Dynamic structure factor in warm dense beryllium

Abstract

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

Warm dense matter through classical molecular dynamics

“…Similar results have already been obtained previously in Ref. [13]. In contrast, for α = 0.65, the DSF displayed in Fig.5(b) is measured in the non-collective scattering regime and accesses the properties of individual electrons as the shape of the DSF reflects the velocities of the electrons in the direction of the scattering vector k. This will permit one to evaluate the importance of the electron degeneracy effects.…”

“…These functions are often interpreted in terms of screening mechanisms as an ionic system built with screened forces between ions can have a similar structure than the one obtained from TCP simulation. Hereafter, the ionic pair correlation functions are compared to those provided by finite-temperature density functional theory molecular dynamics (FT-DFT-MD) simulations [13] and by screened Coulomb one component plasma (Yukawa OCP) simulations. FT-DFT-MD simulations, or ab initio simulations, aim to describe fully interacting quantum systems.…”

“…For a few years, the behavior of warm dense beryllium has been an issue of interest from both a theoretical and experimental point of view [15,16,17,18,19,20,13]. The recent possibility to carry out comparisons with different approaches motivates our interest to develop a pure classical investigation based on classical MD.…”

Ab initiosimulations of the dynamic ion structure factor of warm dense lithium

“…Fitting the Drude model to the dynamic conductivity [63,64] we extract the electron plasma frequency equivalent to an ionization degree of Z f = 1.0 and a DC conductivity of σ DC (ω → 0) = 0.26 × 10 6 S/m. Note that the DC conductivity values and band gaps are dependent on the XC functional and are potentially modified by using higher order functionals, e.g., hybrid functionals [65].…”

LDRD project 151362 : low energy electron-photon transport.

“…At first, we thought we could simply perform a DFT calculation to determine the complex dielectric function as a function of energy loss and momentum transfer, but as already pointed out [Plagemann et al 2012] "…the ab initio approach is so far only applicable for wavenumbers k=0…" This leads to approaches whereby the energy loss function is obtained (traditionally by measurement) together with some approach to extrapolate into k>0. While the extrapolation procedure is necessarily imprecise, it is constrained to obey certain constraints (sum rules).…”