Maximilian P. Böhme

X-ray scattering is a powerful diagnostic for characterizing warm-dense matter, as the scattering spectrum simultaneously encodes details of the plasma thermodynamic state, ionization, and electron correlations. However, scattering measurements from laser-driven samples must contend with not only a short-lived and rapidly evolving state but also small scattering cross sections. A continuous, time-resolved scattering measurement would characterize the evolving thermodynamic state while providing unprecedented access to the temporal evolution of the ion–plasma interaction. To provide the required diagnostic capability for such a measurement, we have designed a high-efficiency x-ray spectrometer coupled to a streak camera for use on the National Ignition Facility. The spectrometer utilizes a conically curved crystal to increase solid angle collection and to sagittally focus the signal onto the millimeter-scale streak camera slit. Characterization of the crystals with a Bremsstrahlung x-ray source demonstrates sensitivities 1000-fold higher than existing spectrometers on the National Ignition Facility. By enabling continuous, time-resolved temperature measurements via x-ray scattering, this new spectrometer will provide key constraints for improving equation-of-state and atomic-physics models of warm-dense matter.

X-ray Thomson scattering (XRTS) is a common diagnostic used in the warm dense matter (WDM) regime to estimate plasma parameters like density, temperature, and charge state. Experimental analysis typically relies on a forward model to obtain estimates for these parameters, as the measured spectrum is a convolution of the dynamic structure factor (DSF) and the source-instrument function. The Chihara decomposition, where the spectrum is separated into contributions from bound and free electrons, is commonly used to estimate DSFs in the WDM regime, as it allows for the fast calculation of DSFs and therefore can easily be applied in a large-scale parameter optimization. Due to the limited availability of XRTS codes, we present “x-ray diagnostics, analysis, verification, and exploration”, a code designed to quickly estimate DSFs using the Chihara decomposition and analyze experimental spectra. The code is validated by re-analyzing an experiment with isochorically heated beryllium at the OMEGA Laser Facility. In addition, we demonstrate the applicability of the code to plan experiments and predict scattering spectra through the coupling to a ray-tracing code. Finally, the importance of accounting for the energy-dependence of spectrometer instrument functions is demonstrated by comparing ray-tracing simulations to the standard convolution for strongly compressed beryllium experiments at the National Ignition Facility, similar to previously published results.

Warm dense matter (WDM) is now routinely created and probed in laboratories around the world, providing unprecedented insights into conditions achieved in stellar atmospheres, planetary interiors, and inertial confinement fusion experiments. However, the interpretation of these experiments is often filtered through models with systematic errors that are difficult to quantify. Due to the simultaneous presence of quantum degeneracy and thermal excitation, transitions in which free electrons are de‐excited into thermally unoccupied bound states transferring momentum and energy to a scattered x‐ray photon become viable. Here we show that such free‐bound transitions are a particular feature of WDM and vanish in the limits of cold and hot temperatures. The inclusion of these transitions into the analysis of recent X‐ray Thomson Scattering experiments on WDM at the National Ignition Facility and the Linac Coherent Light Source is required to obtain a physically consistent temperature from the Chihara decomposition. This interpretation is corroborated by agreement with a recently developed model‐free thermometry technique and presents an important step for precisely characterizing and understanding the complex WDM state of matter.

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.

X-ray Thomson scattering (XRTS) probes the dynamic structure factor of the system, but the measured spectrum is broadened by the combined source-and-instrument function (SIF) of the setup. In order to extract properties such as temperature from an XRTS spectrum, the broadening by the SIF needs to be removed. Recent work [Dornheim et al. Nat. Commun. 13, 7911 (2022)] has suggested that the SIF may be deconvolved using the two-sided Laplace transform. However, the extracted information can depend strongly on the shape of the input SIF, and the SIF is in practice challenging to measure accurately. Here, we propose an alternative approach: we demonstrate that considering ratios of Laplace-transformed XRTS spectra collected at different scattering angles is equivalent to performing the deconvolution, but without the need for explicit knowledge of the SIF. From these ratios, it is possible to directly extract the temperature from the scattering spectra, when the system is in thermal equilibrium. We find the method to be generally robust to spectral noise and physical differences between the spectrometers, and we explore situations in which the method breaks down. Furthermore, the fact that consistent temperatures can be extracted for systems in thermal equilibrium indicates that non-equilibrium effects could be identified by inconsistent temperatures of a few eV between the ratios of three or more scattering angles.

X-ray Thomson scattering (XRTS) has emerged as a valuable diagnostic for matter under extreme conditions, as it captures the intricate many-body physics of the probed sample. Recent advances, such as the model-free temperature diagnostic of Dornheim et al. [Nat. Commun. 13, 7911 (2022)], have demonstrated how much information can be extracted directly within the imaginary-time formalism. However, since the imaginary-time formalism is a concept often difficult to grasp, we provide here a systematic overview of its theoretical foundations and explicitly demonstrate its practical applications to temperature inference, including relevant subtleties. Furthermore, we present recent developments that enable the determination of the absolute normalization, Rayleigh weight, and density from XRTS measurements without reliance on uncontrolled model assumptions. Finally, we outline a unified workflow that guides the extraction of these key observables, offering a practical framework for applying the method to interpret experimental measurements.

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high-quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree—quantities which are otherwise not directly accessible from the physical model—from first-principles path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and nonequilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high-density and high-temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from first-principles quantum Monte Carlo simulations.

Understanding the behavior of polymer foams at high energy density conditions is crucial to advance inertial fusion energy research. Here, we present a new experimental platform designed to measure the thermodynamic state of these materials at megabar pressures. At the Matter in Extreme Conditions Endstation of the Linac Coherent Light Source, we heat samples using an optical, high-intensity, femtosecond laser and dynamically probe them with ultra-short, coherent x-ray pulses of high peak brightness. We perform x-ray Thomson scattering measurements in forward and backward scattering geometries to capture both collective and non-collective electron behavior in the sample. Simultaneously, x-ray fluorescence spectroscopy is used to measure the emission from a mid-Z dopant, providing complementary information on the plasma conditions. By combining these techniques, we obtain temporally resolved temperature measurements of the transient warm dense matter states. Our initial experiments designed to benchmark the platform with carbon samples yielded data resolving the ultrafast response to laser heating with sub-picosecond resolution, measuring plasma temperatures exceeding 50 eV. These findings lay the foundation for precision studies of the dynamic evolution of laser-heated polymer foams.

The study of matter at extreme densities and temperatures has emerged as a highly active frontier at the interface of plasma physics, material science and quantum chemistry with relevance for planetary modeling and inertial confinement fusion. A particular feature of such warm dense matter is the complex interplay of Coulomb interactions, quantum effects, and thermal excitations, making its rigorous theoretical description challenging. Here, we demonstrate how ab initio path integral Monte Carlo simulations allow us to unravel this intricate interplay for the example of strongly compressed beryllium, focusing on two X-ray Thomson scattering data sets obtained at the National Ignition Facility. We find excellent agreement between simulation and experiment with a very high level of consistency between independent observations without the need for any empirical input parameters. Our results call into question previously used chemical models, with important implications for the interpretation of scattering experiments and radiation hydrodynamics simulations.