Ulf Zastrau

Knowledge of the shot-to-shot incident spectrum in X-ray free-electron laser (XFEL) experiments is crucial for the analysis and interpretation of experimental data collected from various spectroscopic techniques such as X-ray Thomson scattering, resonant inelastic X-ray scattering and X-ray pump–probe experiments. In this article, we present a novel spectrometer design capable of accurately measuring the incident self-amplified spontaneous emission (SASE) XFEL spectrum on a shot-to-shot basis that is free of spatial and spectral inhomogeneities, such as chirp and central energy jitter that are inherent to XFEL radiation. The setup consists of glassy carbon as a dispersive element, a flat Si (444) analyzer crystal and a 2D pixel detector. Direct comparisons with existing spectral monitors are obtained using a reconstruction method based on frequency-resolved stochastic correlations between the measured incident SASE spectrum and the well characterized collective scattering excitations from aluminium.

The crystallographic structure of iron under extreme conditions is a key benchmark for state-of-the-art experimental and computational methods. Moreover, it plays a crucial role in our understanding of planetary cores, as it strongly influences the interpretation of observational data and, consequently, our knowledge of their internal structure and dynamics. However, even the crystal structure of pure solid iron under Earth's core conditions remains uncertain, with the commonly expected hexagonal close-packed phase being energetically competitive with several cubic structures. In this study, iron was compressed in a diamond anvil cell to pressures exceeding 200 GPa and dynamically probed near its melting point using MHz-frequency x-ray pulses from the European X-ray Free-Electron Laser. In the pressure range between 120 and 160 GPa, the high temporal resolution of the structural snapshots at elevated temperatures revealed the face-centered cubic phase, extending its observed stability to higher pressures than previously reported. Brief appearances of intermediate or disordered phases, including body-centered cubic (bcc) and stacking-faulted structures, were also observed. Above 230 GPa, new diffraction reflections emerged at high temperatures and are interpreted as evidence for the nucleation of a previously unreported phase, which subsequently evolved into a powderlike diffraction pattern characteristic of the bcc structure. The unprecedented time resolution of the structural data acquired during rapid heating and cooling cycles provides insights into the kinetics and mechanisms of phase transformations in iron at these extreme pressures.

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter (WDM) physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the WDM physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations & experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments of and contemporary challenges for theoretical methods and experimental techniques needed to describe, create and diagnose WDM. A large part of this roadmap is dedicated to specific WDM systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

Electron-ion equilibration dynamics in samples driven into superheated states with multi-eV electron temperatures represent a fundamental process in nonequilibrium physics. A clear picture of the evolving ion temperature is essential for understanding the strength of the electron-ion coupling. However, direct, model-independent measurements of the ion temperature in laser-irradiated samples have remained experimentally elusive. Using inelastic X-ray scattering with meV-resolution in gold samples, the ion response to ultrafast heating by the hot electrons can be resolved, quantifying the electron-ion equilibration dynamics. We report measurements revealing a strongly enhanced energy transfer rate compared to that in weakly excited gold. Moreover, we obtain a quasi-constant electron-ion coupling at the highly elevated electron temperatures. These results place new constraints on electron-ion energy transfer in warm dense matter and establish a path toward quantitative benchmarking of models for nonequilibrium dynamics.

The robust diagnosis of conditions generated in warm dense matter experiments remains a persistent challenge. Here, we describe the measurement of shock-compressed aluminium at 50 GPa with angle-resolved femtosecond x-ray Thomson scattering (XRTS) over a wide range of scattering wave vectors at the European X-Ray Free-Electron Laser. The measured plasmon dispersion and line shape show that the standard approach for analyzing XRTS spectra, using uniform-electron-gas models, systematically overestimates the resonance energy by up to 8 eV. We present an approach using methods that agrees within the experimental uncertainty and demonstrates how accounting for shock-induced disorder in shock-compressed systems is critical for their understanding, providing evidence that treatments are required for reliable XRTS inference in warm dense aluminium.

Ultrafast, high-power lasers operating in the near-infrared (NIR) region are key to accelerating ions to extremely high energies. By changing the laser wavelength from the NIR region to the hard X-ray range, the photon energy increases more than 10 000 times. The interaction mechanisms and, consequently, radiation attenuation lengths differ significantly between these two spectral ranges. Here we report the use of an X-ray free-electron laser (European XFEL, Germany) delivering 9.3 keV photons in 25 fs pulses and a total energy of 0.35 mJ on a solid target. Electrons and ions escaping from an irradiated 3 μm Cu foil into vacuum were investigated by a time-of-flight technique using windowless electron multipliers that enable the measurement of very weak currents. A model based on a shifted Maxwell–Boltzmann velocity distribution of species was used to analyze the detector signals. The method used made it possible to determine the temperatures of hot electrons and protons, their center-of-mass energy, the charge states of the isotopes 63Cu and 65Cu, and the magnitude of the voltage arising in the double layer that accelerated them, and to estimate the repetition frequency of their cascade emission from the plasma. Computer simulations revealed the evolution of the electron density and temperature, the ion charge state distribution, and the time scales of processes occurring in the bulk of irradiated matter. Good correlation of theoretical and experimental results over the range of high-energy-density states demonstrates the capability to provide critical data to develop plasma models in the warm dense matter regime.

We compare the predictions of the dynamic structure factor (DSF) of ambient polycrystalline aluminium from time‐dependent density functional theory (TDDFT) in the pair continuum regime to recent ultrahigh resolution x‐ray Thomson scattering measurements, collected at the European XFEL. TDDFT predicts strong anisotropy in the DSF at the wavenumber examined here, even with ‐blurring accounted for. The experimental spectrum has more than sufficient resolution and signal‐to‐noise levels to resolve these orientation dependencies, and therefore, the orientational averaging of the polycrystalline sample is observed rigorously. Once the orientation averaging is accounted for, TDDFT is able to reproduce the experimental spectrum adequately. Finally, comparisons of predicted DSFs from jellium to experiment demonstrate the importance of accounting for lattice effects in modelling the spectrum from a polycrystal.

Heating and ionization are among the most fundamental processes in relativistic laser–solid interactions; however, their spatiotemporal evolution remains challenging to capture experimentally. Here we present detailed diagnosis of high-intensity laser interactions with wire targets, leveraging the extreme spectral brightness of an X-ray free-electron laser in sub-picosecond time-resolved resonant X-ray emission spectroscopy and absorption imaging. Experimental results are compared with comprehensive simulations using atomic collisional-radiative models, particle-in-cell, and magnetohydrodynamics codes to elucidate the underlying physics. These multi-scale simulations reveal extreme sensitivity of basic plasma parameters with widely used models, such as temperature and ionization depth, which are able to be constrained by incorporating a detailed accounting of laser spatial profiles, pre-plasma conditions, and collisional processes. These results provide new insights into heating and ionization dynamics in the high-energy-density regime relevant to inertial fusion energy research, both as an experimental platform for accessing theoretically challenging conditions and as a benchmark for improving models of high-power laser–plasma interactions.

The development of pulsed intense x-ray sources, such as free electron laser, offers new avenues for high pressure experiments. Here, we study the feasibility and metrology of x-ray heating in diamond anvil cells at the European x-ray free electron laser. This method enables one to volumetrically heat the sample while inhibiting chemical migration and probing the crystallographic structure of the sample throughout the heating with a high repetition rate. We focus our study on iron, whose phase diagram is well established up to 100 GPa, to explore the possibilities and limitations of this technique. We volumetrically heat iron samples at starting pressures ranging from 10 to 138 GPa, using the x-ray beam pulsed at 4.5 MHz in a serial pump-and-probe experimental design. Experimental challenges arise from temperature gradients within the sample, changes in temperature at the 100 ns timescale, the difficulty of direct temperature estimates, the effect of thermal pressure, and the presence of metastable crystallites due to rapid cycles of heating and cooling. Hence, we develop a multi-crystal-like data processing method that allows us to account for sample heterogeneity in probed conditions. We then calibrate our measurements using known physical properties of iron under pressure. Thermal pressure in our experiments increases from 4% of the isochoric prediction at 10 GPa to 23% at 138 GPa, and we show that our data are in agreement with most previous observations of iron in this pressure range. The method can now be implemented at higher pressures and temperatures and on materials with unknown phase diagrams.