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.

Hydrogen-helium demixing plays a central role in the internal structure and evolution of giant planets such as Jupiter and Saturn, where phase separation is believed to drive phenomena like helium rain and influence planetary luminosity [1]. Accurately determining the demixing boundary under extreme pressure-temperature conditions remains a major challenge [2].

We investigate the phase-dependent diffusion behavior of water under extreme conditions using first-principles molecular dynamics simulations. Mean square displacements are analyzed to extract diffusion coefficients for hydrogen and oxygen in the liquid, solid, and superionic regimes. The results provide insight into ionic mobility across phase boundaries and are relevant for understanding water-rich planetary interiors. Particular emphasis is placed on identifying the onset of superionicity and the suppression of diffusion in the solid state.

The mixing behavior of hydrogen with heavier elements plays a key role in modeling the interiors of giant planets such as Jupiter and Saturn. Using density functional theory combined with molecular dynamics, we investigate hydrogen-neon mixtures and find that the minimum pressure required to trigger phase separation is substantially lower than in hydrogen-helium mixtures. Our simulations further reveal that the presence of neon stabilizes hydrogen molecules even at temperatures of approximate to 10,000 K and pressures of approximate to 10 Mbar, similar to trends observed in hydrogen-helium mixtures but significantly more pronounced. This stabilization is accompanied by a reduction of several orders of magnitude in the electrical conductivity compared to pure hydrogen. These results, together with the larger X-ray scattering cross section of neon, establish hydrogen-neon as a valuable experimental surrogate for probing phase separation in hydrogen-rich mixtures and provide new insight into the physical mechanisms in hydrogen and mixtures with heavier elements under planetary interior conditions.

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the warm dense matter 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 and contemporary challenges that are faced by theoretical methods, and experimental techniques needed to create and diagnose warm dense matter. A large part of this roadmap is dedicated to specific warm dense matter systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

Abstract Laser-plasma acceleration of protons offers a compact, ultra-fast alternative to conventional acceleration techniques, and is being widely pursued for potential applications in medicine, industry and fundamental science. Creating a stable, collimated beam of protons at high repetition rates presents a key challenge. Here, we demonstrate the generation of multi-MeV proton beams from a fast-replenishing ambient-temperature liquid sheet. The beam has an unprecedentedly low divergence of 1° (≤20 mrad), resulting from magnetic self-guiding of the proton beam during propagation through a low density vapour. The proton beams, generated at a repetition rate of 5 Hz using only 190 mJ of laser energy, exhibit a hundred-fold increase in flux compared to beams from a solid target. Coupled with the high shot-to-shot stability of this source, this represents a crucial step towards applications.

We report on the development of a robust microfluidic nozzle capable of generating replenishing liquid sheet targets with sub-micron thickness at up to kHz repetition rates, a λ/20 surface flatness over areas of at least 100 μm2, and in-vacuum dimensions of 6 × 1.5 mm2. The platform was evaluated for stability under hundreds of 4.3 J laser shots at 0.5 Hz and 6 × 1020 W/cm2 peak intensity, delivered in burst mode, totaling 2.9 kJ on the target. The key metrics of the platform, including sheet characteristics, nozzle aperture morphology, and proton spectra, showed no measurable degradation in the performance of the liquid sheet platform following this experiment. Beyond its application to ion beam technology, we outline a pathway to further develop the capabilities of the platform into a high-repetition-rate plasma mirror.

Gold is an unreactive metal and its chemical interactions with hydrogen have only recently been explored. Here, we report the formation of gold hydride above 40 GPa and 2200 K in X‐ray free electron laser heated diamond anvil cells using various hydrocarbons as hydrogen sources. Above 40 GPa, a hexagonal phase emerges close to the gold melting point, corresponding to a hydride with stoichiometry , with increasing from 0 to near 1 with pressure from 40 to 80 GPa. This is a high‐temperature phase which reverts to face centered cubic gold on cooling to 295 K. Accompanying DFT‐MD simulations are in excellent agreement with experiment and reveal the structure to consist of an hexagonal close packed gold lattice with atomic hydrogen disordered in the interstices. The hydrogen is superionic and exhibits high diffusivity through the crystalline gold lattice. Our results present the first solid‐state binary compound of gold and hydrogen.

In their landmark study1, Fecht and Johnson unveiled a phenomenon that they termed the 'entropy catastrophe', a critical point where the entropy of superheated crystals equates to that of their liquid counterparts. This point marks the uppermost stability boundary for solids at temperatures typically around three times their melting point. Despite the theoretical prediction of this ultimate stability threshold, its practical exploration has been prevented by numerous intermediate destabilizing events, colloquially known as a hierarchy of catastrophes2-5, which occur at far lower temperatures. Here we experimentally test this limit under ultrafast heating conditions, directly tracking the lattice temperature by using high-resolution inelastic X-ray scattering. Our gold samples are heated to temperatures over 14 times their melting point while retaining their crystalline structure, far surpassing the predicted threshold and suggesting a substantially higher or potentially no limit for superheating. We point to the inability of our samples to expand on these very short timescales as an important difference from previous estimates. These observations provide insights into the dynamics of melting under extreme conditions.

We report time resolved observations of the crystallization from liquid hydrogen, supercooled to temperatures below the melting point, using 11.2 keV X-ray diffraction from the Linac Coherent Light Source (LCLS). Changes to the metastable solid and liquid structure factors have been dynamically measured. This allows for a direct determination of the lowest energy crystal polymorphs, the stacking probabilities, as well as the liquid and solid densities and temperatures. Such measurements provide experimental evidence of an Arrhenius-like growth kinetics along the stacking direction during supercooling.

We describe measurements of the DC electrical conductivity of warm dense matter using ultrafast terahertz (THz) pulses. THz fields are sufficiently slowly varying that they behave like DC fields on the timescale of electron–electron and electron–ion interactions and hence probe DC-like responses. Using a novel single-shot electro-optic sampling technique, the electrical conductivity of the laser-generated warm dense matter was determined with <1 ps temporal resolution. We present the details of the single-shot THz detection methodology as well as considerations for warm dense matter experiments. We, then, provide proof-of-concept studies on aluminum driven to the warm dense matter regime through isochoric heating and shock compression. Our results indicate a decrease in the conductivity when driven to warm dense matter conditions and provide a platform for future warm dense matter studies.

Phonon scattering in metals is one of the most fundamental processes in materials science. However, understanding such processes has remained challenging and requires detailed information on interactions between phonons and electrons. We use an ultrafast electron diffuse scattering technique to resolve the nonequilibrium phonon dynamics in femtosecond–laser-excited tungsten in both time and momentum. We determine transient populations of phonon modes which show strong momentum dependence initiated by electron-phonon coupling. For phonons near Brillouin zone border, we observe a transient rise in their population on a timescale of approximately 1 picosecond driven by the strong electron-phonon coupling, followed by a slow decay on a timescale of approximately 8 picosecond governed by the weaker phonon-phonon relaxation process. We find that the exceptional harmonicity of tungsten is needed for isolating the two processes, resulting in long-lived nonequilibrium phonons in a pure metal. Our finding highlights that electron-phonon scattering can be the determinant factor in the phonon thermal transport of metals.

Indirect Drive Inertial Confinement Fusion Experiments on the National Ignition Facility (NIF) have achieved a burning plasma state with neutron yields exceeding 170 kJ, roughly 3 times the prior record and a necessary stage for igniting plasmas. The results are achieved despite multiple sources of degradations that lead to high variability in performance. Results shown here, for the first time, include an empirical correction factor for mode-2 asymmetry in the burning plasma regime in addition to previously determined corrections for radiative mix and mode-1. Analysis shows that including these three corrections alone accounts for the measured fusion performance variability in the two highest performing experimental campaigns on the NIF to within error. Here we quantify the performance sensitivity to mode-2 symmetry in the burning plasma regime and apply the results, in the form of an empirical correction to a 1D performance model. Furthermore, we find the sensitivity to mode-2 determined through a series of integrated 2D radiation hydrodynamic simulations to be consistent with the experimentally determined sensitivity only when including alpha-heating. Recent improvements in the indirect-drive inertial confinement fusion experiments include the achievement of burning plasma state. Here the authors report the scaling of neutron yield in a burning plasma of Deuterium-Tritium fusion reaction by including the mode-2 asymmetry.

We consider quantum tunneling between fusing nuclei in the presence of a harmonically time-varying field. The tunneling rate is calculated using Floquet/Volkov (FV) and Kramers-Henneberger (KH) approaches, which are both compared to a first-principles numerical solution of the Crank-Nicolson (CN) type. Numerical validation of the FV approach justifies its use in analytical estimates of laser-enhanced reaction rates, while the KH approach does not reproduce the predictions of the others. For a deuterium-tritium plasma at a temperature of 1 keV, it is found that significant enhancement of fusion reactivity requires field strengths on the order of ${10}^{15}$--${10}^{16}$ V/m and photon energies below 1 keV, which is within reach of next-generation x-ray free electron lasers (XFELs).

Calculations for the burn fraction in a laser-created plasma are presented, taking fuel depletion into account. The enhancement from a strong-field laser is analyzed and calculated in the Floquet-Volkoff framework, which was verified to provide an adequate theoretical prediction for laser-enhanced fusion cross sections in a previous work [Phys. Rev. C 109, 044605 (2024)]. Three different fuels were considered for the fusion process, namely deuterium-tritium (DT) fusion, deuterium-helium fusion, and proton-boron fusion. Their laser-enhanced burn fractions are compared in idealistic and realistic settings, where both thermal and nonthermal distributions are considered. It is found that DT fusion gains the least relative enhancement to the burn fraction in all scenarios considered, and that the remaining fuels do not gain an absolute enhancement large enough to be appreciable in comparison with the former.

On the path towards high-gain inertial confinement fusion ignition, foams are being considered to tamp the hohlraum wall-motion, and mitigate laser backscattering from Stimulated Raman Scattering (SRS) and Stimulated Brillouin Scattering (SBS). Here we present the results from an experimental campaign on foam-filled hohlraums conducted at the OMEGA laser facility. SiO2 foam-fills, with densities as low as 1 mg/cm3, successfully reduce the gold wall expansion, with laser backscattering comparable to gas-fill.

Studies of laser-heated materials on femtosecond timescales have shown that the interatomic potential can be perturbed at sufficiently high laser intensities. For gold, it has been postulated to undergo a strong stiffening leading to an increase of the phonon energies, known as phonon hardening. Despite efforts to investigate this behavior, only measurements at low absorbed energy density have been performed, for which the interpretation of the experimental data remains ambiguous. By using in situ single-shot x-ray diffraction at a hard x-ray free-electron laser, the evolution of diffraction line intensities of laser-excited Au to a higher energy density provides evidence for phonon hardening.

Laser-driven dynamic compression experiments of plastic materials have found surprisingly fast formation of nanodiamonds (ND) via X-ray probing. This mechanism is relevant for planetary models, but could also open efficient synthesis routes for tailored NDs. We investigate the release mechanics of compressed NDs by molecular dynamics simulation of the isotropic expansion of finite size diamond from different P-T states. Analysing the structural integrity along different release paths via molecular dynamic simulations, we found substantial disintegration rates upon shock release, increasing with the on-Hugnoiot shock temperature. We also find that recrystallization can occur after the expansion and hence during the release, depending on subsequent cooling mechanisms. Our study suggests higher ND recovery rates from off-Hugoniot states, e.g., via double-shocks, due to faster cooling. Laser-driven shock compression experiments of polyethylene terephthalate (PET) samples with in situ X-ray probing at the simulated conditions found diamond signal that persists up to 11 ns after breakout. In the diffraction pattern, we observed peak shifts, which we attribute to thermal expansion of the NDs and thus a total release of pressure, which indicates the stability of the released NDs.

We report a comprehensive numerical study on laser-induced melting of copper applying the two-temperature description combined with molecular dynamics simulations (TTM-MD). It reveals the internal energy relaxation and melting dynamics of thin copper films irradiated with an ultrafast laser pulse. The TTM-MD simulations were performed utilizing different expressions for the electronic properties of copper including the temperaturedependent heat capacity and the electron-phonon coupling strength. We study the resulting melting times and structural evolution of the lattice that were found to vary in the picosecond range. The importance of the correct choice of the electron-phonon coupling parameter is underlined by its large influence on the heating and melting times of the lattice.