X-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula.

We study ab initio approaches for calculating x-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula that expresses the inelastic contribution in terms of the dielectric function. We study the electronic dynamic structure factor computed from the Mermin dielectric function using an ab initio electron-ion collision frequency in comparison to computations using a linear-response time-dependent density functional theory (LR-TDDFT) framework for hydrogen and beryllium and investigate the dispersion of free-free and bound-free contributions to the scattering signal. A separate treatment of these contributions, where only the free-free part follows the Mermin dispersion, shows good agreement with LR-TDDFT results for ambient-density beryllium, but breaks down for highly compressed matter where the bound states become pressure ionized. LR-TDDFT is used to reanalyze x-ray Thomson scattering experiments on beryllium demonstrating strong deviations from the plasma conditions inferred with traditional analytic models at small scattering angles.

Accurate temperature diagnostics for matter under extreme conditions.

The experimental investigation of matter under extreme densities and temperatures, as in astrophysical objects and nuclear fusion applications, constitutes one of the most active frontiers at the interface of material science, plasma physics, and engineering. The central obstacle is given by the rigorous interpretation of the experimental results, as even the diagnosis of basic parameters like the temperature T is rendered difficult at these extreme conditions. Here, we present a simple, approximation-free method to extract the temperature of arbitrarily complex materials in thermal equilibrium from X-ray Thomson scattering experiments, without the need for any simulations or an explicit deconvolution. Our paradigm can be readily implemented at modern facilities and corresponding experiments will have a profound impact on our understanding of warm dense matter and beyond, and open up a variety of appealing possibilities in the context of thermonuclear fusion, laboratory astrophysics, and related disciplines.

Simultaneous compression and opacity data from time-series radiography with a Lagrangian marker.

Time-resolved radiography can be used to obtain absolute shock Hugoniot states by simultaneously measuring at least two mechanical parameters of the shock, and this technique is particularly suitable for one-dimensional converging shocks where a single experiment probes a range of pressures as the converging shock strengthens. However, at sufficiently high pressures, the shocked material becomes hot enough that the x-ray opacity falls significantly. If the system includes a Lagrangian marker such that the mass within the marker is known, this additional information can be used to constrain the opacity as well as the Hugoniot state. In the limit that the opacity changes only on shock heating, and not significantly on subsequent isentropic compression, the opacity of the shocked material can be determined uniquely. More generally, it is necessary to assume the form of the variation of opacity with isentropic compression or to introduce multiple marker layers. Alternatively, assuming either the equation of state or the opacity, the presence of a marker layer in such experiments enables the non-assumed property to be deduced more accurately than from the radiographic density reconstruction alone. An example analysis is shown for measurements of a converging shock wave in polystyrene at the National Ignition Facility.

A measurement of the equation of state of carbon envelopes of white dwarfs.

White dwarfs represent the final state of evolution for most stars1-3. Certain classes of white dwarfs pulsate4,5, leading to observable brightness variations, and analysis of these variations with theoretical stellar models probes their internal structure. Modelling of these pulsating stars provides stringent tests of white dwarf models and a detailed picture of the outcome of the late stages of stellar evolution6. However, the high-energy-density states that exist in white dwarfs are extremely difficult to reach and to measure in the laboratory, so theoretical predictions are largely untested at these conditions. Here we report measurements of the relationship between pressure and density along the principal shock Hugoniot (equations describing the state of the sample material before and after the passage of the shock derived from conservation laws) of hydrocarbon to within five per cent. The observed maximum compressibility is consistent with theoretical models that include detailed electronic structure. This is relevant for the equation of state of matter at pressures ranging from 100 million to 450 million atmospheres, where the understanding of white dwarf physics is sensitive to the equation of state and where models differ considerably. The measurements test these equation-of-state relations that are used in the modelling of white dwarfs and inertial confinement fusion experiments7,8, and we predict an increase in compressibility due to ionization of the inner-core orbitals of carbon. We also find that a detailed treatment of the electronic structure and the electron degeneracy pressure is required to capture the measured shape of the pressure-density evolution for hydrocarbon before peak compression. Our results illuminate the equation of state of the white dwarf envelope (the region surrounding the stellar core that contains partially ionized and partially degenerate non-ideal plasmas), which is a weak link in the constitutive physics informing the structure and evolution of white dwarf stars9.

Ionization potential depression and Pauli blocking in degenerate plasmas at extreme densities.

New facilities explore warm dense matter (WDM) at conditions with extreme densities (exceeding ten times condensed matter densities) so that electrons are degenerate even at temperatures of 10-100 eV. Whereas in the nondegenerate region correlation effects such as Debye screening are relevant for the ionization potential depression (IPD), new effects have to be considered in degenerate plasmas. In addition to the Fock shift of the self-energies, the bound-state Pauli blocking becomes important with increasing density. Standard approaches to IPD such as Stewart-Pyatt and widely used opacity tables (e.g., OPAL) do not contain Pauli blocking effects for bound states. The consideration of degeneracy effects leads to a reduction of the ionization potential and to a higher degree of ionization. As an example, we present calculations for the ionization degree of carbon plasmas at T = 100 eV and extreme densities up to 40 g/cm^{3}, which are relevant to experiments that are currently scheduled at the National Ignition Facility.

Absolute Hugoniot measurements from a spherically convergent shock using x-ray radiography.

The canonical high pressure equation of state measurement is to induce a shock wave in the sample material and measure two mechanical properties of the shocked material or shock wave. For accurate measurements, the experiment is normally designed to generate a planar shock which is as steady as possible in space and time, and a single state is measured. A converging shock strengthens as it propagates, so a range of shock pressures is induced in a single experiment. However, equation of state measurements must then account for spatial and temporal gradients. We have used x-ray radiography of spherically converging shocks to determine states along the shock Hugoniot. The radius-time history of the shock, and thus its speed, was measured by radiographing the position of the shock front as a function of time using an x-ray streak camera. The density profile of the shock was then inferred from the x-ray transmission at each instant of time. Simultaneous measurement of the density at the shock front and the shock speed determines an absolute mechanical Hugoniot state. The density profile was reconstructed using the known, unshocked density which strongly constrains the density jump at the shock front. The radiographic configuration and streak camera behavior were treated in detail to reduce systematic errors. Measurements were performed on the Omega and National Ignition Facility lasers, using a hohlraum to induce a spatially uniform drive over the outside of a solid, spherical sample and a laser-heated thermal plasma as an x-ray source for radiography. Absolute shock Hugoniot measurements were demonstrated for carbon-containing samples of different composition and initial density, up to temperatures at which K-shell ionization reduced the opacity behind the shock. Here we present the experimental method using measurements of polystyrene as an example.

Ultrafast x-ray Thomson scattering of shock-compressed matter.

Spectrally resolved scattering of ultrafast K-alpha x-rays has provided experimental validation of the modeling of the compression and heating of shocked matter. The elastic scattering component has characterized the evolution and coalescence of two shocks launched by a nanosecond laser pulse into lithium hydride with an unprecedented temporal resolution of 10 picoseconds. At shock coalescence, we observed rapid heating to temperatures of 25,000 kelvin when the scattering spectra show the collective plasmon oscillations that indicate the transition to the dense metallic plasma state. The plasmon frequency determines the material compression, which is found to be a factor of 3, thereby reaching conditions in the laboratory relevant for studying the physics of planetary formation.

Ion induced snowballs as a diagnostic tool to investigate the caging of metal clusters in large helium droplets.

Metal clusters embedded in ultracold helium nanodroplets are exposed to femtosecond laser pulses with intensities of 10(13)-10(14) W/cm2. The influence of the matrix on the ionization and fragmentation dynamics is studied by pump-probe time-of-flight mass spectrometry. Special attention is paid to the generation of helium snowballs around positive metal ions (Me(z+)He(N), z=1,2). Closings of the first and second helium shells are found for silver at N(1)=10,12 and N(2)=32,44, as well as for magnesium at N1=19-20. The distinct abundance enhancement of helium snowballs in the presence of isolated atoms and small clusters in the droplets is used as a diagnostics to explore the cage effect. For silver, a reaggregation of the clusters is observed at 30 ps after femtosecond laser excitation.

Photoelectron studies of neutral Ag3 in helium droplets.

Photoelectron spectra of neutral silver trimers, grown in ultracold helium nanodroplets, are recorded after ionization with laser pulses via a strong optical resonance of this species. Varying the photon energy reveals that direct vertical two-photon ionization is hindered by a rapid relaxation into the lower edge of a long-living excited state manifold. An analysis of the ionization threshold of the embedded trimer yields an ionization potential of 5.74+/-0.09 eV consistent with the value found in the gas phase. The asymmetrical form of the electron energy spectrum, which is broadened toward lower kinetic energies, is attributed to the influence of the matrix on the photoionization process. The lifetime of the excited state was measured in a two-color pump-probe experiment to be 5.7+/-0.6 ns.

Excited-state relaxation of Ag8 clusters embedded in helium droplets.

Neutral silver clusters Ag(N) are grown in ultracold helium nanodroplets. By exploiting a strong absorption resonance recently found for Ag8, first photoelectron spectra of this neutral species are recorded. Variation of the laser photon energy reveals that direct vertical two-photon ionization is hindered by rapid relaxation into the lower edge of a long-living excited state manifold. The analysis of the dynamics gives a precise value of (6.89+/-0.09) eV for the vertical ionization potential of Ag8. The influence of the helium matrix on photoemission is discussed.