We calculate the dynamic structure factor (DSF) in warm dense beryllium by means of ab initio molecular dynamics simulations. The dynamic conductivity is derived from the Kubo-Greenwood formula, and a Drudelike behaviour is observed. The corresponding dielectric function is used to determine the DSF. Since the ab initio approach is so far only applicable for wavenumbers k = 0, the k-dependence of the dielectric function is modelled via the Mermin ansatz. We present the results for the dielectric function and DSF of warm dense beryllium and compare these with perturbative treatments such as the Born-Mermin approximation. We found considerable differences between the results of these approaches; this underlines the need for a first-principles determination of the DSF of warm dense matter. Gesellschaft checked with benchmarking experiments. A versatile and reliable tool for this purpose is x-ray Thomson scattering (XRTS) [1,2], which gains the plasma parameters directly from the dynamic structure factor (DSF) [3]. X-rays penetrate dense matter, and intense x-ray sources are now available to perform scattering experiments. For instance, intense x-ray pulses are produced either by energetic optical lasers or by free-electron lasers in the soft or hard x-ray regimes.X-rays emitted from laser-produced plasmas [4,5] can probe the region from warm dense matter (WDM) [6,7] with temperatures of several eV and densities close to solid density [8][9][10] up to compressed matter well above solid density and at electron temperatures of 0.1 eV and several tens of eV [11][12][13][14][AQ ID=Q1]. The outstanding applications of XRTS are, e.g., in-flight measurements of laser-driven implosion dynamics of inertial confinement fusion capsules [15] and of radiative heating and cooling dynamics of matter [16], both on ns time scales. Plasmas in the near-solid density regime have also been probed by combining optical lasers (pump) and soft x-rays (probe) [17].The plasma parameters electron temperature T e , free-electron density n e and the mean ionization state Z can be derived by analyzing the XRTS signal. The electron temperature can be inferred from the universal detailed balance relation, whereas the electron density follows from the plasmon dispersion in the collective scattering mode [8,18,19].XRTS experiments have been performed on beryllium for different conditions [8,10,12,20]. It is a potential ablator material in inertial confinement fusion capsules [21] and also relevant for astrophysics considering the neutrino capture reactions in the Sun and the problem of neutrino oscillations [22]. In this paper, we determine the DSF for uncompressed beryllium (u-Be [10]: T e = 12 eV, ρ = 1.85 g cm −3 ) and threefold compressed beryllium (c-Be [12]: T e = 13 eV, ρ = 5.5 g cm −3 ), thereby studying the effect of strong correlations characterized by electron coupling parameters e = e 2 4π 0 k B T e 4πn e 3

The spectrum of x-ray Thomson scattering is proportional to the dynamic structure factor. An important contribution is the ion feature which describes elastic scattering of x rays off electrons. We apply an ab initio method for the calculation of the form factor of bound electrons, the slope of the screening cloud of free electrons, and the ion-ion structure factor in warm dense beryllium. With the presented method we can calculate the ion feature from first principles. These results will facilitate a better understanding of x-ray scattering in warm dense matter and an accurate measurement of ion temperatures which would allow determining nonequilibrium conditions, e.g., along shock propagation.

We report on the first measurements of the structure of compressed liquid boron, as it crosses the melt line in dynamic shock-compression experiments at a pressure of 100 GPa. Temporally, spectrally and angularly resolving x-ray scattering provides an independent and accurate measurement of the compression factor 1.5 and the electron density of 4 × 10 23 cm −3 at moderate temperatures of 0.2-1 eV. At these conditions, the elastic scattering measurements provide the structure factor and indicate the liquid compressed phase with a coordination number of 8.3 in good agreement with predictions from first-principles molecular dynamic simulations.