C. Fortmann

Thomson scattering from near-solid density plasmas using soft x-ray free electron lasers

We propose a collective Thomson scattering experiment at the VUV free electron laser facility at DESY (FLASH) which aims to diagnose warm dense matter at near-solid density. The plasma region of interest marks the transition from an ideal plasma to a correlated and degenerate many-particle system and is of current interest, e.g. in ICF experiments or laboratory astrophysics. Plasma diagnostic of such plasmas is a longstanding issue. The collective electron plasma mode (plasmon) is revealed in a pump-probe scattering experiment using the high-brilliant radiation to probe the plasma. The distinctive scattering features allow to infer basic plasma properties. For plasmas in thermal equilibrium the electron density and temperature is determined from scattering off the plasmon mode.

Cluster virial expansion for the equation of state of partially ionized hydrogen plasma.

We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-virial expansion. We use the Beth-Uhlenbeck approach to calculate the second virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase shifts and binding energies. Experimental scattering cross-sections as well as phase shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase shift calculation, we generalize the cluster-virial expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the virial expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semiempirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second virial coefficient for the electron-atom interaction represents a benchmark for other, semiempirical approaches.

X-ray radiography and scattering diagnosis of dense shock-compressed matter

Highly coupled Boron plasma has been probed by spectrally resolving an x-ray source scattered by the plasma. Electron density was inferred from the inelastic feature in the collective scattering regime. In addition, the mass density inferred from the noncollective x-ray Thomson scattering has been tested with independent characterization using x-ray radiography in the same drive condition. High-intensity laser produced K-alpha radiation was used as a backlighter for these dynamically compressed plasma experiments providing a high temporal resolution of the measurements. Mass density measurements from both methods are in good agreement. The measurements yield a compression of 1.3 in agreement with detailed radiation-hydrodynamic modeling. From the charge state measured in the noncollective regime and the electron density measured in the collective regime mass density can then be constrained to 3.15±0.7.

Dynamic structure factor in warm dense beryllium

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 Drude- like 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.

Influence of local-field corrections on Thomson scattering in collision-dominated two-component plasmas

The dynamic structure factor, which determines the Thomson scattering spectrum, is calculated via an extended Mermin approach. It incorporates the dynamical collision frequency as well as the local-field correction factor. This allows to study systematically the impact of electron-ion collisions as well as electron-electron correlations due to degeneracy and short-range interaction on the characteristics of the Thomson scattering signal. As such, the plasmon dispersion and damping width is calculated for a two-component plasma, where the electron subsystem is completely degenerate. Strong deviations of the plasmon resonance position due to the electron-electron correlations are observed at increasing Brueckner parameters r(s). These results are of paramount importance for the interpretation of collective Thomson scattering spectra, as the determination of the free electron density from the plasmon resonance position requires a precise theory of the plasmon dispersion. Implications due to different approximations for the electron-electron correlation, i.e., different forms of the one-component local-field correction, are discussed.

Probing near-solid density plasmas using soft X-ray scattering

X-ray scattering using highly brilliant x-ray free-electron laser (FEL) radiation provides new access to probe free-electron density, temperature and ionization in near-solid density plasmas. First experiments at the soft x-ray FEL FLASH at DESY, Hamburg, show the capabilities of this technique. The ultrashort FEL pulses in particular can probe equilibration phenomena occurring after excitation of the plasma using ultrashort optical laser pumping. We have investigated liquid hydrogen and find that the interaction of very intense soft x-ray FEL radiation alone heats the sample volume. As the plasma establishes, photons from the same pulse undergo scattering, thus probing the transient, warm dense matter state. We find a free-electron density of (2.6 ± 0.2) × 1020 cm−3 and an electron temperature of 14 ± 3.5 eV. In pump–probe experiments, using intense optical laser pulses to generate more extreme states of matter, this interaction of the probe pulse has to be considered in the interpretation of scattering data. In this paper, we present details of the experimental setup at FLASH and the diagnostic methods used to quantitatively analyse the data.

Observations of strong ion-ion correlations in dense plasmas

Using simultaneous spectrally, angularly, and temporally resolved x-ray scattering, we measure the pronounced ion-ion correlation peak in a strongly coupled plasma. Laser-driven shock-compressed aluminum at ∼3× solid density is probed with high-energy photons at 17.9 keV created by molybdenum He-α emission in a laser-driven plasma source. The measured elastic scattering feature shows a well-pronounced correlation peak at a wave vector of k=4A−1. The magnitude of this correlation peak cannot be described by standard plasma theories employing a linear screened Coulomb potential. Advanced models, including a strong short-range repulsion due to the inner structure of the aluminum ions are however in good agreement with the scattering data. These studies have demonstrated a new highly accurate diagnostic technique to directly measure the state of compression and the ion-ion correlations. We have since applied this new method in single-shot wave-number resolved S(k) measurements to characterize the physical pro...

Thomson scattering in dense plasmas with density and temperature gradients

Abstract Collective X-ray Thomson scattering has become a versatile tool for the diagnostics of dense plasmas. Assuming homogeneous density and temperature throughout the target sample, these parameters can be determined directly from the plasmon dispersion and the ratio of plasmon amplitudes via detailed balance. In inhomogeneous media, the scattering signal is an average of the density and temperature dependent scattering cross-section weighted with the density and temperature profiles. We analyse Thomson scattering spectra in the XUV range from near solid density hydrogen targets generated by free electron laser radiation. The influence of plasma inhomogeneities on the scattering spectrum is investigated by comparing density and temperature averaged scattering signals to calculations assuming homogeneous targets. We find discrepancies larger than 10% between the mean electron density and the effective density as well as between the mean temperature and the effective temperature.

X-ray scattering measurements of dissociation-induced metallization of dynamically compressed deuterium

Hydrogen, the simplest element in the universe, has a surprisingly complex phase diagram. Because of applications to planetary science, inertial confinement fusion and fundamental physics, its high-pressure properties have been the subject of intense study over the past two decades. While sophisticated static experiments have probed hydrogens structure at ever higher pressures, studies examining the higher-temperature regime using dynamic compression have mostly been limited to optical measurement techniques. Here we present spectrally resolved x-ray scattering measurements from plasmons in dynamically compressed deuterium. Combined with Compton scattering, and velocity interferometry to determine shock pressure and mass density, this allows us to extract ionization state as a function of compression. The onset of ionization occurs close in pressure to where density functional theory-molecular dynamics (DFT-MD) simulations show molecular dissociation, suggesting hydrogen transitions from a molecular and insulating fluid to a conducting state without passing through an intermediate atomic phase.

X-ray Thomson scattering measurements of temperature and density from multi-shocked CH capsulesa)

Proof-of-principle measurements of the electron densities, temperatures, and ionization states of spherically compressed multi-shocked CH (polystyrene) capsules have been achieved using spectrally resolved x-ray Thomson scattering. A total energy of 13.5 kJ incident on target is used to compress a 70 μm thick CH shell above solid-mass density using three coalescing shocks. Separately, a laser-produced zinc He-α x-ray source at 9 keV delayed 200 ps-800 ps after maximum compression is used to probe the plasma in the non-collective scattering regime. The data show that x-ray Thomson scattering enables a complete description of the time-dependent hydrodynamic evolution of shock-compressed CH capsules, with a maximum measured density of ρ > 6 g cm−3. In addition, the results demonstrate that accurate measurements of x-ray scattering from bound-free transitions in the CH plasma demonstrate strong evidence that continuum lowering is the primary ionization mechanism of carbon L-shell electrons.