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

Average-atom approach for transport properties of shocked argon in the presence of a magnetic field

We present electron transport calculations of shocked argon based on an average-atom modeling of the plasma and compare them with measurements, involving both incident and reflected shock waves. Since the corresponding experiments are subject to a 5 T magnetic field, the impact of the latter on the Rankine-Hugoniot equations is taken into account, starting from the magnetoresistive hydrodynamics, and the resistivity tensor is deduced from the Boltzmann equation. The resistivity tensor yields the electrical and Hall resistivities. Our average-atom code Paradisio provides the quantities required for the calculation of electrical resistivity within the Ziman-Evans formalism, as well as for the Hall resistivity. We obtain good agreement between calculated conductivities and experimental values, both for the incident and reflected shocks. Our values of the Hall constant are compared to experimental values derived from Hall voltage measurements, as well as to theoretical ones based on the quantum statistical linear-relaxation-time approach.

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.

Ionization of carbon at 10-100 times the diamond density and in the 10^{6} K temperature range

The behavior of partially ionized hot compressed matter is critical to the study of planetary interiors as well as nuclear fusion studies. A recent quantum study of carbon in the 10-70 Gbar range and at a temperature of 100 eV used N-atom density functional theory (DFT) with N∼32-64 and molecular dynamics (MD). This involves band-structure-type electronic calculations and averaging over many MD-generated ion configurations. The calculated average number of free electrons per ion, viz., Z[over ¯], was systematically higher than from a standard average-atom quantum calculation. To clarify this offset, we examine the effect of the self-interaction error in such estimates and the possibility of carbon being in a granular plasma state containing Coulomb crystals with a magic number. The electrical conductivity, pressure, and compressibility of the carbon system are examined. The very low conductivity and the high-Z[over ¯] results of DFT MD point to the existence of carbon in a complex, nonuniform, low-conducting dispersed phase, possibly containing magic-number Coulomb crystals. The neutral pseudoatom estimate of Z[over ¯], conductivity, compressibility, and pressure reported here pertain to the uniform liquid.

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}).

Consistent approach for electrical resistivity within Ziman's theory from solid state to hot dense plasma: Application to aluminum

The approach presented in this work allows a consistent calculation of electrical conductivity of dense matter from the solid state to the hot plasma using the same procedure, consisting in dropping elastic scattering contributions to solid's and liquid's structure factors in the framework of the Ziman theory. The solid's structure factor was computed using a multiphonon expansion. The elastic part is the zero-phonon term and corresponds to Bragg peaks, thermally damped by Debye-Waller attenuation factors. For the liquid, a similar elastic contribution to the structure factor results from a long-range order persisting during the characteristic electron-ion scattering time. All the quantities required for the calculation of the resistivities are obtained from our average-atom model, including the total hypernetted-chain structure factor used from the liquid state to the plasma. No interpolation between two limiting structure factors is required. We derive the correction to apply to the resistivity in order to account for the transient long-range order in the liquid and show that it improves considerably the agreement with quantum-molecular dynamics simulations and experimental aluminum's isochoric and isobaric conductivities. Our results suggest that the long-range order in liquid aluminum could be a slightly compressed fcc one. Two series of ultrafast experiments performed on aluminum were also considered, the first one by Milchberg et al. using short laser pulses and the second one by Sperling et al. involving x-ray heating and carried out on the Linac Coherent Light Source facility. Our attempts to explain the latter assuming an initial liquid state at an ion temperature much smaller than the electron one suggest that the actual initial state before main heating is neither perfectly solid nor a normal liquid.

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.

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

Dharma-wardana et al. [M. W. C. Dharma-wardana et al., Phys. Rev. E 96, 053206 (2017)2470-004510.1103/PhysRevE.96.053206] recently calculated dynamic electrical conductivities for warm dense matter as well as for nonequilibrium two-temperature states termed "ultrafast matter" (UFM) [M. W. C. Dharma-wardana, Phys. Rev. E 93, 063205 (2016)2470-004510.1103/PhysRevE.93.063205]. In this Comment we present two evident reasons why these UFM calculations are neither suited to calculate dynamic conductivities nor x-ray Thomson scattering spectra in isochorically heated warm dense aluminum. First, the ion-ion structure factor, a major input into the conductivity and scattering spectra calculations, deviates strongly from that of isochorically heated aluminum. Second, the dynamic conductivity does not show a non-Drude behavior which is an essential prerequisite for a correct description of the absorption behavior in aluminum. Additionally, we clarify misinterpretations by Dharma-wardana et al. concerning the conductivity measurements of Gathers [G. R. Gathers, Int. J. Thermophys. 4, 209 (1983)IJTHDY0195-928X10.1007/BF00502353].

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.