Frequency-dependent reflectivity of shock-compressed xenon plasmas

The relevance of electronic perturbations in the warm dense electron gas

Warm dense matter (WDM) has emerged as one of the frontiers of both experimental physics and theoretical physics and is a challenging traditional concept of plasma, atomic, and condensed-matter physics. While it has become common practice to model correlated electrons in WDM within the framework of Kohn-Sham density functional theory, quantitative benchmarks of exchange-correlation (XC) functionals under WDM conditions are yet incomplete. Here, we present the first assessment of common XC functionals against exact path-integral Monte Carlo calculations of the harmonically perturbed thermal electron gas. This system is directly related to the numerical modeling of x-ray scattering experiments on warm dense samples. Our assessment yields the parameter space where common XC functionals are applicable. More importantly, we pinpoint where the tested XC functionals fail when perturbations on the electronic structure are imposed. We indicate the lack of XC functionals that take into account the needs of WDM physics in terms of perturbed electronic structures.

Polarized angular-dependent reflectivity and density-dependent profiles of shock-compressed xenon plasmas

New data for the reflectivity of shock-compressed xenon plasmas at pressures of 10-12 GPa at large incident angles are presented. In addition, measurements have been performed at different densities. These data allow to analyze the free-electron density profile across the shock wave front. Assuming a Fermi-like density profile, the width of the front layer is inferred. The reflectivity coefficients for the s- and p-polarized waves are calculated. The influence of atoms, which was taken into account on the level of the collision frequency, proves to be essential for the understanding of the reflection process. Subsequently, a unique density profile is sufficient to obtain good agreement with the experimental data at different incident angles and at all investigated optical laser frequencies. Reflectivity measurements for different densities allow to determine the dependence of shock-front density profiles on the plasma parameters. As a result, it was found that the width of the front layer increases with decreasing density.

Dynamic conductivity and partial ionization in dense fluid hydrogen

A theoretical description for optical conduction experiments in dense fluid hydrogen is presented. Different quantum statistical approaches are used to describe the mechanism of electronic transport in hydrogen's high-temperature dense phase. We show that at the onset of the metallic transition, optical conduction could be described by a strong rise in atomic polarizability, due to increased ionization, whereas in the highly degenerate limit, the Ziman weak scattering model better accounts for the observed saturation of reflectance. The inclusion of effects of partial ionization in the highly degenerate region provides great agreement with experimental results. Hydrogen's fluid metallic state is revealed to be a partially ionized free-electron plasma. Our results provide some of the first theoretical transport models that are experimentally benchmarked, as well as an important guide for future studies.

Conductivity and dissociation in liquid metallic hydrogen and implications for planetary interiors

Liquid metallic hydrogen (LMH) is the most abundant form of condensed matter in our solar planetary structure. The electronic and thermal transport properties of this metallic fluid are of fundamental interest to understanding hydrogen's mechanism of conduction, atomic or pairing structure, as well as the key input for the magnetic dynamo action and thermal models of gas giants. Here, we report spectrally resolved measurements of the optical reflectance of LMH in the pressure region of 1.4-1.7 Mbar. We analyze the data, as well as previously reported measurements, using the free-electron model. Fitting the energy dependence of the reflectance data yields a dissociation fraction of 65 ± 15%, supporting theoretical models that LMH is an atomic metallic liquid. We determine the optical conductivity of LMH and find metallic hydrogen's static electrical conductivity to be 11,000-15,000 S/cm, substantially higher than the only earlier reported experimental values. The higher electrical conductivity implies that the Jovian and Saturnian dynamo are likely to operate out to shallower depths than previously assumed, while the inferred thermal conductivity should provide a crucial experimental constraint to heat transport models.

Brewster angle and reflectivity of optically nonuniform dense plasmas

We provide theoretical analysis of the reflectance of shock-compressed plasmas and warm dense matter for normal incidence of laser radiation as well as for the dependence of s- and p-polarized reflectivity on the incidence angle. The self-consistent approach for the calculation of the optical and electronic properties of warm dense matter and nonideal plasmas developed in our previous works is extended for the description of normal and polarized reflectivity from the broadened optically nonuniform medium. Two methods are applied for the calculation of the reflectivity from spatially broadened optically nonuniform medium. The first one is based on the solution of the Helmholtz equation for the amplitudes of the electromagnetic field. Another one is based on Drude theory of reflection. It allows us to calculate the ratio of the s- and p-polarized reflectivity if dependence of the dielectric function on distance is known. For the case of the polarized reflectivity, the particular attention is concentrated on the Brewster angle. The calculation results for the dielectric function, obtained within the framework of the density-functional theory with the longitudinal expression for the dielectric tensor, are applied for the calculation of the reflectivity. Comparison with the experimental data for shock-compressed xenon is performed.

Optical conductivity of warm dense matter within a wide frequency range using quantum statistical and kinetic approaches

Fundamental properties of warm dense matter are described by the dielectric function, which gives access to the frequency-dependent electrical conductivity; absorption, emission, and scattering of radiation; charged particles stopping; and further macroscopic properties. Different approaches to the dielectric function and the related dynamical collision frequency are compared in a wide frequency range. The high-frequency limit describing inverse bremsstrahlung and the low-frequency limit of the dc conductivity are considered. Sum rules and Kramers-Kronig relation are checked for the generalized linear response theory and the standard approach following kinetic theory. The results are discussed in application to aluminum, xenon, and argon plasmas.

Opacity and conductivity measurements in noble gases at conditions of planetary and stellar interiors

The noble gases are elements of broad importance across science and technology and are primary constituents of planetary and stellar atmospheres, where they segregate into droplets or layers that affect the thermal, chemical, and structural evolution of their host body. We have measured the optical properties of noble gases at relevant high pressures and temperatures in the laser-heated diamond anvil cell, observing insulator-to-conductor transformations in dense helium, neon, argon, and xenon at 4,000-15,000 K and pressures of 15-52 GPa. The thermal activation and frequency dependence of conduction reveal an optical character dominated by electrons of low mobility, as in an amorphous semiconductor or poor metal, rather than free electrons as is often assumed for such wide band gap insulators at high temperatures. White dwarf stars having helium outer atmospheres cool slower and may have different color than if atmospheric opacity were controlled by free electrons. Helium rain in Jupiter and Saturn becomes conducting at conditions well correlated with its increased solubility in metallic hydrogen, whereas a deep layer of insulating neon may inhibit core erosion in Saturn.

Ab initio calculation of shocked xenon reflectivity

Reflectivity of shocked compressed xenon plasma is calculated within the framework of the density functional theory approach. Dependencies on the frequency of incident radiation and on the plasma density are analyzed. The Fresnel formula for the reflectivity is used. The longitudinal expression in the long-wavelength limit is applied for the calculation of the imaginary part of the dielectric function. The real part of the dielectric function is calculated by means of the Kramers-Kronig transformation. The results are compared with experimental data. The approach for the calculation of plasma frequency is developed.

Hugoniot measurements of double-shocked precompressed dense xenon plasmas

The current partially ionized plasmas models for xenon show substantial differences since the description of pressure and thermal ionization region becomes a formidable task, prompting the need for an improved understanding of dense xenon plasmas behavior at above 100 GPa. We performed double-shock compression experiments on dense xenon to determine accurately the Hugoniot up to 172 GPa using a time-resolved optical radiation method. The planar strong shock wave was produced using a flyer plate impactor accelerated up to ∼6 km/s with a two-stage light-gas gun. The time-resolved optical radiation histories were acquired by using a multiwavelength channel optical transience radiance pyrometer. Shock velocity was measured and mass velocity was determined by the impedance-matching methods. The experimental equation of state of dense xenon plasmas are compared with the self-consistent fluid variational calculations of dense xenon in the region of partial ionization over a wide range of pressures and temperatures.

Second sum rule for the hot plasma permittivity

Based on linear response theory, Kramers-Kronig relations, and diagram techniques of perturbation theory, it is shown that the second sum rule is satisfied for hot plasma permittivity. An explicit analytical expression for the second sum rule in the limit of weak nonideality is derived.

Molecular dynamics simulations of optical conductivity of dense plasmas

The optical conductivity sigma (omega) for dense Coulomb systems is investigated using molecular dynamics simulations on the basis of pseudopotentials to mimic quantum effects. Starting from linear response theory, the response in the long-wavelength limit k=0 can be expressed by different types of autocorrelation functions (ACF's) such as the current ACF, the force ACF, or the charge density ACF. Consistent simulation data for transverse as well as longitudinal ACF's are shown which are based on calculations with high numerical accuracy. Results are compared with perturbation expansions which are restricted to small values of the plasma parameter. The relevance with respect to a quantum Coulomb plasma is discussed. Finally, results are presented showing a consistent description of these model plasmas in comparison to quantum statistical approaches and to experimental data.

Internal versus external conductivity of a dense plasma: many-particle theory and simulations

In the long-wavelength limit k=0, the response function has been investigated with respect to the external and internal fields which is expressed by the external and internal conductivity, respectively. Molecular dynamics simulations are performed to obtain the current-current correlation function and the dynamical collision frequency which are compared with analytical expressions. Special attention is given to the dynamical collision frequency and the description of plasma oscillations in the case of k=0. The relation between the external and internal conductivity and the current-current correlation function is analyzed.