Abstract
Understanding how laser pulses compress solids into high-energy-density states requires diagnostics that simultaneously resolve macroscopic geometry and nanometer-scale structure. Here we present a combined X-ray imaging (XRM) and small-angle X-ray scattering (SAXS) approach that bridges this diagnostic gap. Using the Matter in Extreme Conditions end station at LCLS, we irradiated copper wires with , , pulses at while probing with XFEL pulses. XRM visualizes the evolution of ablation, compression, and inward-propagating fronts with resolution, while SAXS quantifies their nanometer-scale sharpness via the time-resolved evolution of scattering streaks. The joint analysis reveals that an initially smooth compression steepens into a nanometer-sharp shock front after , consistent with an analytical steepening model and hydrodynamic simulations. The front reaches a velocity of and a lateral width of several tens of microns, demonstrating direct observation of shock formation and decay at solid density for the first time with few-nanometer precision. This integrated XRM–SAXS method establishes a quantitative, multi-scale diagnostic of laser-driven shocks in dense plasmas relevant to inertial confinement fusion, warm dense matter, and planetary physics.
1 Introduction
The controlled compression of matter to extreme pressures and densities is a central objective in high-energy-density (HED) and inertial confinement fusion (ICF) research. Conventional approaches rely on long-pulse, high-energy lasers to compress spherical fuel capsules either indirectly, via X-rays generated in a hohlraum, or directly by irradiating the capsule surface. While these schemes have achieved remarkable success—notably ignition at the National Ignition Facility—they require large, costly facilities, which limits experimental access and constrains the development of new target concepts and diagnostics.
Alternative routes based on short-pulse, high-intensity lasers have recently gained attention as compact drivers for transient, extreme compression [1–4]. In the latter case, an ultra-intense pulse irradiates a solid target, typically a thin wire or planar foil, generating energetic electrons that drive return currents in the bulk. The associated magnetic fields and ablation counterpressures launch inward-moving compression waves that can steepen into shocks. For cylindrical wires, upon convergence on the target axis these shocks can produce Gbar-level pressures and strongly heated, highly ionized states of matter [1–4]—conditions directly relevant for ICF physics, planetary interiors, and laboratory astrophysics.
The ability to characterize these laser-driven shocks on multiple scales is critical. After earlier attempts of X-ray imaging in the diffractive regime [5], X-ray microscopy (XRM) in direct imaging geometry [6] has recently enabled the visualization of plasma density evolution including blast waves, hole-boring, wire implosions, and filamentation with spatial resolutions down to a few hundred nanometers [4, 7]. However, even this resolution is insufficient to resolve the nanometer-scale sharpness of shock fronts themselves. Measurements in Small-angle X-ray scattering geometry (SAXS), in contrast, can provide sensitivity to structural variations at the nanometer scale and has recently been applied to diagnose phase interfaces and density gradients in laser-compressed solids [8–11]. Yet, previous SAXS experiments suffered from two main limitations: the scattering signal was often too weak for quantitative analysis, and the lack of complementary real-space imaging left the interpretation of the scattering features ambiguous.
In this work, we overcome these limitations by combining XRM and SAXS in a joint, spatially correlated diagnostic setup. XRM provides real-space constraints on the macroscopic morphology and evolution of the compression fronts, while SAXS delivers quantitative information on their nanometer-scale sharpness and evolution in time. This integrated approach enables simultaneous access to global geometry and local structure, bridging the gap between hydrodynamic and microscopic descriptions of laser-driven compression.
2 Methods
The experiment was conducted at the Matter in Extreme Conditions (MEC) end station of the Linac Coherent Light Source (LCLS) X-ray free-electron laser (XFEL) at SLAC National Accelerator Laboratory, see Figure 1. We irradiated copper wires of µm diameter with pulses of duration , energy , and wavelength from the MEC short-pulse high-intensity (HI) laser, focused to a spot of µm full width at half maximum (FWHM). This corresponds to a peak intensity of and a normalized vector potential . The plasma dynamics were probed by XFEL pulses (, per pulse). Both beams were focused to the wire cylinder surface, with angle encompassed between them. The SAXS geometry to measure the small angle X-ray signal was optimized for high photon fluence and dynamic range, employing a µm XFEL spot size on target that was centered to the HI laser side of the target. After a propagation distance the X-ray signal was recorded with an ePix10k-540k detector behind a beam stop and adjustable attenuation system to control the low- signal. This allowed full use of the XFEL intensity without detector saturation and coverage of a large -range down to small values close to the XFEL beam waist, a major improvement over earlier experiments that required severe flux reduction [11]. Here and in the following we refer to SAXS as elastic scattering outside the zeroth order into small angles (such that ), while in parts of the SAXS literature the term “SAXS” is implicitly associated with the kinematic (Born/Rayleigh–Debye–Gans) regime, i.e., weak phase/amplitude objects where the scattered field is proportional to the Fourier transform of the volume density contrast [12–14]. However, as we show in Supplement, the kinematic regime can be applied in our conditions.
FIGURE 1
For XRM, we used the MEC X-ray imager (MXI) platform [6]. A larger XFEL spot of approx. µm was used to illuminate a broader target region while protecting the downstream Beryllium compound refractive lens stack (CRL) used to image the target to an Andor Neo 5.5 sCMOS scintillator camera. The configuration followed the high-resolution setup described in [7], achieving a spatial resolution of , as verified with a Siemens star test pattern. Note that due to the setup the laser interaction region appears inside the target in the XFEL projection. The change from SAXS to MXI setup could be facilitated in less than . Together, this dual-diagnostic scheme provides a comprehensive, quantitative probe of laser-driven compression from tens of microns to nanometers—a capability essential for disentangling the formation, evolution, and decay of shock fronts in dense plasmas.
3 Results
3.1 X-ray microscopy (XRM)
Figure 2 summarizes representative XRM data obtained for probe delays between and after the short-pulse laser irradiation. The overall evolution reveals a rapid onset of surface deformation, followed by the emergence of distinct compression and recession fronts. As early as , a small reduction in transmission appears on the laser-facing side of the wire (hereafter referred to as the front surface), extending roughly 10 µm transversely around the laser axis. By , this feature spans the full transverse field of view and becomes visible also on the opposite (rear) side. Simultaneously, a zone of increased transmission develops toward the vacuum interface (region A in Figure 2a). Such contrast changes are consistent with surface ablation and recession accompanied by local compression of the adjacent material—a process driven by the combination of return-current heating and magnetic counter-pressure [4]. Bound–bound absorption near the Cu K line at 8 keV may further contribute to the apparent opacity increase in the compressed regions [15].
FIGURE 2
At later times (), the front surface begins to curve inward (compare Figures 2d,e), forming a quasi-Gaussian profile that deepens progressively into the bulk (region B). Around , this deformation detaches from the surface, indicating the propagation of a distinct inward-moving compression front. This front appears to be best described by two Gaussians: a narrow one similar to the laser focus width and a wider one with several tens of microns width describing the shallow rather straight front at a transverse offset. This latter front moves inwards with a velocity of a few tens of km/s (region D in Figure 2g). The front reaches a maximum inclination of approximately near and subsequently relaxes.
Concurrently, a pronounced, stochastically modulated zone forms around the laser impact point, featuring filamentary modulations with characteristic wavelengths of µm (after ) to µm (after ). These modulations coincide spatially with the expected position of the laser–plasma interaction and are consistent with resistive filamentation observed under similar conditions [7]. A distinct, hole-boring-like feature [16] (region C) appears around the focal projection at , which expands in diameter over time and evolves into a blast-wave-like structure beyond . The region behind this front shows significant shot-to-shot variability, indicative of hydrodynamic instabilities and mixing between compressed and unperturbed material.
Interpretation of the XRM data requires care due to the 45 inclination between the pump and probe beams. The laser interacts with the cylindrical surface at normal incidence, so that the apparent “left” and “right” wire surfaces in projection do not correspond directly to the true front and rear surfaces w.r.t. the laser incidence. To clarify the correspondence, we constructed an analytic wire-density model and compared its projections with the experimental images. The model parameterized the two fronts by two superimposed Gaussian density perturbations, respectively (one Gaussian for the more localized hole-boring fronts (B,C), and an additional Gaussian for the wide compression front (D)), whose projected density distributions reproduce the observed transmission profiles (see Figure 5b for an example at delay).
Despite the lower drive intensity compared with the cylindrical-convergence experiment reported in [4], the same fundamental physical processes seem to appear here. In particular, an inward traveling compression front appears at the surface, that extends quite far transversely even several times the laser focal width away from the laser axis, and which is consistent with either a shock front driven by return-current heating or direct heating by out-of-focus laser intensity. In the present experiment with less pump laser intensity than that used in [4] the propagation ceases after .
3.2 Small-angle X-ray signal
Complementary small angle X-ray patterns are presented in Figure 3 for various probe delays. At , vertical streaks perpendicular to the target surface begin to split and tilt, indicating curvature of the scattering interface. With increasing delay, the tilt angle grows and multiple streaks appear, particularly in the data from the second experimental day. In contrast to earlier, lower-intensity experiments—which exhibited numerous streaks attributed to small-scale surface ripples [8]—the present data show only a few, well-defined streaks corresponding to larger, more controlled structures.
FIGURE 3
The minimum and maximum streak angles as a function of delay are plotted in Figure 4a. Streaks from day 1 are near the lower bound of those from day 2. The absence of higher angle streaks suggests a small transverse offset between the XFEL probe and optical pump on day 1 since at larger distance to the HI laser the angle of the compression front seen in XRM are shallower, consistent with the lowest angle streaks (cp. Figure 5. Using the XRM images as spatial reference, we can assign the observed streaks to specific regions of the target: D in Figure 3); larger-angle streaks (b, c) correspond to the more central, inward-curving fronts seen near the focal spot (B, C) (cp. Figure 5). This spatial correspondence confirms that the small angle X-ray signal originates from the same compression structures imaged by XRM, allowing quantitative inference of specific front sharpnesses.
FIGURE 4
FIGURE 5
In the following we analyse the lower angle streaks, i.e., surfaces consistent with the transversely offset compression front (feature D). We plot the profiles along streaks (a) for the pumped wires up to probe delay in Figure 4b, together with the respective profiles along the streak in the respective XFEL-only reference. We limit this analysis to data from day 1, since there the lower q data is less disturbed by overlap of neighboring streaks; and the signal strength of the streaks of interest was larger due to the better XFEL coverage. Note, however, that the same qualitative behaviour was observed on day 2, as well as for the streaks at larger angles. As can be seen, initially the slope of the pumped streak is slightly increased relative to the reference at delay. At the streak recovers and the slope is similar to the reference again. Later the slope sharply decreases between 45 and before it drops again.
To quantify the sharpness, we first benchmark against the cold (unpumped) reference wire scattering streaks, which follow , consistent with a smooth surface profile and an average roughness (see Methods). The pumped data were then fitted relative to this reference usingyielding the change in effective roughness as a function of delay (Figure 4C). Initially (), , consistent with slight surface expansion. At , approaches zero, indicating recovery. Subsequently becomes negative, reaching its minimum (i.e., sharpest surface) near . At this time, almost matches the cold-surface roughness, implying a fully developed, nanometer-sharp shock front. Beyond , the slope increases again, suggesting relaxation and decay of the shock—and in agreement with the stagnation of the front seen in XRM.
The correspondence between model, XRM morphology, and SAXS-derived nanometer-scale roughness confirms that the observed compression front indeed represents a shock front. Overall, the joint XRM–SAXS analysis bridges spatial scales from the micron level down to few nanometers, resolving the full evolution from macroscopic front geometry to cc. The combination of the two diagnostic capabilities allows, for the first time, quantitative verification of nanometer-scale shock formation in a solid-density plasma driven by a Joule-class femtosecond laser pulse.
3.3 Shock formation
The shock formation is not instantaneous, rather we find a considerable delay. At , is negative, indicating expansion, while later it is first around zero and after starting to become positive. We can estimate the breaking time assuming an isentropic flow of a fluid with local velocity , finite local sound speed where is the entropy of the fluid element, and with flux . Neglecting heat flux, from the continuity equation and Euler momentum equations one can infer the shock formation time in the strong shock limit for an ideal gas (, where is the upstream density, is the shock compressed one) for Gaussian heating profile (see Supplemental) [We added a missing factor ; we also moved the equation for the shock velocity to the Supplemental, and rather moved the equation for the Drude skin depth from Supplemental here.]with the shock velocity . To get an estimate for our experimental condition we can approximate with the Drude skin depth(where is the electron plasma frequency, is the free electron density, is the collision frequency, and is the Spitzer resistivity, and the frequency is given by the heating return current pulse duration which is similar to the laser pulse duration, [4, 17, 18]. The resulting shock formation time and shock velocity are plotted in Figure 6 as function of the temperature of the laser heated plasma. Specifically, from the imaging data we find that the shock front corresponding to the smallest angle streak has moved about µm after , i.e., corresponding to a temperature of . Then the average ionization is approximately from Saha equilibrium with one electron in the conduction band at room temperature, and the skin depth is approximately . We then obtain the estimate compared to from a FLASH [19] hydrodynamic simulation at that shock velocity (see Methods). Considering the simplicity of the rough analytical estimate, the two are in good agreement with each other and with the SAXS results. There, a slight reduction of the slope can be seen after for , indicating already (partial) shock development. After the streak is perpendicular to and at it is almost perfectly following , i.e., the shock is fully developed. Eventually at even later times the shock seems to decay as the slope increases again.
FIGURE 6
4 Discussion and conclusion
This study demonstrates that combining XRM with SAXS yields a self-consistent, multi-scale view of laser-driven compression in solids—from the global morphology of hole-boring and compression fronts (microns) down to their nanometer-scale sharpness (few nanometers). XRM constrains the geometry and kinematics of the fronts, while SAXS isolates local interface sharpness through the asymptotic fall-off and its temporal evolution. Taken together, these observables let us identify which XRM-visible interfaces generate the dominant small angle streaks and convert streak slopes into an effective interfacial width , even when the real-space image cannot resolve the front.
Three central findings emerge. First, the cold-wire reference shows an interfacial width . During the pump–probe sequence, small angle streaks associated with the laser-facing compression front initially broaden (negative at , consistent with rarefaction), then steepen sharply between and . By the slope reaches the limit characteristic of a discontinuous density jump, implying a fully developed shock. XRM confirms coincident front detachment, curvature, and compression, indicating that the apparent interface corresponds to a propagating shock rather than a smooth compression gradient.
Second, using the measured temperature profile and sound-speed gradient, the estimated breaking time matches the observed small angle streak evolution. This agreement supports an interpretation where the shock arises from nonlinear steepening of an initially smooth compression wave in the heated surface layer, rather than from instantaneous ablation-driven discontinuities. It is consistent with return current heating in a skin depth layer at the surface.
Identifying the front as a shock is crucial because shocks mark the onset of irreversible thermodynamic processes such as entropy production, dissipative heating, and rapid pressure buildup. In a smooth compression wave, energy remains largely mechanical and reversible; the local temperature increases only adiabatically with density. A shock, by contrast, converts directed kinetic energy into internal energy. This entropy jump determines the downstream equation of state, the achievable pressure, and the efficiency of converting laser energy into compressive work.
In the present context, the existence of a true shock means that the ablation does not merely push the material inward but dissipatively compresses it. In the context of inertial confinement fusion energy, the ability to diagnose shock strength and sharpness directly enables validation of models of shock-induced heating and mix. Distinguishing a shock from a continuous compression wave validates the use of Rankine–Hugoniot relations, allowing for inference of temperature and density from front velocities and providing benchmarks for kinetic and hydrodynamic simulations.
5 Limitations
This experiment closes the long-standing diagnostic gap between micron-scale imaging and nanometer-scale interface sensitivity. By combining MXI and SAXS, we can attribute specific small angle features to real-space fronts and quantify their evolution. The pump–probe projection, limited angular sampling, and overlapping streaks constrain the precision of front localization. Limited sampling at higher values due to low signal and small detector active area limit the accuracy of the fits, which prohibits using more sophisticated fitting models. Hence, small angle streak-derived values are, e.g., spatially averaged and underestimate the sharpest local gradients since the fits did not take into account partial shock formation or variation across the relevant surface areas. Also, the used model of error-function density slopes is only a simple estimate and could be improved in the future, e.g., by using simulation-based profiles.
6 Outlook
The observation of a shock–and its quantifiable formation dynamics–has direct implications for inertial confinement fusion physics, warm dense matter studies, and high-energy-density material science. The MXI–SAXS platform provides, e.g., a benchmark for validating resistive and ablative shock models including entropy production, a pathway to infer full Rankine–Hugoniot states from combined geometry, velocity, and sharpness data and a diagnostic foundation for exploring shock coalescence, radiative precursors, and turbulence onset in dense plasmas.
Future extensions should integrate tomography or multi-view XRM to reconstruct three-dimensional shock geometry. Angle-resolved and energy-tuned SAXS could further distinguish electron-density and ionization-opacity contributions, enabling element-specific shock diagnostics.
Methods
SAXS setup
In the SAXS setup, a sequence of precision slits was used to suppress higher-order (third harmonic) X-ray scattering contributions. The first slit, located at 84 cm upstream of the interaction point (TCC), was part of the MEC beamline infrastructure and oriented horizontally. Additionally, two JJ X-RAY AT-F7-AIR slit sets were installed 36 cm (tungsten) and 26 cm (silicon) upstream, each composed of orthogonal slits rotated by 45° with respect to the horizontal and vertical axes.
On the downstream end of the target chamber, just before the vacuum tube, a radiation protection aperture limited he available -range to approx. 1/µm. After propagation distance from TCC through a vacuum pipe the beam exited the vacuum through a Kapton window.
At a 2 cm distance (4.32 m from the TCC) molybdenum foils (beam stops) of 50, 100, or 150 µm thickness and 2–6 mm width were used to attenuate the central beam. These were glued to a Kapton support foil mounted on motorised stages for precise alignment and remote exchange in different absorber (see below) and beam configurations. Strong scattering signal in the low q region of the streaks could be reduced using two triangularly tapered titanium absorbers (50 µm thick) positioned at 4.49 m and 4.58 m downstream, oriented at 45° to the horizontal. The absorbers were motorized similarly to the beam stops, so that the width of the attenuated region could be controlled by the beam position along the taper.
The scattered X-rays were recorded on an ePix10k-540k detector (four 384 352 pixel modules, 100 µm pixel size) positioned 4.88 m downstream of the TCC.
Fits
All fits were performed by globally minimizing , assuming a density following the cumulative distribution function of a Gaussian (normal) distribution, . Then the intensity of XFEL-only data was fitted by . (, where is the wire radius), see Supplement for full derivation. The smoothness parameter was obtained by fitting only the Gaussian to the ratio of the unpumped over pumped signal.
FLASH simulations parameters
The FLASH simulations performed to retrieve the shock speed were 1D simulations. The simulation domain is of a length of 30 m over a adaptative refinement mesh with 6 levels of refinement. The smallest size possible for a cell is defined by m. These simulations are ran for 50 ps.
The FLASH target is defined by an Copper target of solid density at room temperature (300 K) except for a skin depth Gaussian temperature profile defined by nm and eV on the left hand side of the target which we chose to match the experimental condition w.r.t. the shock velocity. Note that these values are slightly different from the values given in the main text for the ideal gas approximation. The EOS used in our simulations for the Copper material are generated using IONMIX [20]A for a temperature range between and 530 eV. The resulting temperature and density temporal evolution is given in the supplement.
Statements
Data availability statement
The data presented in this study are available under DOI 10.14278/rodare.4557.
Author contributions
TK: Funding acquisition, Resources, Validation, Formal Analysis, Supervision, Project administration, Visualization, Investigation, Software, Data curation, Writing – review and editing, Writing – original draft, Methodology, Conceptualization. AH-P: Visualization, Writing – original draft, Methodology, Validation, Investigation, Writing – review and editing. JS: Investigation, Writing – original draft, Visualization, Validation, Writing – review and editing, Data curation, Formal Analysis. NC: Methodology, Conceptualization, Writing – review and editing. MF: Investigation, Writing – review and editing, Writing – original draft. EG: Writing – original draft, Investigation, Writing – review and editing, Conceptualization, Methodology. MG: Writing – original draft, Supervision, Writing – review and editing. JG: Resources, Writing – original draft, Writing – review and editing. CG: Writing – review and editing, Writing – original draft, Methodology, Supervision. LH: Investigation, Writing – review and editing, Writing – original draft, Methodology, Supervision. UH: Writing – review and editing, Resources, Writing – original draft. MI: Investigation, Writing – review and editing, Writing – original draft. HL: Supervision, Methodology, Conceptualization, Writing – review and editing, Writing – original draft, Investigation. DK: Investigation, Writing – original draft, Conceptualization, Writing – review and editing, Methodology. WM: Investigation, Writing – review and editing, Writing – original draft. BM: Methodology, Writing – review and editing, Writing – original draft, Investigation. MN: Writing – review and editing, Supervision, Methodology, Writing – original draft. PO: Conceptualization, Investigation, Methodology, Writing – original draft, Writing – review and editing. FP-B: Conceptualization, Writing – review and editing, Methodology, Investigation, Writing – original draft. AP: Writing – review and editing, Writing – original draft, Investigation. LR: Methodology, Writing – review and editing, Conceptualization, Investigation, Writing – original draft. H-PS: Methodology, Project administration, Supervision, Conceptualization, Investigation, Resources, Writing – review and editing, Writing – original draft. CS: Writing – review and editing, Software, Investigation, Writing – original draft, Visualization, Formal Analysis, Validation, Methodology. MŠ: Data curation, Software, Writing – review and editing, Methodology, Investigation, Writing – original draft. LY: Writing – review and editing, Investigation, Writing – original draft. US: Writing – original draft, Writing – review and editing, Supervision. TC: Writing – original draft, Funding acquisition, Writing – review and editing, Supervision.
Funding
The author(s) declared that financial support was received for this work and/or its publication. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. This research was supported by SC, Fusion Energy Science, FWP 100106: The LaserNetUS Initiative at Matter in Extreme Conditions, under Contract No. DE-AC02-76SF00515. We appreciate the support of HIBEF (www.hibef.eu). This research used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy User Facility using NERSC award instaplas-ERCAP∼0036515. We also appreciate the support and use of resources of the HZDR high-performance data centre. The software used in this work was developed in part by the DOE NNSA- and DOE Office of Science-supported Flash Center for Computational Science at the University of Chicago and the University of Rochester. MF, MG and CS are supported by US DOE Fusion Energy Sciences under FWP 100182. WM acknowledges support from the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-2146755. CG acknowledges funding by the consortium DAPHNE4NFDI in association with the German National Research Data Infrastructure (NFDI) e.V. – project number 4602487. LR and CG acknowledge funding by the German Federal Ministry of Research, Technology and Space (BMFTR) Project No. 05K24PSA.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The reviewer SM declared a past co-authorship with the author(s) MN and AP to the handling editor.
Generative AI statement
The author(s) declared that generative AI was used in the creation of this manuscript. Improve language and grammar as well as typesetting the equations in the appendix.
Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
1.
TabakMHammerJGlinskyMEKruerWLWilksSCWoodworthJet alIgnition and high gain with ultrapowerful lasers. Phys Plasmas (1994) 1:1626–34. 10.1063/1.870664
2.
RothMCowanTEKeyMHHatchettSPBrownCFountainWet alFast ignition by intense laser-accelerated proton beams. Phys Rev Lett (2001) 86:436–9. 10.1103/PhysRevLett.86.436
3.
RuhlHKornG. A laser-driven mixed fuel nuclear fusion micro-reactor concept (2022).
4.
GarciaALYangLBouffetierVAppelKBaehtzCHagemannJet alCylindrical compression of thin wires by irradiation with a joule-class short-pulse laser. Nat Commun (2024) 15:7896. 10.1038/s41467-024-52232-6
5.
SchroppAHoppeRMeierVPatommelJSeibothFPingYet alImaging shock waves in diamond with both high temporal and spatial resolution at an xfel. Scientific Rep (2015) 5:11089. 10.1038/srep11089
6.
GaltierELeeHJKhaghaniDBoiadjievaNMcGeheePArnottAet alX-ray microscopy and talbot imaging with the matter in extreme conditions x-ray imager at lcls. Scientific Rep (2025) 15:7588. 10.1038/s41598-025-91989-8
7.
SchoenwaelderCMarretAAssenbaumSCurryCBCunninghamEDyerGet alTime-resolved x-ray imaging of the current filamentation instability in solid density plasmas. Nat Commun (2026) 17:467. 10.1038/s41467-025-67160-2
8.
KlugeTRödelCRödelMPelkaAMcBrideEEFletcherLBet alNanometer-scale characterization of laser-driven compression, shocks, and phase transitions, by x-ray scattering using free electron lasers. Phys Plasmas (2017) 24:102709. 10.1063/1.5008289
9.
KlugeTRödelMMetzkes-NgJPelkaAGarciaALPrencipeIet alObservation of ultrafast solid-density plasma dynamics using femtosecond x-ray pulses from a free-electron laser. Phys Rev X (2018) 8:031068. 10.1103/PhysRevX.8.031068
10.
GausLBischoffLBussmannMCunninghamECurryCBEJet alProbing ultrafast laser plasma processes inside solids with resonant small-angle x-ray scattering. Phys Rev Res (2021) 3:043194. 10.1103/PhysRevResearch.3.043194
11.
KlugeTBussmannMGaltierEGlenzerSGrenzerJGuttCet alProbing shock dynamics inside micro-wire targets after high-intensity laser irradiation using small angle x-ray scattering of a free-electron laser. New J Phys (2023) 25:103036. 10.1088/1367-2630/acfab5
12.
GuinierAFournetGYudowitchKL. Small-angle scattering of x-rays (1955).
13.
GlatterOKratkyO. Small angle X-ray scattering. Academic Press Inc. Ltd. (1982). 10.1002/actp.1985.010360520
14.
FeiginLASvergunDI. Structure analysis by small-angle X-ray and neutron scattering, 1. Springer (1987).
15.
KlugeTBussmannMChungH-KGuttCHuangLGZachariasMet alNanoscale femtosecond imaging of transient hot solid density plasmas with elemental and charge state sensitivity using resonant coherent diffraction. Phys Plasmas (2016) 23:033103. 10.1063/1.4942786
16.
Author anonymous (2025). Note, that the compression surface is likely a shock front following the hole boring acceleration during the laser irradiation, not the hole-boring process itself (which would be limited only to the laser irradiation phase). For better readability we refer to it with the term hole-boring front.
17.
YangLRehwaldMKlugeTGarciaALToncianTZeilKet alDynamic convergent shock compression initiated by return current in high-intensity laser–solid interactions. Matter Radiat Extremes (2024) 9:047204. 10.1063/5.0181321
18.
YangLHerbertM-LBähtzCBouffetierVBrambrinkEDornheimTet alScaling of thin wire cylindrical compression after 100 fs joule surface heating with material. In: Diameter and laser energy (2025).
19.
FryxellBOlsonKRickerPTimmesFXZingaleMLambDQet alFlash: an adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. The Astrophysical J Suppl Ser (2000) 131:273–334. 10.1086/317361
20.
MacfarlaneJJ. Ionmix - a code for computing the equation of state and radiative properties of lte and non-lte plasmas. Computer Phys Commun (1989) 56:259–78. 10.1016/0010-4655(89)90023-4
Summary
Keywords
high power laser, ion acceleration, physics, plasma, shock formation
Citation
Kluge T, Hirsch-Passicos A, Schulz J, Czapla N, Frost M, Galtier E, Gauthier M, Grenzer J, Gutt C, Huang L, Hübner U, Ikeya M, Lee HJ, Khaghani D, Martin WM, Marré BE, Nakatsutsumi M, Ordyna P, Paschke-Bruehl F, Pelka A, Randolph L, Schlenvoigt H-P, Schoenwaelder C, Šmíd M, Yang L, Schramm U and Cowan TE (2026) Microscopy X-ray imaging enriched with small angle X-ray scattering for few nanometer resolution reveals shock waves and compression in intense short pulse laser irradiation of solids. Front. Phys. 14:1753058. doi: 10.3389/fphy.2026.1753058
Received
24 November 2025
Revised
05 February 2026
Accepted
25 February 2026
Published
30 April 2026
Volume
14 - 2026
Edited by
Dean Rusby, Lawrence Livermore National Laboratory (DOE), United States
Reviewed by
Theyencheri Narayanan, European Synchrotron Radiation Facility, France
Sergei Makarov, Joint Institute for High Temperatures (RAS), Russia
Updates
Copyright
© 2026 Kluge, Hirsch-Passicos, Schulz, Czapla, Frost, Galtier, Gauthier, Grenzer, Gutt, Huang, Hübner, Ikeya, Lee, Khaghani, Martin, Marré, Nakatsutsumi, Ordyna, Paschke-Bruehl, Pelka, Randolph, Schlenvoigt, Schoenwaelder, Šmíd, Yang, Schramm and Cowan.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Thomas Kluge, t.kluge@hzdr.de
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.