Properties Of Warm Dense Matter Research Articles

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization.

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.

Investigation of warm dense matter using time-resolved X-ray absorption spectroscopy with third- and fourth- generation light sources

The advent of high-power lasers has provided insights into laboratory high energy density (>1011 J/m3) physics. In particular, the properties of warm dense matter (WDM) with temperatures of 104–106 K and near-solid densities is a research area that has garnered significant interest recently. However, owing to the high temperatures and pressures associated with WDM, the measurement of fundamental properties is difficult, and insufficient data has been a significant setback in WDM research. Herein, we review recent developments in time-resolved X-ray absorption spectroscopy with synchrotron and X-ray free electron lasers for WDM research. Various physical properties, such as atomic bonding, electronic structures, electron–phonon coupling, and thermal conductivity of various elements in WDM conditions are investigated via this noble X-ray technique at various time scales from 100 ps to 100 fs.

Calculation of optical properties with spin-orbit coupling for warm dense matter

Optical properties of warm dense matter are computed within linear response theory using the Kubo-Greenwood formula in the framework of Density Functional Theory and the Projector Augmented–Wave (PAW) method. For transition metals, the effect of spin-orbit coupling (SOC) has to be taken into account. We present the theoretical framework to introduce SOC in the PAW formalism and then to compute optical properties including SOC using the Kubo-Greenwood formula. This formulation has been implemented in the abinit software. Moreover, for high energy absorption spectra, we use Dirac relativistic core wave functions from the atompaw code to obtain the correct SOC energy splitting. This implementation enables a description of optical properties for warm dense metals including SOC for both core and valence orbitals. Example calculations are presented for warm dense gold and copper.

Reduced ionic diffusion by the dynamic electron–ion collisions in warm dense hydrogen

The dynamic electron–ion collisions play an important role in determining the static and transport properties of warm dense matter (WDM). The electron force field (EFF) method is applied to study the ionic transport properties of warm dense hydrogen. Compared with the results from quantum molecular dynamics and orbital-free molecular dynamics, the ionic diffusions are largely reduced by involving the dynamic collisions of electrons and ions. This physics is verified by the quantum Langevin molecular dynamics (QLMD) simulations, which includes electron–ion collision-induced friction (EI-CIF) into the dynamic equation of ions. Based on these new results, we proposed a model including the correction of collision-induced friction of the ionic diffusion. The CIF model has been verified to be valid in a wide range of densities and temperatures. We also compare the results with the Yukawa one-component plasma (YOCP) model and Effective OCP (EOCP) model. We proposed to calculate the self-diffusion coefficients using the EOCP model modified by the CIF model to introduce the dynamic electron–ion collision effect.

Influence of different charge-state ion distribution on elastic X-ray scattering in warm dense matter

The study of warm dense matter is very important for the evolution of celestial bodies and inertial confinement fusion, which often contains a mixture of multiple elements and different charge-state ions. The ionic structure and distribution of different charge-states directly affect the diagnosis and physical properties of warm dense matter. At the same time, the influence of high-temperature dense plasma on the ionic structure should be considered when we study the physical properties from the first-principle calculation of electron structure. In the present work, the radial distribution functions of multiple charge-state ions (gold, carbon-hydrogen mixture, and aluminum) are developed in the hypernetted-chain approximation, and elastic x-ray scattering of different charge-state ions are calculated in the warm dense matter regime. Firstly, the electron structure of different charge-state ions is self-consistently computed in the ionic sphere, in which the ion-sphere radii are determined by the plasma density and their charges. And then the ionic fraction is obtained by solving the modified Saha equation, with the interactions among different charge-state ions taken into account, and ion-ion pair potentials are obtained by Yukawa model. Finally, the ion features of x-ray elastic scattering for Al are calculated on the basis of electronic distribution around the nuclei and ionic radial distribution function. By comparing the results of different charge-sate ions with the result of mean charge-sate ion, it is shown that different statistical methods can affect the physical properties which are dependent on the electronic and ionic structure.

Thermal hybrid exchange-correlation density functional for improving the description of warm dense matter

Finite-temperature density functional theory has become a standard tool for first-principles calculations of the properties of warm dense matter (WDM) relevant to high-energy-density physics (HEDP) applications. Here we present theoretical grounds of thermal hybrid exchange-correlation (XC) functionals within the generalized Mermin-Kohn-Sham scheme for an improved description of WDM. Building on the previously developed KSDT (Karasiev-Sjostrom-Dufty-Trickey) [Karasiev et al., Phys. Rev. Lett. 112, 076403 (2014)] local density approximation (LDA) and the KDT16 (Karasiev-Dufty-Trickey 2016) [Karasiev et al., Phys. Rev. Lett. 120, 076401 (2018)] generalized-gradient approximation (GGA) XC free-energy density functionals, we construct a novel thermal hybrid XC functional, referred to here as KDT0. The KDT0 model at low temperature reduces to the popular ground-state PBE0 hybrid due to properties of the used KDT16 density functional approximation. Application to static calculations of electronic band gap and band structure at a wide range of temperatures for various systems of interest to HEDP show that KDT0 provides a significant improvement to the lower LDA and GGA rung XC functionals and to the ground-state PBE0 hybrid.

Magma as a Generator of Plasma and Thermonuclear Fusion in the Bowels of the Earth

The idea behind this article is the work of physicists on the study of the properties of warm dense matter (WDM) and thermonuclear fusion based on the reaction of muon-catalyzed melting (μCF). According to our calculations, when the magma moves through the magma channel, hydraulic shocks occur, reaching the power of several Terawatts, which is enough to “ignite” WDM. With the subsequent mandatory expansion of WDM, a collision of electrons and positrons with the formation of muons will occur according to the well-known scheme: e- + e + → µ- + µ +. Born muons will replace electrons in atoms with the formation of mesoatoms. Since the Bohr radius is inversely proportional to the mass of the particle moving around the atomic nucleus, and the muon mass mμ = 206.7 me is approximately 200 times greater than the electron mass, the size of the newly formed atom orbital will be ~ 200 times smaller than the electron one. Plus, replacing electrons with muons will leads to a decrease in the diameter of protons by ~ 10%. These facts will allow the atoms to approach to a distance less than two mesoatomic units [(~ 2aμ = 2h2 / mμe2 ~ 5⋅10−13m.) - 10%], which will lead to the start of the classical reaction μCF, to the fusion of atomic nuclei and the start of the reaction natural thermonuclear fusion, the energy of which may well be the source of mysterious deep-focus earthquakes.

AbInitio Studies on the Stopping Power of Warm Dense Matter with Time-Dependent Orbital-Free Density Functional Theory.

Electronic transport properties of warm dense matter, such as electrical or thermal conductivities and nonadiabatic stopping power, are of particular interest to geophysics, planetary science, astrophysics, and inertial confinement fusion (ICF). One example is the α-particle stopping power of dense deuterium-tritium (DT) plasmas, which must be precisely known for current small-margin ICF target designs to ignite. We have developed a time-dependent orbital-free density functional theory (TD-OF-DFT) method for abinitio investigations of the charged-particle stopping power of warm dense matter. Our current dependent TD-OF-DFT calculations have reproduced the recently well-characterized stopping power experiment in warm dense beryllium. For α-particle stopping in warm and solid-density DT plasmas, the abinitio TD-OF-DFT simulations show a lower stopping power up to ∼25% in comparison with three stopping-power models often used in the high-energy-density physics community.

First-Principles Estimation of Electronic Temperature from X-Ray Thomson Scattering Spectrum of Isochorically Heated Warm Dense Matter

Through the perturbation formula of time-dependent density functional theory broadly employed in the calculation of solids, we provide a first-principles calculation of x-ray Thomson scattering spectrum of isochorically heated aluminum foil, as considered in the experiments of Sperling etal. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001], where ions were constrained near their lattice positions. From the calculated spectra, we find that the electronic temperature cannot exceed 2eV, much smaller than the previous estimation of 6eV via the detailed balance relation. Our results may well be an indication of unique electronic properties of warm dense matter, which can be further illustrated by future experiments. The lower electronic temperature predicted partially relieves the concern on the heating of x-ray free electron laser to the sample when used in structure measurement.

Experimental methods for warm dense matter research

The study of structure, thermodynamic state, equation of state (EOS) and transport properties of warm dense matter (WDM) has become one of the key aspects of laboratory astrophysics. This field has demonstrated its importance not only concerning the internal structure of planets, but also other astrophysical bodies such as brown dwarfs, crusts of old stars or white dwarf stars. There has been a rapid increase in interest and activity in this field over the last two decades owing to many technological advances including not only the commissioning of high energy optical laser systems, z-pinches and X-ray free electron lasers, but also short-pulse laser facilities capable of generation of novel particle and X-ray sources. Many new diagnostic methods have been developed recently to study WDM in its full complexity. Even ultrafast nonequilibrium dynamics has been accessed for the first time thanks to subpicosecond laser pulses achieved at new facilities. Recent years saw a number of major discoveries with direct implications to astrophysics such as the formation of diamond at pressures relevant to interiors of frozen giant planets like Neptune, metallic hydrogen under conditions such as those found inside Jupiter’s dynamo or formation of lonsdaleite crystals under extreme pressures during asteroid impacts on celestial bodies. This paper provides a broad review of the most recent experimental work carried out in this field with a special focus on the methods used. All typical schemes used to produce WDM are discussed in detail. Most of the diagnostic techniques recently established to probe WDM are also described. This paper also provides an overview of the most prominent examples of these methods used in experiments. Even though the main emphasis of the publication is experimental work focused on laboratory astrophysics primarily at laser facilities, a brief outline of other methods such as dynamic compression with z-pinches and static compression using diamond anvil cells (DAC) is also included. Some relevant theoretical and computational efforts related to WDM and astrophysics are mentioned in this review.

Electronic and optical properties of warm dense lithium: strong coupling effects

The optical properties of atoms in a hot and dense environment are of critical importance and a great challenge. In a warm dense matter, strong coupling effects between ions induce new physics which is difficult to be included in statistical isolated atom models such as the average atom model or the detailed level accounting model. Here we study the optical properties of warm dense Li from ab initio molecular dynamics with Kubo–Greenwood relations. We compare the absorption coefficients with those from detailed level accounting methods, which can show a significant difference. The analyses of ionic structures and charge density distribution show that the strongly coupled ions induce local ordered structures and redistributions of the electrons away from the homogeneous electron gases. Also, we study the electronic structures of warm dense Li within the same theoretical framework, and we discover how the local environment of different atoms affects the density of states of the system, which will directly alter the optical properties of warm dense matter.

Warm Dense Matter Demonstrating Non-Drude Conductivity from Observations of Nonlinear Plasmon Damping.

We present simulations using finite-temperature density-functional-theory molecular dynamics to calculate the dynamic electrical conductivity in warm dense aluminum. The comparison between exchange-correlation functionals in the Perdew-Burke-Enzerhof and Heyd-Scuseria-Enzerhof (HSE) approximation indicates evident differences in the density of states and the dc conductivity. The HSE calculations show excellent agreement with experimental Linac Coherent Light Source x-ray plasmon scattering spectra revealing plasmon damping below the widely used random phase approximation. These findings demonstrate non-Drude-like behavior of the dynamic conductivity that needs to be taken into account to determine the optical properties of warm dense matter.

Review and progress in the study of the properties of warm dense matter

Warm dense matter (WDM) belongs to a part of high energy density physics, which includes both extensive and rich physics phenomena. It is an important state of the evolution and presence of matters in inertial confinement fusion (ICF), heavy-ion fusion, Z-pinch processes and so on. In particular, thermodynamic, optical, and radiated characteristic of warm dense matter plays an important role in determining for the macro fluid movement of matter and determining for the energy transportation and transfer in the interactions of radiated field with matter in the evolution process. Therefore, further investigation of the properties of warm dense matter and precision improvements on its related parameters, such as equations of state and radiation transportation, are of science significant and applied background in many research fields such as ICF, Z-pinch, earth’s and planetary interior structure. The important research progress in the techniques of production, diagnostics, and simulation of warm dense matter under the laboratory conditions are briefly introduced and reviewed. The topics on the techniques of creating WDM were discussed, including experimental capabilities and facilities enabling the synthesis and confinement of warm dense states. These experimental capabilities include energetic materials, short pulse and high-energy-density lasers, ion beams, static high-pressure diamond-anvil cells, radiation- synchrotron sources, and mechanical impact techniques such as gas-gun launchers. Advanced diagnostics required for the characterization and interrogation of warm dense states were employ in these experiments accordingly. A general review on the theoretical approaches and computational capabilities enabling the prediction of the thermodynamic properties of matter in the warm dense regime were given. These approaches include quantum-based finite-temperature methods based on density functional theory, finite-temperature average-atom method, molecular dynamics, and various plasma physics-based theoretical approaches. In our National Key Laboratory for Shock Wave and Detonation Physics (LSD), warm dense matter was created by multiple shock reverberation technique. The multi-shock compressed states were directly determined by the multi-wavelength channel optical transience radiance pyrometry (MCOP), Doppler pins system (DPS), streak optical pyrometer (SOP), and spectrum analyser. The gas sample is confined between a 304 steel baseplate at the impact end and a composite window at the other end. The strong plain shock wave was produced using the flyer plate impact accelerated up to about several km/s by a two-stage light gas gun on the target baseplate and introduced into the plenum gas sample, which was pre-compressed from environmental pressure to 20–40 MPa. The optical radiation histories recorded by two sets of MCOPs were used to determine shock velocity. Simultaneously, the particle velocity profiles of gas sample-window interface were measured with four DPSs and the time-resolved spectrum was determined by SOP. The states of multi-shock compression gas sample were determined from the measured shock velocities combining the particle velocity profiles. The multi-shock temperatures were obtained from the measured radiation histories and spectrum of warm dense matter. We performed the experiments on warm dense helium, deuterium, argon, and xenon to reach to above one hundred GPa. The experimental results are used to validate our developed self-consistent fluid variational theoretical model, to check the existing WDM theoretical model, and to create new theoretical ones. Finally, some suggestions, summary, and outlook in the future development tendency and direction of warm dense matter are presented.

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.

Input energy measurement toward warm dense matter generation using intense pulsed power generator

In order to investigate properties of warm dense matter (WDM) in inertial confinement fusion (ICF), evaluation method for the WDM with isochoric heating on the implosion time-scale using an intense pulsed power generator ETIGO-II (∼1 TW, ∼50 ns) has been considered. In this study, the history of input energy into the sample is measured from the voltage and the current waveforms. To achieve isochoric heating, a foamed aluminum with pore sizes 600 μm and with 90% porosity was packed into a hollow glass capillary (ø 5 mm × 10 mm). The temperature of the sample is calculated from the numerical calculation using the measured input power. According to the above measurements, the input energy into a sample and the achievable temperature are estimated to be 300 J and 6000 K. It indicates that the WDM state is generated using the proposed method with ICF implosion time-scale.

Study on Exploding Wire Compression for Evaluating Electrical Conductivity in Warm-Dense Diamond-Like-Carbon

To improve a coupling efficiency for the fast ignition scheme of the inertial confinement fusion, fast electron behaviors as a function of an electrical conductivity are required. To evaluate the electrical conductivity for low-Z materials as a diamond-like-carbon (DLC), we have proposed a concept to investigate the properties of warm dense matter (WDM) by using pulsed-power discharges. The concept of the evaluation of DLC for WDM is a shock compression driven by an exploding wire discharge with confined by a rigid capillary. The qualitatively evaluation of the electrical conductivity for the WDM DLC requires a small electrical conductivity of the exploding wire. To analyze the electrical conductivity of exploding wire, we have demonstrated an exploding wire discharge in water for gold. The results indicated that the electrical conductivity of WDM gold for 5000 K of temperature has an insulator regime. It means that the shock compression driven by the exploding wire discharge with confined by the rigid capillary is applied for the evaluation of electrical conductivity for WDM DLC.

Density functional theory for dielectric properties of warm dense matter

ABSTRACTDensity functional theory (DFT) is applied for the calculation of the dielectric function (DF), reflectivity, conductivity, plasma frequency and effective free electron density of warm dense matter (WDM). Shock-compressed xenon plasma and warm dense hydrogen are considered. The longitudinal expression in the long wavelength limit is applied for the calculation of the imaginary part of the DF. The real part of the DF is calculated by means of the Kramers–Kronig transformation. Sum rule within the framework of the DFT is used for determination of the plasma frequency and effective free electron density. Corrections to the reflectivity are considered, which allow for the finite width of the transient layer (wave front) at the WDM border.

Evaluation of Transport Properties in Warm Dense Matter Generated by Pulsed-power Discharge for Nuclear Fusion Systems

Abstract To achieve the thermonuclear fusion systems, the physical properties of warm dense matter (WDM) are key parameters. In this paper, we review the evaluation of physical properties in WDM by using pulsed-power discharges. To evaluate the thermal conductivity for a divertor wall in magnetic confinement fusion, we investigate a semi-empirical evaluation based on the experimental values for electrical resistivity. The results indicate that, in the region between the interme- diate degeneracy and the non-degeneracy, the evaluated thermal conductivity has an inflection point. To evaluate the electrical resistivity for the fuel target in the inertial confinement fusion, an isochoric heating by using pulsed-power discharge in the pressure vessel has been demonstrated. The results indicate that the electrical resistivity in WDM for gold is 100 μΩ m at 0.1ρ s (ρ s : solid density) of density and the internal energy is 1MJ / kg.

Generation of warm dense matter using an argon based capillary discharge laser

Argon based capillary discharge lasers operating in the extreme ultra violet (EUV) at 46.9 nm with output up to 0.5 mJ energy per pulse and repetition rates up to 10 Hz are capable of focused irradiances of 109–1012 W cm−2 and can be used to generate plasma in the warm dense matter regime by irradiating solid material. To model the interaction between such an EUV laser and solid material, the 2D radiative-hydrodynamic code POLLUX has been modified to include absorption via direct photo-ionisation, a super-configuration model to describe the ionization-dependent electronic configurations and a calculation of plasma refractive indices for ray tracing of the incident EUV laser radiation. A simulation study is presented, demonstrating how capillary discharge lasers of 1200 ps pulse duration can be used to generate warm dense matter at close to solid densities with temperatures of a few eV and energy densities up to 1 × 105 J cm−3. Plasmas produced by EUV laser irradiation are shown to be useful for examining the properties of warm dense matter as, for example, plasma emission is not masked by hotter, less dense plasma emission that occurs with visible/infra-red laser target irradiation.