Partial ionization in dense plasmas: comparisons among average-atom density functional models

Self-consistent and detailed opacities from a non-equilibrium average-atom model

Modern density functional theory (DFT) is a powerful tool for accurately predicting self-consistent material properties such as equations of state, transport coefficients and opacities in high energy density plasmas, but it is generally restricted to conditions of local thermodynamic equilibrium (LTE) and produces only averaged electronic states instead of detailed configurations. We propose a simple modification to the bound-state occupation factor of a DFT-based average-atom model that captures essential non-LTE effects in plasmas-including autoionization and dielectronic recombination-thus extending DFT-based models to new regimes. We then expand the self-consistent electronic orbitals of the non-LTE DFT-AA model to generate multi-configuration electronic structure and detailed opacity spectra. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Plasma ionization balance in chemical-picture and average-atom models

We propose an approximate method to calculate ion partition functions in the context of the chemical-picture representation of plasmas as an interacting mixture of various ions and free electrons under the local-thermodynamic-equilibrium conditions. The method uses the superconfiguration approach and implies that the first-order corrections to the energies of excited electron configurations due to the electron-electron interaction may be replaced by a similar first-order correction to the energy of the basic configuration of an ion with the same number of bound electrons. The method enables one to significantly speed up the calculations and generally provides quite accurate results. Using the method proposed, plasma ionization balance and average ion charges calculated on the base of the chemical-picture representation show a good agreement with the relevant average-atom data. For the case of weak electron-ion nonideality, we provide approximate relations between the chemical-picture and average-atom values of the average ion charge, chemical potential, and plasma-density depression of ionization potential.

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.

Equivalence between pressure- and structure-defined ionization in hot dense carbon

The determination of the ionization of a system in the hot dense regime is a long standing issue. Recent studies have shown inconsistencies between standard predictions using average atom models and evaluations deduced from electronic transport properties computed with quantum molecular dynamics simulations [Bethkenhagen et al., Phys. Rev. Res. 2, 023260 (2020)]2643-156410.1103/PhysRevResearch.2.023260. Here, we propose a definition of the ionization based on its effect on the plasma structure as given by the pair distribution function (PDF), and on the concept of effective one-component plasma (eOCP). We also introduce a definition based on the total pressure and on a modelization of the electronic pressure. We show the equivalence of these definitions on two studies of carbon along the 100 eV isotherm and the 10 g/cm^{3} isochor. Simulations along the 100 eV isotherm are obtained with the newly implemented Ext. First principles molecular dynamics (Fpmd) method in Abinit for densities ranging from 1 to 500 g/cm^{3}and along the 10 g/cm^{3} isochor with the recently published Spectral quadrature DFT (Sqdft) simulations, between 8 and 860 eV. The resulting ionizations are compared to the predictions of the average-atom code Qaam which is based on the muffin-tin approximation. A disagreement between the eOCP and the actual PDFs (non-OCP behavior) is interpreted as the onset of bonding in the system.

Effect of ionic disorder on the principal shock Hugoniot

The effect of ionic disorder on the principal Hugoniot is investigated using multiple scattering theory to very high pressure (Gbar). Calculations using molecular dynamics to simulate ionic disorder are compared to those with a fixed crystal lattice, for both carbon and aluminum. For the range of conditions considered here we find that ionic disorder has a relatively minor influence. It is most important at the onset of shell ionization and we find that, at higher pressures, the subtle effect of the ionic environment is overwhelmed by the larger number of ionized electrons with higher thermal energies.

Multifidelity regression of sparse plasma transport data available in disparate physical regimes

Physical data are typically generated by experiments and computations in limited parameter regimes. When datasets generated using such disparate methods are combined into one dataset, the resulting dataset is typically sparse, with dense "islands" in a potentially high-dimensional parameter space, and predictions must be interpolated among such islands. Using plasma transport data as our example, we propose a multifidelity Gaussian-process regression framework that incorporates physical data from multiple sources at multiple fidelities. The impact of the proposed framework varies from little improvement over simpler approaches to qualitatively changing the prediction with consistently increased confidence in regions lacking high-fidelity data. By varying low- and high-fidelity data sources, we demonstrate an approach for determining when multifidelity Gaussian-process regression adds value over single-fidelity regression and therefore when its additional computational costs are merited. We also examine the case in which the outputs of the low- and high-fidelity models correspond to different physical quantities, one of which may be intrinsically computationally cheaper to compute. We conclude by analyzing strategies for sampling high-fidelity data for use in this framework, and we develop a simple sampling approach for reducing regression error across large gaps in data.

Carbon ionization from a quantum average-atom model up to gigabar pressures

We use a nonrelativistic average-atom model to calculate carbon ionization at megabar and gigabar pressures. The pressure is calculated using the stress-tensor method. The electronic electrical conductivity is also considered using the Kubo-Greenwood approach. Comparisons are made with quantum molecular dynamic simulations. A good agreement is obtained for the pressure between the average-atom model and the quantum molecular dynamic simulations in the regime of gigabar pressures. However, the discrepancy already seen with the PURGATORIO code for the average ionization deduced from the quantum molecular dynamic simulations is also observed here with the present average-atom model. Excellent agreement with the PURGATORIO code is found for the average ionization.

Influence of dissipation and effective interaction on the dense plasma dynamic structure factor

The ionic dynamic structure factor is examined to assess the relative roles of dissipation and the effective ionic interaction. Two disparate physically based models of dissipation, which can differ numerically by orders of magnitude, are used in molecular dynamics. We find a negligible impact on the amplitudes of the dynamic structure factors for physically realistic parameter values. We then examine the effective ionic interaction by varying its strength, the size of the atomic core (through a pseudopotential), and the screening model. We find that "diffusive" peaks in the dynamic structure factor are very sensitive to the form of the ionic interaction, and this sensitivity arises primarily from atomic physics through the pseudopotential. This suggests that it would be useful to employ the measured zero-frequency dynamic structure factor S_{ii}(k,0) as a constraint on the effective interaction, which in turn can be used to compute physical properties.

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}).

Machine Learning Discovery of Computational Model Efficacy Boundaries

Computational models are formulated in hierarchies of variable fidelity, often with no quantitative rule for defining the fidelity boundaries. We have constructed a dataset from a wide range of atomistic computational models to reveal the accuracy boundary between higher-fidelity models and a simple, lower-fidelity model. The symbolic decision boundary is discovered by optimizing a support vector machine on the data through iterative feature engineering. This data-driven approach reveals two important results: (i) a symbolic rule emerges that is independent of the algorithm, and (ii) the symbolic rule provides a deeper understanding of the fidelity boundary. Specifically, our dataset is composed of radial distribution functions from seven high-fidelity methods that cover wide ranges in the features (element, density, and temperature); high-fidelity results are compared with a simple pair-potential model to discover the nonlinear combination of the features, and the machine learning approach directly reveals the central role of atomic physics in determining accuracy.

Liquid-Liquid Phase Transitions in Silicon

We use computationally simple neutral pseudoatom ("average atom") density functional theory (DFT) and standard DFT to elucidate liquid-liquid phase transitions (LPTs) in liquid silicon. An ionization-driven transition and three LPTs including the known LPT near 2.5  g/cm^{3} are found. They are robust even to 1 eV. The pair distributions functions, pair potentials, electrical conductivities, and compressibilites are reported. The LPTs are elucidated within a Fermi liquid picture of electron scattering at the Fermi energy that complements the transient covalent bonding picture.

A wide-range multiphase equation of state for platinum

The paper presents a semi-empirical wide-range equation of state (EOS) for platinum with account for melting, evaporation, and ionization. The equation is based on a wide spectrum of experimental and calculation data. Parameters for the EOS were adjusted using a genetic algorithm which proved to perform well for optimizations in big data processing. In the regions where no experimental data were available, we used results of first-principles and average-atom model calculations. The EOS was used to calculate the melting curve of platinum to pressures above 1 TPa, sound velocities along the Hugoniot curve, parameters of melting under shock compression, and parameters of the critical point. An improved model is proposed for the shear modulus in (V,T) coordinates and its variation along the shock adiabat is calculated.

Measurements of pressure-induced Kβ line shifts in ramp compressed cobalt up to 8 Mbar

We report measurements of K-shell fluorescence lines induced by fast electrons in ramp-compressed Co targets. The fluorescence emission was stimulated by fast electrons generated through short-pulse laser-solid interaction with an Al target layer. Compression up to 2.1× solid density was achieved while maintaining temperatures well below the Fermi energy, effectively removing the thermal effects from consideration. We observed small but unambiguous redshifts in the Kβ fluorescence line relative to unshifted Cu Kα. Redshifts up to 2.6 eV were found to increase with compression and to be consistent with predictions from self-consistent models based on density-functional theory.

Electron-ion coupling factor for temperature relaxation in dense plasmas

We compare two formulas obtained from first principles to calculate the electron-ion coupling factor for temperature relaxation in dense plasmas. The quantum average-atom model is used to calculate this electron-ion coupling factor. It is shown that if the two formulas agree at sufficiently high temperature so that the potential energy is of limited importance, i.e., when the plasma is said to be kinetic, and are consistent with the Landau-Spitzer formula, then they strongly differ in the warm-dense-matter regime. Only one of the two is shown to be consistent with quantum molecular dynamics approach. We use this point to determine which formula is valid to describe temperature relaxation between electrons and ions in warm and hot dense plasmas.

Electrical resistivity calculations in dense plasmas

We present calculations of electrical resistivity in dense plasmas using the average-atom model. The Born approximation is proposed to improve the computations especially in the hot domain of the density and temperature plane. Both the nonrelativistic and relativistic regimes are considered. Numerical examples are given.

Pressure in warm and hot dense matter using the average-atom model

Expressions of pressure in warm and hot dense matter using the average-atom model are presented. They are based on the stress-tensor approach. Nonrelativistic and relativistic cases are considered. The obtained formulas are simple and can be easily implemented in an average-atom model code. Comparisons with experimental data and quantum molecular dynamics and path integral Monte Carlo simulations are shown. The present formalism agrees well with experimental results for a large variety of elements in the warm dense matter regime and with ab initio simulations in the warm and hot dense matter regime for aluminum.

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.

Density effects on electronic configurations in dense plasmas

We present a quantum mechanical model to describe the density effects on electronic configurations inside a plasma environment. Two different approaches are given by starting from a quantum average-atom model. Illustrations are shown for an aluminum plasma in local thermodynamic equilibrium at solid density and at a temperature of 100 eV and in the thermodynamic conditions of a recent experiment designed to characterize the effects of the ionization potential depression treatment. Our approach compares well with experiment and is consistent in that case with the approach of Stewart and Pyatt to describe the ionization potential depression rather than with the method of Ecker and Kröll.

Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation

In this work, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly coupled plasma from the Lenard-Balescu equation. With some minor approximations, we derive an analytic formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electron-ion temperature ratios and arbitrary electron degeneracy. For large temperature ratios, we derive the necessary correction to account for the coupled-mode effect, which can be evaluated very efficiently using ordinary Gaussian quadrature.

Interfacial mixing in high-energy-density matter with a multiphysics kinetic model

We have extended a recently developed multispecies, multitemperature Bhatnagar-Gross-Krook model [Haack et al., J. Stat. Phys. 168, 822 (2017)JSTPBS0022-471510.1007/s10955-017-1824-9], to include multiphysics capabilities that enable modeling of a wider range of physical conditions. In terms of geometry, we have extended from the spatially homogeneous setting to one spatial dimension. In terms of the physics, we have included an atomic ionization model, accurate collision physics across coupling regimes, self-consistent electric fields, and degeneracy in the electronic screening. We apply the model to a warm dense matter scenario in which the ablator-fuel interface of an inertial confinement fusion target is heated, but for larger length and time scales and for much higher temperatures than can be simulated using molecular dynamics. Relative to molecular dynamics, the kinetic model greatly extends the temperature regime and the spatiotemporal scales over which we are able to model. In our numerical results we observe hydrogen from the ablator material jetting into the fuel during the early stages of the implosion and compare the relative size of various diffusion components (Fickean diffusion, electrodiffusion, and barodiffusion) that drive this process. We also examine kinetic effects, such as anisotropic distributions and velocity separation, in order to determine when this problem can be described with a hydrodynamic model.

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.

Multidimensional Chebyshev interpolation for warm and hot dense matter

We propose a scheme based on a multidimensional Chebyshev interpolation to approximate smooth functions that depend on more than one variable. The present method generalizes the one dimensional Chebyshev approximation. The multidimensional approach can be used for generating databases like equation of state in the warm and hot dense matter. It is well suited to the present advance of massively parallel supercomputers.

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.

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.

Measurements of continuum lowering in solid-density plasmas created from elements and compounds

The effect of a dense plasma environment on the energy levels of an embedded ion is usually described in terms of the lowering of its continuum level. For strongly coupled plasmas, the phenomenon is intimately related to the equation of state; hence, an accurate treatment is crucial for most astrophysical and inertial-fusion applications, where the case of plasma mixtures is of particular interest. Here we present an experiment showing that the standard density-dependent analytical models are inadequate to describe solid-density plasmas at the temperatures studied, where the reduction of the binding energies for a given species is unaffected by the different plasma environment (ion density) in either the element or compounds of that species, and can be accurately estimated by calculations only involving the energy levels of an isolated neutral atom. The results have implications for the standard approaches to the equation of state calculations.

Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter

The influence of finite relaxation times on Thomson scattering from warm dense plasmas is examined within the framework of the average-atom approximation. Presently most calculations use the collision-free Lindhard dielectric function to evaluate the free-electron contribution to the Thomson cross section. In this work, we use the Mermin dielectric function, which includes relaxation time explicitly. The relaxation time is evaluated by treating the average atom as an impurity in a uniform electron gas and depends critically on the transport cross section. The calculated relaxation rates agree well with values inferred from the Ziman formula for the static conductivity and also with rates inferred from a fit to the frequency-dependent conductivity. Transport cross sections determined by the phase-shift analysis in the average-atom potential are compared with those evaluated in the commonly used Born approximation. The Born approximation converges to the exact cross sections at high energies; however, differences that occur at low energies lead to corresponding differences in relaxation rates. The relative importance of including relaxation time when modeling x-ray Thomson scattering spectra is examined by comparing calculations of the free-electron dynamic structure function for Thomson scattering using Lindhard and Mermin dielectric functions. Applications are given to warm dense Be plasmas, with temperatures ranging from 2 to 32 eV and densities ranging from 2 to 64 g/cc.

Ionic transport in high-energy-density matter

Ionic transport coefficients for dense plasmas have been numerically computed using an effective Boltzmann approach. We have developed a simplified effective potential approach that yields accurate fits for all of the relevant cross sections and collision integrals. Our results have been validated with molecular-dynamics simulations for self-diffusion, interdiffusion, viscosity, and thermal conductivity. Molecular dynamics has also been used to examine the underlying assumptions of the Boltzmann approach through a categorization of behaviors of the velocity autocorrelation function in the Yukawa phase diagram. Using a velocity-dependent screening model, we examine the role of dynamical screening in transport. Implications of these results for Coulomb logarithm approaches are discussed.

Unified Concept of Effective One Component Plasma for Hot Dense Plasmas

Orbital-free molecular dynamics simulations are used to benchmark two popular models for hot dense plasmas: the one component plasma (OCP) and the Yukawa model. A unified concept emerges where an effective OCP (EOCP) is constructed from the short-range structure of the plasma. An unambiguous ionization and the screening length can be defined and used for a Yukawa system, which reproduces the long-range structure with finite compressibility. Similarly, the dispersion relation of longitudinal waves is consistent with the screened model at vanishing wave number but merges with the OCP at high wave number. Additionally, the EOCP reproduces the overall relaxation time scales of the correlation functions associated with ionic motion. In the hot dense regime, this unified concept of EOCP can be fruitfully applied to deduce properties such as the equation of state, ionic transport coefficients, and the ion feature in x-ray Thomson scattering experiments.

Strongly-coupled plasmas formed from laser-heated solids

We present an analysis of ion temperatures in laser-produced plasmas formed from solids with different initial lattice structures. We show that the equilibrium ion temperature is limited by a mismatch between the initial crystallographic configuration and the close-packed configuration of a strongly-coupled plasma, similar to experiments in ultracold neutral plasmas. We propose experiments to demonstrate and exploit this crystallographic heating in order to produce a strongly coupled plasma with a coupling parameter of several hundred.

Generalized hydrodynamics model for strongly coupled plasmas

Beginning with the exact equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we obtain the density, momentum, and stress tensor-moment equations. We close the moment equations with two closures, one that guarantees an equilibrium state given by density-functional theory and another that includes collisions in the relaxation of the stress tensor. The introduction of a density functional-theory closure ensures self-consistency in the equation-of-state properties of the plasma (ideal and excess pressure, electric fields, and correlations). The resulting generalized hydrodynamics thus includes all impacts of Coulomb coupling, viscous damping, and the high-frequency (viscoelastic) response. We compare our results with those of several known models, including generalized hydrodynamic theory and models obtained using the Singwi-Tosi-Land-Sjolander approximation and the quasilocalized charge approximation. We find that the viscoelastic response, including both the high-frequency elastic generalization and viscous wave damping, is important for correctly describing ion-acoustic waves. We illustrate this result by considering three very different systems: ultracold plasmas, dusty plasmas, and dense plasmas. The new model is validated by comparing its results with those of the current autocorrelation function obtained from molecular-dynamics simulations of Yukawa plasmas, and the agreement is excellent. Generalizations of this model to mixtures and quantum systems should be straightforward.

Measurement of charged-particle stopping in warm dense plasma

We measured the stopping of energetic protons in an isochorically heated solid-density Be plasma with an electron temperature of ∼32  eV, corresponding to moderately coupled [(e^{2}/a)/(k_{B}T_{e}+E_{F})∼0.3] and moderately degenerate [k_{B}T_{e}/E_{F}∼2] "warm-dense matter" (WDM) conditions. We present the first high-accuracy measurements of charged-particle energy loss through dense plasma, which shows an increased loss relative to cold matter, consistent with a reduced mean ionization potential. The data agree with stopping models based on an ad hoc treatment of free and bound electrons, as well as the average-atom local-density approximation; this work is the first test of these theories in WDM plasma.

Unified description of linear screening in dense plasmas

Electron screening of ions is among the most fundamental properties of plasmas, determining the effective ionic interactions that impact all properties of a plasma. With the development of new experimental facilities that probe high-energy-density physics regimes ranging from warm dense matter to hot dense matter, a unified framework for describing dense plasma screening has become essential. Such a unified framework is presented here based on finite-temperature orbital-free density functional theory, including gradient corrections and exchange-correlation effects. We find a new analytic pair potential for the ion-ion interaction that incorporates moderate electronic coupling, quantum degeneracy, gradient corrections to the free energy, and finite temperatures. This potential can be used in large-scale "classical" molecular dynamics simulations, as well as in simpler theoretical models (e.g., integral equations and Monte Carlo), with no additional computational complexity. The new potential theoretically connects limits of Debye-Hückel-Yukawa, Lindhard, Thomas-Fermi, and Bohmian quantum hydrodynamics descriptions. Based on this new potential, we predict ionic static structure factors that can be validated using x-ray Thomson scattering data.

Electric microfields in dense carbon-hydrogen plasmas

Classical molecular dynamics is used to investigate stationary and time-dependent properties of microfields in hot, solid density, electron-ion plasmas. Even at the high temperatures considered here, such simulations require quantum statistical potentials (QSPs) to mimic the essential effects of diffraction and exchange symmetry for electrons. Fortunately, key results relevant to microfield distributions are found to be insensitive to different, plausible QSP choices. Atomic processes in plasmas will depend on the time average of the microfields. It is not clear, a priori, what the time duration of this average should be. The question of how best to extract the quasistatic (low-frequency) microfield from a classical molecular dynamics simulation is explored in some detail, and the time-averaging approach we adopt involves both plasma and atomic time scale constraints. One of the major findings described in the paper is that for a large time interval, the time-averaged microfield does not significantly change. Our discussion of this suite of large simulations for plasma mixtures focuses on understanding various features and trends revealed by data for C-H plasmas having carbon fractions ranging from 0.01 to 1, and different temperatures well above TFermi.

Diffusivity in asymmetric Yukawa ionic mixtures in dense plasmas

In this paper we present molecular dynamics (MD) calculations of the interdiffusion coefficient for asymmetric mixed plasma for thermodynamic conditions relevant to astrophysical and inertial confinement fusion plasmas. Specifically, we consider mixtures of deuterium and argon at temperatures of 100-500 eV and a number density ∼10(25) ions/cm(3). The motion of 30,000-120,000 ions is simulated in which the ions interact via the Yukawa (screened Coulomb) potential. The electric field of the electrons is included in this effective interaction; the electrons are not simulated explicitly. The species diffusivity is then calculated using the Green-Kubo approach using an integral of the interdiffusion current autocorrelation function, a quantity calculated in the equilibrium MD simulations. Our MD simulation results show that a widely used expression relating the interdiffusion coefficient with the concentration-weighted sum of self-diffusion coefficients overestimates the interdiffusion coefficient. We argue that this effect due to cross-correlation terms in velocities is characteristic of asymmetric mixed plasmas. Comparison of the MD results with predictions of kinetic theories also shows a discrepancy with MD giving effectively a larger Coulomb logarithm.

Thomson scattering from a three-component plasma

A model for a three-component plasma consisting of two distinct ionic species and electrons is developed and applied to study x-ray Thomson scattering. Ions of a specific type are assumed to be identical and are treated in the average-atom approximation. Given the plasma temperature and density, the model predicts mass densities, effective ionic charges, and cell volumes for each ionic type, together with the plasma chemical potential and free-electron density. Additionally, the average-atom treatment of individual ions provides a quantum-mechanical description of bound and continuum electrons. The model is used to obtain parameters needed to determine the dynamic structure factors for x-ray Thomson scattering from a three-component plasma. The contribution from inelastic scattering by free electrons is evaluated in the random-phase approximation. The contribution from inelastic scattering by bound electrons is evaluated using the bound-state and scattering wave functions obtained from the average-atom calculations. Finally, the partial static structure factors for elastic scattering by ions are evaluated using a two-component version of the Ornstein-Zernike equations with hypernetted chain closure, in which electron-ion interactions are accounted for using screened ion-ion interaction potentials. The model is used to predict the x-ray Thomson scattering spectrum from a CH plasma and the resulting spectrum is compared with experimental results obtained by Feltcher et al. [Phys. Plasmas 20, 056316 (2013)].

Thomas-Fermi Z-scaling laws and coupling stabilization for plasmas

Extending the well-known Thomas-Fermi Z-scaling laws to the Coulomb coupling parameter, we investigate the stabilization of the ionic coupling in isochoric heating [Clérouin et al., Phys. Rev. E 87, 061101 (2013)]. This stabilization is restricted to a domain in atomic number Z, temperature, and density, including strong limitations on high couplings, that can only be obtained for high-Z elements. Contact is made with recent isochoric heating experiments. The consequences for corresponding states with respect to ionic coupling are also quantified via orbital free molecular dynamics simulations. This opens avenues for future isochoric heating experiments.