV. We find that the ionic structure of the plasma has a modest effect that peaks at temperatures of a few eV and that the features arising from the electronic structure agree well with ab initio simulations.

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.

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.

Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime

We present simulations of a four-component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5-200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. Additionally, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

Ion-ion dynamic structure factor of warm dense mixtures

The ion-ion dynamic structure factor of warm dense matter is determined using the recently developed pseudoatom molecular dynamics method [Starrett et al., Phys. Rev. E 91, 013104 (2015)]. The method uses density functional theory to determine ion-ion pair interaction potentials that have no free parameters. These potentials are used in classical molecular dynamics simulations. This constitutes a computationally efficient and realistic model of dense plasmas. Comparison with recently published simulations of the ion-ion dynamic structure factor and sound speed of warm dense aluminum finds good to reasonable agreement. Using this method, we make predictions of the ion-ion dynamical structure factor and sound speed of a warm dense mixture-equimolar carbon-hydrogen. This material is commonly used as an ablator in inertial confinement fusion capsules, and our results are amenable to direct experimental measurement.

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.

Pseudoatom molecular dynamics

An approach to simulating warm and hot dense matter that combines density-functional-theory-based calculations of the electronic structure to classical molecular dynamics simulations with pair interaction potentials is presented. The method, which we call pseudoatom molecular dynamics, can be applied to single-component or multicomponent plasmas. It gives equation of state and self-diffusion coefficients with an accuracy comparable to orbital-free molecular dynamics simulations but is computationally much more efficient.

Integral equation model for warm and hot dense mixtures

In a previous work [C. E. Starrett and D. Saumon, Phys. Rev. E 87, 013104 (2013)] a model for the calculation of electronic and ionic structures of warm and hot dense matter was described and validated. In that model the electronic structure of one atom in a plasma is determined using a density-functional-theory-based average-atom (AA) model and the ionic structure is determined by coupling the AA model to integral equations governing the fluid structure. That model was for plasmas with one nuclear species only. Here we extend it to treat plasmas with many nuclear species, i.e., mixtures, and apply it to a carbon-hydrogen mixture relevant to inertial confinement fusion experiments. Comparison of the predicted electronic and ionic structures with orbital-free and Kohn-Sham molecular dynamics simulations reveals excellent agreement wherever chemical bonding is not significant.

Quantum molecular dynamics study on the structures and dc conductivity of warm dense silane

The ionic and electronic structures of warm dense silane at the densities of 1.795, 2.260, 3.382, and 3.844 g/cm(3) have been studied with temperatures from 1000 K to 3 eV using quantum molecular dynamics simulations. At all densities, the structures are melted above 1000 K. The matter states are characterized as polymeric from 1000 to 4000 K and become dense plasma states with further increasing temperature to 1 eV. At two lower densities of 1.795 and 2.260 g/cm(3), silane first dissociates and then becomes the polymeric state via a chain state from the initial crystalline structure. At higher densities, however, no dissociation stage was found. These findings can help us understand how the warm dense matter forms. A rise is found for the direct current electric conductivity at T ∼ 1000 K, indicating the nonmetal-to-metal transition. The conductivity decreases slightly with the increase of temperature, which is due to the more disordered structures at higher temperatures.

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.