Compton scatter profiles for warm dense matter

A viscous quantum hydrodynamics model based on dynamic density functional theory

Dynamic density functional theory (DDFT) is emerging as a useful theoretical technique for modeling the dynamics of correlated systems. We extend DDFT to quantum systems for application to dense plasmas through a quantum hydrodynamics (QHD) approach. The DDFT-based QHD approach includes correlations in the the equation of state self-consistently, satisfies sum rules and includes irreversibility arising from collisions. While QHD can be used generally to model non-equilibrium, heterogeneous plasmas, we employ the DDFT-QHD framework to generate a model for the electronic dynamic structure factor, which offers an avenue for measuring hydrodynamic properties, such as transport coefficients via x-ray Thomson scattering.

Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter

The influence of finite relaxation times on Thomson scattering from warm dense plasmas is examined within the framework of the average-atom approximation. Presently most calculations use the collision-free Lindhard dielectric function to evaluate the free-electron contribution to the Thomson cross section. In this work, we use the Mermin dielectric function, which includes relaxation time explicitly. The relaxation time is evaluated by treating the average atom as an impurity in a uniform electron gas and depends critically on the transport cross section. The calculated relaxation rates agree well with values inferred from the Ziman formula for the static conductivity and also with rates inferred from a fit to the frequency-dependent conductivity. Transport cross sections determined by the phase-shift analysis in the average-atom potential are compared with those evaluated in the commonly used Born approximation. The Born approximation converges to the exact cross sections at high energies; however, differences that occur at low energies lead to corresponding differences in relaxation rates. The relative importance of including relaxation time when modeling x-ray Thomson scattering spectra is examined by comparing calculations of the free-electron dynamic structure function for Thomson scattering using Lindhard and Mermin dielectric functions. Applications are given to warm dense Be plasmas, with temperatures ranging from 2 to 32 eV and densities ranging from 2 to 64 g/cc.

Equilibration dynamics and conductivity of warm dense hydrogen

We investigate subpicosecond dynamics of warm dense hydrogen at the XUV free-electron laser facility (FLASH) at DESY (Hamburg). Ultrafast impulsive electron heating is initiated by a ≤ 300-fs short x-ray burst of 92-eV photon energy. A second pulse probes the sample via x-ray scattering at jitter-free variable time delay. We show that the initial molecular structure dissociates within (0.9 ± 0.2) ps, allowing us to infer the energy transfer rate between electrons and ions. We evaluate Saha and Thomas-Fermi ionization models in radiation hydrodynamics simulations, predicting plasma parameters that are subsequently used to calculate the static structure factor. A conductivity model for partially ionized plasma is validated by two-temperature density-functional theory coupled to molecular dynamic simulations and agrees with the experimental data. Our results provide important insights and the needed experimental data on transport properties of dense plasmas.

Predictions of x-ray scattering spectra for warm dense matter

We present calculations of x-ray scattering spectra based on ionic and electronic structure factors that are computed from a new model for warm dense matter. In this model, which has no free parameters, the ionic structure is determined consistently with the electronic structure of the bound and free states. The x-ray scattering spectrum is thus fully determined by the plasma temperature, density and nuclear charge, and the experimental parameters. The combined model of warm dense matter and of the x-ray scattering theory is validated against an experiment on room-temperature, solid beryllium. It is then applied to experiments on warm dense beryllium and aluminum. Generally good agreement is found with the experiments. However, some significant discrepancies are revealed and appraised. Based on the strength of our model, we discuss the current state of x-ray scattering experiments on warm dense matter and their potential to determine plasma parameters, to discriminate among models, and to reveal interesting and difficult to model physics in dense plasmas.

Thomson scattering in the average-atom approximation

The average-atom model is applied to study Thomson scattering of x-rays from warm dense matter with emphasis on scattering by bound electrons. Parameters needed to evaluate the dynamic structure function (chemical potential, average ionic charge, free electron density, bound and continuum wave functions, and occupation numbers) are obtained from the average-atom model. The resulting analysis provides a relatively simple diagnostic for use in connection with x-ray scattering measurements. Applications are given to dense hydrogen, beryllium, aluminum, and titanium plasmas. In the case of titanium, bound states are predicted to modify the spectrum significantly.

Thomson scattering on inhomogeneous targets

The introduction of brilliant free-electron lasers enables new pump-probe experiments to characterize warm dense matter states. For instance, a short-pulse optical laser irradiates a liquid hydrogen jet that is subsequently probed with brilliant soft x-ray radiation. The strongly inhomogeneous plasma prepared by the optical laser is characterized with particle-in-cell simulations. The interaction of the soft x-ray probe radiation for different time delays between pump and probe with the inhomogeneous plasma is also taken into account via radiative hydrodynamic simulations. We calculate the respective scattering spectrum based on the Born-Mermin approximation for the dynamic structure factor considering the full density and temperature-dependent Thomson scattering cross section throughout the target. We can identify plasmon modes that are generated in different target regions and monitor their temporal evolution. Therefore, such pump-probe experiments are promising tools not only to measure the important plasma parameters density and temperature but also to gain valuable information about their time-dependent profile through the target. The method described here can be applied to various pump-probe scenarios by combining optical lasers and soft x ray, as well as x-ray sources.

X-ray Thomson scattering in warm dense matter at low frequencies

The low-frequency portion of the x-ray Thomson scattering spectrum is determined by electrons that follow the slow ion motion. This ion motion is characterized by the ion-ion dynamic structure factor, which contains a wealth of information about the ions, including structure and collective modes. The frequency-integrated (diffraction) contribution is considered first. An effective dressed-particle description of warm dense matter is derived from the quantum Ornstein-Zernike equations, and this is used to identify a Yukawa model for warm dense matter. The efficacy of this approach is validated by comparing a predicted structure with data from the extreme case of a liquid metal; good agreement is found. A Thomas-Fermi model is then introduced to allow the separation of bound and free states at finite temperatures, and issues with the definition of the ionization state in warm dense matter are discussed. For applications, analytic structure factors are given on either side of the Kirkwood line. Finally, several models are constructed for describing the slow dynamics of warm dense matter. Two classes of models are introduced that both satisfy the basic sum rules. One class of models is the "plasmon-pole"-like class, which yields the dispersion of ion-acoustic waves. Damping is then included via generalized hydrodynamics models that incorporate viscous contributions.