Observing the onset of pressure-driven K-shell delocalization.

The gravitational pressure in many astrophysical objects exceeds one gigabar (one billion atmospheres)1-3, creating extreme conditions where the distance between nuclei approaches the size of the K shell. This close proximity modifies these tightly bound states and, above a certain pressure, drives them into a delocalized state4. Both processes substantially affect the equation of state and radiation transport and, therefore, the structure and evolution of these objects. Still, our understanding of this transition is far from satisfactory and experimental data are sparse. Here we report on experiments that create and diagnose matter at pressures exceeding three gigabars at the National Ignition Facility5 where 184 laser beams imploded a beryllium shell. Bright X-ray flashes enable precision radiography and X-ray Thomson scattering that reveal both the macroscopic conditions and the microscopic states. The data show clear signs of quantum-degenerate electrons in states reaching 30 times compression, and a temperature of around two million kelvins. At the most extreme conditions, we observe strongly reduced elastic scattering, which mainly originates from K-shell electrons. We attribute this reduction to the onset of delocalization of the remaining K-shell electron. With this interpretation, the ion charge inferred from the scattering data agrees well with ab initio simulations, but it is significantly higher than widely used analytical models predict6.

Towards performing high-resolution inelastic X-ray scattering measurements at hard X-ray free-electron lasers coupled with energetic laser drivers.

High-resolution inelastic X-ray scattering is an established technique in the synchrotron community, used to investigate collective low-frequency responses of materials. When fielded at hard X-ray free-electron lasers (XFELs) and combined with high-intensity laser drivers, it becomes a promising technique for investigating matter at high temperatures and high pressures. This technique gives access to important thermodynamic properties of matter at extreme conditions, such as temperature, material sound speed, and viscosity. The successful realization of this method requires the acquisition of many identical laser-pump/X-ray-probe shots, allowing the collection of a sufficient number of photons necessary to perform quantitative analyses. Here, a 2.5-fold improvement in the energy resolution of the instrument relative to previous works at the Matter in Extreme Conditions (MEC) endstation, Linac Coherent Light Source (LCLS), and the High Energy Density (HED) instrument, European XFEL, is presented. Some aspects of the experimental design that are essential for improving the number of photons detected in each X-ray shot, making such measurements feasible, are discussed. A careful choice of the energy resolution, the X-ray beam mode provided by the XFEL, and the position of the analysers used in such experiments can provide a more than ten-fold improvement in the photometrics. The discussion is supported by experimental data on 10 µm-thick iron and 50 nm-thick gold samples collected at the MEC endstation at the LCLS, and by complementary ray-tracing simulations coupled with thermal diffuse scattering calculations.

Metallization of Shock-Compressed Liquid Ammonia.

Ammonia is predicted to be one of the major components in the depths of the ice giant planets Uranus and Neptune. Their dynamics, evolution, and interior structure are insufficiently understood and models rely imperatively on data for equation of state and transport properties. Despite its great significance, the experimentally accessed region of the ammonia phase diagram today is still very limited in pressure and temperature. Here we push the probed regime to unprecedented conditions, up to ∼350 GPa and ∼40 000 K. Along the Hugoniot, the temperature measured as a function of pressure shows a subtle change in slope at ∼7000 K and ∼90 GPa, in agreement with ab initio simulations we have performed. This feature coincides with the gradual transition from a molecular liquid to a plasma state. Additionally, we performed reflectivity measurements, providing the first experimental evidence of electronic conduction in high-pressure ammonia. Shock reflectance continuously rises with pressure above 50 GPa and reaches saturation values above 120 GPa. Corresponding electrical conductivity values are up to 1 order of magnitude higher than in water in the 100 GPa regime, with possible significant contributions of the predicted ammonia-rich layers to the generation of magnetic dynamos in ice giant interiors.

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.

Resolving ultrafast heating of dense cryogenic hydrogen.

We report on the dynamics of ultrafast heating in cryogenic hydrogen initiated by a ≲300 fs, 92 eV free electron laser x-ray burst. The rise of the x-ray scattering amplitude from a second x-ray pulse probes the transition from dense cryogenic molecular hydrogen to a nearly uncorrelated plasmalike structure, indicating an electron-ion equilibration time of ∼0.9 ps. The rise time agrees with radiation hydrodynamics simulations based on a conductivity model for partially ionized plasma that is validated by two-temperature density-functional theory.

Probing the interiors of the ice giants: shock compression of water to 700 GPa and 3.8 g/cm³.

Recently, there has been a tremendous increase in the number of identified extrasolar planetary systems. Our understanding of their formation is tied to exoplanet internal structure models, which rely upon equations of state of light elements and compounds such as water. Here, we present shock compression data for water with unprecedented accuracy that show that water equations of state commonly used in planetary modeling significantly overestimate the compressibility at conditions relevant to planetary interiors. Furthermore, we show that its behavior at these conditions, including reflectivity and isentropic response, is well-described by a recent first-principles based equation of state. These findings advocate that this water model be used as the standard for modeling Neptune, Uranus, and "hot Neptune" exoplanets and should improve our understanding of these types of planets.

Virial expansion of the electrical conductivity of hydrogen plasmas.

The low-density limit of the electrical conductivity σ(n,T) of hydrogen as the simplest ionic plasma is presented as a function of the temperature T and mass density n in the form of a virial expansion of the resistivity. Quantum statistical methods yield exact values for the lowest virial coefficients which serve as a benchmark for analytical approaches to the electrical conductivity as well as for numerical results obtained from density functional theory-based molecular dynamics simulations (DFT-MD) or path-integral Monte Carlo simulations. While these simulations are well suited to calculate σ(n,T) in a wide range of density and temperature, in particular, for the warm dense matter region, they become computationally expensive in the low-density limit, and virial expansions can be utilized to balance this drawback. We present new results of DFT-MD simulations in that regime and discuss the account of electron-electron collisions by comparison with the virial expansion.

Ultrafast multi-cycle terahertz measurements of the electrical conductivity in strongly excited solids.

Key insights in materials at extreme temperatures and pressures can be gained by accurate measurements that determine the electrical conductivity. Free-electron laser pulses can ionize and excite matter out of equilibrium on femtosecond time scales, modifying the electronic and ionic structures and enhancing electronic scattering properties. The transient evolution of the conductivity manifests the energy coupling from high temperature electrons to low temperature ions. Here we combine accelerator-based, high-brightness multi-cycle terahertz radiation with a single-shot electro-optic sampling technique to probe the evolution of DC electrical conductivity using terahertz transmission measurements on sub-picosecond time scales with a multi-undulator free electron laser. Our results allow the direct determination of the electron-electron and electron-ion scattering frequencies that are the major contributors of the electrical resistivity.

High-resolution inelastic x-ray scattering at the high energy density scientific instrument at the European X-Ray Free-Electron Laser.

We introduce a setup to measure high-resolution inelastic x-ray scattering at the High Energy Density scientific instrument at the European X-Ray Free-Electron Laser (XFEL). The setup uses the Si (533) reflection in a channel-cut monochromator and three spherical diced analyzer crystals in near-backscattering geometry to reach a high spectral resolution. An energy resolution of 44 meV is demonstrated for the experimental setup, close to the theoretically achievable minimum resolution. The analyzer crystals and detector are mounted on a curved-rail system, allowing quick and reliable changes in scattering angle without breaking vacuum. The entire setup is designed for operation at 10 Hz, the same repetition rate as the high-power lasers available at the instrument and the fundamental repetition rate of the European XFEL. Among other measurements, it is envisioned that this setup will allow studies of the dynamics of highly transient laser generated states of matter.

Observation of ultrafast nonequilibrium collective dynamics in warm dense hydrogen.

We investigate ultrafast (fs) electron dynamics in a liquid hydrogen sample, isochorically and volumetrically heated to a moderately coupled plasma state. Thomson scattering measurements using 91.8 eV photons from the free-electron laser in Hamburg (FLASH at DESY) show that the hydrogen plasma has been driven to a nonthermal state with an electron temperature of 13 eV and an ion temperature below 0.1 eV, while the free-electron density is 2.8x10{20} cm{-3}. For dense plasmas, our experimental data strongly support a nonequilibrium kinetics model that uses impact ionization cross sections based on classical free-electron collisions.

Electronic structure of an XUV photogenerated solid-density aluminum plasma.

By use of high intensity XUV radiation from the FLASH free-electron laser at DESY, we have created highly excited exotic states of matter in solid-density aluminum samples. The XUV intensity is sufficiently high to excite an inner-shell electron from a large fraction of the atoms in the focal region. We show that soft-x-ray emission spectroscopy measurements reveal the electronic temperature and density of this highly excited system immediately after the excitation pulse, with detailed calculations of the electronic structure, based on finite-temperature density functional theory, in good agreement with the experimental results.

An approach for the measurement of the bulk temperature of single crystal diamond using an X-ray free electron laser.

We present a method to determine the bulk temperature of a single crystal diamond sample at an X-Ray free electron laser using inelastic X-ray scattering. The experiment was performed at the high energy density instrument at the European XFEL GmbH, Germany. The technique, based on inelastic X-ray scattering and the principle of detailed balance, was demonstrated to give accurate temperature measurements, within [Formula: see text] for both room temperature diamond and heated diamond to 500 K. Here, the temperature was increased in a controlled way using a resistive heater to test theoretical predictions of the scaling of the signal with temperature. The method was tested by validating the energy of the phonon modes with previous measurements made at room temperature using inelastic X-ray scattering and neutron scattering techniques. This technique could be used to determine the bulk temperature in transient systems with a temporal resolution of 50 fs and for which accurate measurements of thermodynamic properties are vital to build accurate equation of state and transport models.

Measurements of ionic structure in shock compressed lithium hydride from ultrafast x-ray Thomson scattering.

We present the first ultrafast temporally, spectrally, and angularly resolved x-ray scattering measurements from shock-compressed matter. The experimental spectra yield the absolute elastic and inelastic scattering intensities from the measured density of free electrons. Laser-compressed lithium-hydride samples are well characterized by inelastic Compton and plasmon scattering of a K-alpha x-ray probe providing independent measurements of temperature and density. The data show excellent agreement with the total intensity and structure when using the two-species form factor and accounting for the screening of ion-ion interactions.

Electronic band structure of Cu(2)O by spin density functional theory.

The band structure of Cu(2)O is calculated using density functional theory in the generalized gradient approximation. By taking spin-orbit coupling into account the split between the Γ(7)(+) and the Γ(8)(+) valence band states is obtained as 128 meV. The highest valence band shows a noticeable nonparabolicity close to the Γ point. This is important for the quantitative description of excitons in this material, which is considered to be the best candidate for the confirmation that Bose-Einstein condensation also occurs in excitonic systems.

Thomson scattering from dense inhomogeneous plasmas.

X-ray Thomson scattering experiments in the soft and hard x-ray regime yield information on fundamental parameters of high-density systems. Pump-probe experiments with variable time delay provide insight into the excitation and relaxation dynamics in dense plasmas. On short time scales, a local thermodynamic equilibrium description might not be sufficient. Besides nonequilibrium effects on the electron distribution function, spatial inhomogeneities influence the scattering signal. Generalizing previous approaches of Belyi [Phys. Rev. E 97, 053204 (2018)2470-004510.1103/PhysRevE.97.053204] and Kozlowski et al. [Sci. Rep. 6, 24283 (2016)2045-232210.1038/srep24283], we discuss implications for Thomson scattering spectra for inhomogeneous plasmas in the warm dense matter regime based on a gradient expansion within real-time Green's-functions theory. Especially in the collective scattering regime, Thomson scattering spectra are modifed substantially by spatial inhomogeneities. Within a first-order gradient expansion, the dispersion relation for plasmons is determined. In particular, the ratio of the heights of the plasmon peaks is changed which prevents a simple estimation of the plasma temperature from the detailed balance relation.

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].

Laser-driven shock compression of "synthetic planetary mixtures" of water, ethanol, and ammonia.

Water, methane, and ammonia are commonly considered to be the key components of the interiors of Uranus and Neptune. Modelling the planets' internal structure, evolution, and dynamo heavily relies on the properties of the complex mixtures with uncertain exact composition in their deep interiors. Therefore, characterising icy mixtures with varying composition at planetary conditions of several hundred gigapascal and a few thousand Kelvin is crucial to improve our understanding of the ice giants. In this work, pure water, a water-ethanol mixture, and a water-ethanol-ammonia "synthetic planetary mixture" (SPM) have been compressed through laser-driven decaying shocks along their principal Hugoniot curves up to 270, 280, and 260 GPa, respectively. Measured temperatures spanned from 4000 to 25000 K, just above the coldest predicted adiabatic Uranus and Neptune profiles (3000-4000 K) but more similar to those predicted by more recent models including a thermal boundary layer (7000-14000 K). The experiments were performed at the GEKKO XII and LULI2000 laser facilities using standard optical diagnostics (Doppler velocimetry and optical pyrometry) to measure the thermodynamic state and the shock-front reflectivity at two different wavelengths. The results show that water and the mixtures undergo a similar compression path under single shock loading in agreement with Density Functional Theory Molecular Dynamics (DFT-MD) calculations using the Linear Mixing Approximation (LMA). On the contrary, their shock-front reflectivities behave differently by what concerns both the onset pressures and the saturation values, with possible impact on planetary dynamos.

Plasmon resonance in warm dense matter.

Collective Thomson scattering with extreme ultraviolet light or x rays is shown to allow for a robust measurement of the free electron density in dense plasmas. Collective excitations like plasmons appear as maxima in the scattering signal. Their frequency position can directly be related to the free electron density. The range of applicability of the standard Gross-Bohm dispersion relation and of an improved dispersion relation in comparison to calculations based on the dielectric function in random phase approximation is investigated. More important, this well-established treatment of Thomson scattering on free electrons is generalized in the Born-Mermin approximation by including collisions. We show that, in the transition region from collective to noncollective scattering, the consideration of collisions is important.

Bremsstrahlung and line spectroscopy of warm dense aluminum plasma heated by xuv free-electron-laser radiation.

We report the creation of solid-density aluminum plasma using free-electron laser (FEL) radiation at 13.5nm wavelength. Ultrashort pulses were focused on a bulk Al target, yielding an intensity of 2x10;{14}Wcm;{2} . The radiation emitted from the plasma was measured using an xuv spectrometer. Bremsstrahlung and line intensity ratios yield consistent electron temperatures of about 38eV , supported by radiation hydrodynamics simulations. This shows that xuv FELs heat up plasmas volumetrically and homogeneously at warm-dense-matter conditions, which are accurately characterized by xuv spectroscopy.

Determination of the electron-lattice coupling strength of copper with ultrafast MeV electron diffraction.

Electron-lattice coupling strength governs the energy transfer between electrons and the lattice and is important for understanding the material behavior under highly non-equilibrium conditions. Here we report the results of employing time-resolved electron diffraction at MeV energies to directly study the electron-lattice coupling strength in 40-nm-thick polycrystalline copper excited by femtosecond optical lasers. The temporal evolution of lattice temperature at various pump fluence conditions were obtained from the measurements of the Debye-Waller decay of multiple diffraction peaks. We observed the temperature dependence of the electron-lattice relaxation time which is a result of the temperature dependence of electron heat capacity. Comparison with two-temperature model simulations reveals an electron-lattice coupling strength of (0.9 ± 0.1) × 1017 W/m3/K for copper.