Probing ultrafast heating and ionization dynamics in solid density plasmas with time-resolved resonant X-ray absorption and emission

Domain: biology
Published: 2026-04-03
Editorial outcome: minor_revision

Abstract
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.

Introduction
Upon irradiation of a solid target by an ultra-short relativistic laser pulse, electrons within the interaction region are promptly ionized and accelerated to kinetic energies of up to several tens of MeV. The non-thermal energetic electrons then transport into the bulk of the target, initiating abundant subsequent phenomena, including the generation of resistive return currents and extreme electromagnetic fields, the growth of plasma instabilities, Bremsstrahlung and line radiation emission, as well as ion acceleration. Ultra-fast heating and ionization are among the most fundamental processes, determining the key plasma parameters such as current density, temperature, opacity and resistivity that in turn govern the electron transport dynamics [1]. Understanding the complex dynamics is crucial for advancing the applications of laser plasma-based accelerators [2], creation of high energy-density matter [3] and laser-driven fusion energy [4,5]. To date, predictive insights into the heating and ionization physics of solid-density plasmas primarily rely on large-scale numerical plasma simulations [6–9], as experimental efforts remain a major challenge due to the limited accessibility of over-critical density and the inadequate spatio-temporal resolution of conventional diagnostics. X-ray emission spectroscopy (XES) serves as a powerful diagnostic to probe the plasma temperature and density, typically through analysis of the intensity and ratios of characteristic X-ray lines at specific transition energies, such as K\alpha, K\beta, and He\alpha emissions [10–13]. Integrating an X-ray streak camera with XES enables time-resolved spectroscopy. However, its temporal resolution is currently limited to approximately 1 ps [14], which is insufficient to resolve the ultrafast dynamics occurring during the intra-laser–matter interaction phase. Monochromatic Bragg crystal imaging has also been developed to provide spatially resolved ionization maps. Yet, its spatial resolution is typically limited to scales larger than ∼10 µm [15,16].

Over the last decade, the advent of ultra-short, high-brilliance X-ray free electron lasers (XFELs) with an extremely high photon number per pulse (in the order of 10^12), ultra-short duration (tens of fs) and narrow spectral bandwidth (∼20 eV in self-amplified spontaneous emission mode or ∼1 eV in seeding mode) exhibiting nearly full transverse coherence [17], provides unprecedented opportunities to probe the transient, non-thermal, solid-density plasmas under extreme conditions driven by high-intensity optical lasers. XFELs enable visualization of plasma dynamics with temporal resolution on the order of tens of fs and spatial resolution ranging from a few nm to sub-µm scales simultaneously. Recent pioneering work at the existing large scale facilities equipped with both optical high power laser and XFEL has demonstrated the exceptional capability to observe, in detail, phenomena such as solid-density plasma expansion [18,19], kinetic instabilities [20,21], and cylindrical compression [19,22]. Experimental measurements of plasma opacity and ionization have also been proposed and carried out using resonant small-angle X-ray scattering [23,24]. Most recently, the novel experimental pump-probe platforms have been employed to investigate the heating and ionization dynamics of high intensity laser irradiated Cu foils, via X-ray transmission imaging near the Cu K-edge [25]. However, due to the stochastic nature of the XFEL beam—particularly its spatial and temporal jitter—the resulting transmission imaging maps may suffer from significant uncertainties. In this work, we explore the heating and ionization dynamics in high-power laser-driven Cu wires using time-resolved resonant X-ray emission spectroscopy, combined with simultaneous X-ray absorption imaging. Compared with the Cu foils used in the previous experiments [25], the cylindrical target geometry eases the alignment and overlap of the optical laser and XFEL on the target, as well as significantly localising heating effects of electron collisions with reduced target dimensions. Furthermore, the initial uncertainties in laser–target coupling caused by beam jitter can be quantified through measurements of the K-satellite and He\alpha emission yields, and the transmitted X-ray imaging profiles. These diagnostic advantages make the wire target particularly well-suited for maximizing the capabilities of high-energy-density (HED) facilities.

In this experiment, the XFEL photon energy was tuned to 8.2 keV to be resonant with an electron transition between two bound states of highly charged nitrogen-like Cu22+ ions generated by the high-power optical laser. When the specific charged state is populated, the XFEL photons resonantly excite a K-shell bound electron to a higher L-shell state with a corresponding increase in plasma opacity, resulting in enhanced resonant emission through de-excitation. By varying the time delay between the XFEL and optical laser driver, we observed a clear rise in the resonant X-ray emission yield—proportional to the Cu22+ ion population—that peaks at approximately ∼2.5 ps after the laser pulse maximum and decays over a timescale of up to 10 ps. Furthermore, a distinct correlation between resonant emission and attenuation of X-ray beam is observed, inferring the consistent underlying heating, ionization and recombination dynamics. Such simultaneous measurements isolate the contribution from a single charge state with sub-picosecond time resolution, enabling quantitative tracking of both the evolution of a specific ionic population and the resonant opacity at solid density. This observed correlation implies that the resonant features are confined to a small spatial scale length near the front surface, on the order of µm. To our best knowledge, no previous diagnostic has provided time-resolved access to both charge-state–selective resonant absorption and emission in a highly transient, solid-density plasma. In addition, neighboring satellite emissions in the vicinity of resonant XFEL photon energy are clearly detected. These features reflect complex atomic processes in which, besides the dominant on-resonance radiative decay, Auger decay and collisional relaxation of excited electrons can also contribute to the de-excitation following X-ray resonant pumping, thereby altering the electronic configuration and emitted spectrum. Such off-resonance emission has also been reported in previous XFEL-only studies [26]; however, it is now observed in a laser-generated hot dense plasma, where non-thermal electron populations with MeV energies can significantly modify collisional rates. Here, the off-resonance emission line intensities on both sides of the XFEL photon energy are similar, suggesting that the collisional ionization and recombination rates are comparable and within an order of magnitude of the radiative K-L transition rate. To unveil the complex dynamics, comprehensive simulations using atomic collisional-radiative, particle-in-cell (PIC) and magneto-hydrodynamics (MHD) codes were performed, incorporating both local thermodynamic equilibrium (LTE) and non-LTE (NLTE) ionization models. Comparison with experimental data highlights the sensitivity of the predictive capability of the simulation framework to the initial laser–target interaction parameters and modeling choices. Specifically, a realistic peak laser intensity, based on measured laser spatial profiles, together with appropriate preplasma conditions, is found to be essential for state-of-the-art simulations incorporating non-equilibrium collisional processes to reproduce the experimentally observed plasma heating and ionization dynamics.

Results
Experimental overview

The pump-probe experiment was performed at the HEED-HiBEF instrument located at the European XFEL using the ultra-intense optical laser ReLaX to create the solid density plasmas. ReLaX is a Ti:sapphire-based facility delivering 3 J, 30 fs pulses at a 10 Hz repetition rate [17, 27]. Based on the measured laser intensity profile, the actual focus deviates from a perfect Gaussian, with only 44% of the energy in the central focus (9% relative standard deviation) and FWHM sizes of 3.9 µm × 3.6 µm (12% and 11% relative standard deviations) in the horizontal and vertical directions. Fluctuations in laser energy and pulse duration are negligible. Combining all of these factors yields a peak intensity of 2.5×10^20 W/cm^2, with a relative standard fluctuation below 25%, upon normal-incidence irradiation of 10 µm-diameter Cu wires. The XFEL beam generated by the principle of self-amplified spontaneous emission (SASE) with the energy of ∼1.5 mJ, FWHM pulse duration of ∼25 fs, FWHM spot size of ∼10 µm and photon energy centered at 8.2 keV with a FWHM bandwidth of ∼18 eV was used to probe the solid density plasmas. The heating and ionization dynamics were investigated primarily through time-resolved resonant X-ray emission spectroscopy (RXES) in backward direction, complemented by simultaneous X-ray absorption imaging acquired via a scintillator screen coupled to an Andor Zyla CMOS camera. Spectra were recorded using a von Ha´mos spectrometer equipped with a Highly Annealed Pyrolytic Graphite (HAPG) crystal [28]. A schematic illustration of the experimental setup, along with detailed experimental conditions, is described in the Methods section and our previous publication [19].

Atomic simulation

In order to understand the mechanism of atomic processes in resonant X-ray emission, we firstly conducted simulations with the widely used atomic collisional radiative code SCFLY, which solves the rate equations governing ionization balance by accounting for various processes such as collisional ionization, radiative and three-body recombination, excitation, de-excitation, Auger ionization, and dielectronic recombination [29]. Figure 1(a) shows the calculated opacity spectra of solid-density Cu plasmas with a thickness of 10 µm, over a temperature range from 150 eV to 1 keV. A distribution of multiple satellite lines with slightly overlapping peaks can be observed. Each peak corresponds to a bound-bound transition, with its transition energy depending on the number of other electrons in L-shell and thus Cu charge state. In the case of plasma temperature at 150 eV, only doublet peaks of K\alpha1 and K\alpha2 of Cu at 8.047 keV, 8.027 keV are clearly visible. As plasma temperature increases, the average charge state of the ions rises, as shown in Fig. 1(b). This leads to a shift of the spectral peak positions toward higher photon energies, due to reduced electron screening of the nuclear Coulomb potential. Consequently, the transition energies increase, opening the possibility of using resonant X-ray absorption as a diagnostic for probing atomic processes in the plasma.

In this experiment, the XFEL photon energy was tuned to 8.2 keV, which is predominantly in resonance with the bound-bound transition of highly charged nitrogen-like Cu22+ ion in plasmas with specific charge state. The correlation between plasma temperature, charge state distribution, and opacity at this selected photon energy (E_photon = 8.2 keV) is illustrated in Fig. 1(b). When the Cu22+ ion population reaches its maximum—corresponding to a plasma temperature of approximately 500 eV—the plasma opacity also peaks, and the probability of XFEL resonance absorption is at its highest. As the solid-density plasma continues to heat beyond this point, further ionization results in charge states exceeding Cu22+. With fewer bound electrons available to support the resonant transition, both plasma opacity and XFEL absorption decrease. In the hot, dense plasmas driven by the optical laser, X-ray emission from the studied transition can occur spontaneously. When an intense XFEL with photon energy E_photon = 8.2 keV is applied, the innermost K-shell electrons are resonantly excited by X-ray photons to higher-energy L-shell states. The excited electrons then mainly decay through radiative process, leading to enhanced X-ray fluorescence yield at the resonant energy as shown in Fig. 1(c). Furthermore, enhanced neighboring emissions in the energy range beyond the XFEL bandwidth (FWHM=18 eV) on either side of the resonance are observed, suggesting that Auger decay, collisional ionization, and recombination via dielectronic and three-body processes also contribute to the total emission, in addition to the dominant on-resonance radiative decay, as also reported in previous XFEL-only studies [26]. It is important to note that the atomic simulations performed here assume uniform plasma conditions. In contrast, the solid-density plasma generated by a high-power laser is typically non-equilibrium and exhibit significant temperature and density gradients. As a result, the realistic X-ray emission spectrum is a composite of contributions from regions with varying plasma conditions, as illustrated in Fig. 2.

Diagnosis of heating and ionization dynamics

Figure 2(a) shows time-resolved X-ray resonant emission spectra from selected shots, measured at pump–probe delays from 1 ps before to 10 ps after the peak laser pulse, with 0.5 ps temporal resolution. These shots were selected based on consistently elevated He\alpha emission yields and similar transmitted X-ray imaging profiles, which indicate comparable initial laser–target coupling and XFEL probing conditions. The justification criteria for shot selection are detailed in the Methods section. The prominent K\alpha doublet lines at 8.02 and 8.04 keV and He\alpha transitions between 8.28 and 8.42 keV are observed in all the shots. These transitions have no interference with the XFEL probe, their X-ray emission is time-integrated during the entire laser-solid interaction. The similarity in both spectral shape and absolute yield of the K\alpha and He\alpha emissions lines further confirms consistent initial conditions across the selected shots. The measured number of K\alpha photons is ∼(8.0±1.5)×10^10, corresponding to a total emitted energy of ∼ 1.36 mJ assuming isotropic emission, corresponding to the conversion efficiency of ∼4.3×10^-4 relative to the ReLaX laser energy. Prior to the peak pulse arrival, the spectra show that the spontaneous X-ray fluorescence within the energy window covered by the XFEL bandwidth is weak and insufficient to surpass the self-emission background, and thus buried in the continuum radiation due to the rapid heating. After the peak intensity irradiating on the wires, a clear rise-and-fall temporal evolution of stimulated X-ray emission yield is exhibited within the XFEL bandwidth. Specifically, the resonant X-ray emission yield becomes visible at ∼0.5 ps, rapidly ascends to its maximum at ∼2.5 ps, and then decays over a timescale of up to 10 ps till it vanishes in the background. The distinct feature is imprinted to the population history of the resonant bound-bound transition of the selected highly charged Cu22+ ion, and thus is directly correlated to the dynamics of plasma heating, ionization and recombination. According to SCFLY simulations shown above, the measured temporal evolution of the resonant emission suggests that the temperature within the solid-density plasma remains above 500 eV for up to 10 ps. It is worth noting that the same physical principle has been successfully applied to generate highly coherent, attosecond-duration atomic X-ray lasers, where atoms are heated and pumped by intense XFEL pulses [30–32].

Figure 2(b) shows the time-resolved resonant X-ray emission yield alongside the corresponding XFEL transmission. A clear inverse correlation between the two is observed, as further presented in Fig. 2(c), indicating consistent underlying processes of plasma heating, ionization, and recombination. The observed correlation between the resonant X-ray emission yield and the XFEL absorption in Fig. 2(c) indicates the small scale length of the resonant features, as otherwise absorption becomes saturated, while backward resonant emission yield is dominated by the first absorption length thickness. In this way having both resonant backscatter (sensitive to the x-ray absorption depth) and transmission (bulk) are complementary diagnostics yielding additional information from their combination. For the resonant charge state corresponding to peak absorption at the XFEL photon energy, the effective absorption length is on the order of one micrometer, O(µm). This implies that, for linear proportionality, the projected thickness must be smaller than this value, indicating that the ionization is highly localized near the front surface, rather than producing a uniform charge state. Furthermore, although the features are smaller than the XFEL focal size, variations in direct beam overlap due to beam jitter introduce only minor fluctuations in the total absorption signal. Forward X-ray propagation simulations show that the absorption variation is less than 0.1 assuming ±5 µm jitter, which is consistent with the experimental data shown in Fig. 2(b) at negative delays. Consequently, changes in the resonant absorption remain clearly distinguishable when the effects of beam jitter are taken into account. Thus, while resonant emission serves as an ionization diagnostic and is extensible to thicker or layered targets containing a suitable resonance due to its spectral sensitivity, the observed correlation in resonant absorption can be used here to infer an approximate scale length even without direct imaging.

In particular, in the case of strongest XFEL stimulation at 2.5 ps, the resonant X-ray yield reaches maxima at 2.27×10^10 photons/sr, that corresponds to (0.37±0.02) mJ over the full 4π solid angle. It is ∼ (47±3)% of the XFEL pulse energy measured with ∼ 0.787 mJ. For comparison, the attenuation length of cold solid Cu at the photon energy of 8.2 keV is 22.73 µm according to the Henke Tables [33]. For an XFEL beam with a ∼ 10 µm field of view (FoV) centered on the 10 µm-diameter cold Cu wire, the total XFEL absorption is calculated to be 22%. This is equivalent to ∼ 46% of the absorption measured in the hot dense plasma at 2.5 ps, consistent with the increased attenuation observed in the resonant case and the opacity predictions shown in Fig. 1, as well as the correlations shown in Fig. 2(b). Since the radiative decay rate is proportional to the ion number density [29], the measured resonant emission yield directly reflects the population of the selected Cu22+ ion, and thus ionization and recombination evolution. It is worth noting that the duration of the resonant X-ray emission lasts significantly longer in the Cu wires, as observed in an ongoing study, where the emission decays completely at approximately 3 ps. The slower evolution and enhanced emission observed in wires is attributed to lower heat dissipation caused by stronger refluxing and reduced spatial spreading of the surface-confined hot electrons [34].

In the hot, dense plasma state created by the optical relativistic laser pulse, the electronic configurations of Cu ions with K-shell vacancies—pumped by resonant XFEL radiation—can become highly complex. Each spectrum peak shown in Fig. 2(a) is contributed by an average of many different configurations of Cu ions with different statistical weights and slightly different K-L transition energies. In particular, the resonantly excited L-shell electrons could be relaxed by the channels of radiation decay, Auger decay or collisions. The first case will result in the resonant emission at the same wavelength as the incident XFEL beam, while the other two channels will re-distribute the electronic configuration and thus will result in the K-satellite emission of neighboring states, as discussed in Fig. 1(c). To analyze these features, the experimental spectra were fitted by a set of 14 gaussian functions, corresponding to the distribution of each individual satellite emission between K\alpha and He\alpha. The central energy of the gaussian functions, except the resonant photon energy with XFEL, are fixed as inferred from the SCFLY atomic simulations shown in Fig. 1(a) and the XFEL-only heating experimental data in well-defined conditions [35], namely, 8.027 keV, 8.047 keV, 8.055 keV, 8.08 keV, 8.12 keV, 8.16 keV, ∼8.2 keV, 8.255 keV, 8.3 keV, 8.322 keV, 8.335 keV, 8.352 keV, 8.372 keV and 8.395 keV, labeled with line indices from 0 to 13, respectively. Each index identifies a specific bound-bound transition associated with emission at a characteristic energy. Fig. 3(a) shows an example of fitted spectrum at 2.5 ps delay, corresponding to the peak of resonant emission yield. To mitigate the uncertainties of initial laser-wire coupling conditions, the intensity of each fitted line is furthermore normalized to the mean value of the shots with negative delays, that are analogous to the laser-only shots since the resonant channel is not opened yet as already seen in Fig. 2(a). Figure 3(b) shows the normalized line intensity of the fitted spectra at different delays. A prominent line (line 6) at approximately 8.2 keV is clearly observed, attributed to dominant on-resonance radiative decay. In addition, off-resonance lines on either side—at 8.16 keV (line 5) and 8.255 keV (line 7)—within an energy window of roughly 100 eV, are simultaneously pumped by the XFEL field, while the evolution of other lines is not distinct. Since the FWHM bandwidth of XFEL beam is only ∼18 eV which is not broaden enough to drive the neighboring satellites, the off-resonance emissions are attributed to the Auger decay, collisional ionization (increasing the charge state), as well as recombination (decreasing the charge state) through dielectronic and three-body processes, which modify the L-shell electron occupancy between resonant excitation and subsequent emission. The ratios of line intensities can therefore be used to measure collisional rates (ionization and recombination) relative to the radiative rate. Here, the off-resonance emission line intensities on both sides of the XFEL photon energy are similar, suggesting comparable ionization and recombination rates, though they are a few times lower than the radiative decay rate. The observed neighboring satellite emissions near the resonant XFEL photon energy is consistent with the SCRFLY simulations shown in Fig. 1(c). A similar feature was reported in an ultra thin warm dense plasma (∼54 nm) isochorically heated by XFEL pulses [26]. In this work, such on- and off-resonance feature is observed in a laser-generated hot dense plasma (∼ 10 µm thick) exhibiting steep temperature and density gradients, where non thermal electron populations with MeV energies can strongly alter collisional rates. In conjunction with time-resolved spectroscopic measurements, X-ray absorption imaging can be further used to probe the spatial distribution of ionization within plasmas, as recently demonstrated in short-pulse laser-driven warm/hot dense matter experiments [25].

Kinetic and MHD simulations

To further reveal the ultrafast heating and ionization dynamics, two-dimensional (2D) PIC and MHD simulations were performed under realistic laser and target conditions. The PIC simulations employ both a LTE-based pressure ionization model and a NLTE-based impact ionization model implemented within the PICLS code [36]. It is noticed that the LTE model implicitly accounts for recombination via a empirical Thomas–Fermi equation of state (EOS) that constrains the cell-averaged ion charge, while the NLTE model uses a probabilistic Monte Carlo approach to compute the impact ionization rate but neglects recombination. The treatment of the ionization models in the code is detailed in previous theoretical work [8, 37]. Additionally, plasma heating is modeled using a relativistic binary collision operator [36] in all the cases. The PIC simulations summarized in Fig. 4 were performed with a lower-bound peak intensity within the standard deviation based on the measured spatial laser profiles, i.e., 1.875×10^20 W/cm^2, that accounts for the non-negligible fraction of energy distributed outside the central focus region. Additionally, the simulations employed a preplasma profile predicted by MHD simulations using the FLASH code with the IONMIX equation-of-state (EOS) library [38], which shows good agreement with experimental measurements obtained via nanometer-sensitive small-angle X-ray scattering (SAXS) diagnostics in our recent work [19]. Details of the simulation setup are provided in the Methods section. Firstly, we examine the comparison of plasma temperature and ionization for the LTE and NLTE ionization models using a circular geometry that represents a top-down view of a wire target at 0.1 ps shown in Fig. 4(a) and (b). In both cases, the front surface temperature at the interaction point is heated up to ∼ 3 keV and experiences a rapid decline within the target. In the bulk, although the NLTE model predicts temperatures that are a few hundred eV higher, the resulting ionization depth for the highly ionized resonant charge state Cu22+ is much smaller—about 2 µm compared with 5 µm in the LTE model. The lower ionization is consistent with the higher temperature observed in NLTE case, since less thermal energy is extracted from the bulk plasma for ionization than in the LTE case. High-intensity, ultrafast laser–generated solid-density plasmas often deviate from LTE conditions characterized by a Maxwellian particle energy distribution. The NLTE ionization model is more accurate in this regime, as it accounts for arbitrary electron energy distributions, including relativistic tails. As shown in Fig. 4(f), the NLTE ionization model provides a closer match to the experimental data, which reveals localized surface ionization as discussed in Fig. 2. These comparisons demonstrate the critical role of non-equilibrium collisional processes in improving the predictive capability of the simulations. Furthermore, we conducted additional 2D PIC simulations employing the NLTE ionization model in a planar configuration, depicting the side view of the wire target as plotted in Fig. 4(c). It is evident that both the surface and in-depth heating and ionization levels caused by the electron transport are notably reduced in comparison to the previous circular scenarios. This reduction occurs because the hot electrons spread laterally along the planar target surface nearly at the speed of light, being primarily constrained by the longitudinal sheath fields. In contrast, within the context of a mass-limited circular geometry, the hot electrons are effectively confined or reflected by strong sheath fields encompassing its entire surface. In this case, the ionization depth for the resonant charge state Cu22+ is further reduced to ∼1.5 µm, in excellent agreement with the experimentally measured effective absorption length discussed earlier. Limited by computational power, we are only able to run the PIC simulations with realistic solid density up to 100 fs when the laser intensity drops far below the relativistic intensity. To extend the temporal analysis, we have run a MHD simulation using the PIC predicted distributions of electron and ion temperatures to model the plasma adiabatic cooling through the hydrodynamic expansion and thermal equilibration. As shown in Fig. 4(d), 2.5 ps after the laser–solid interaction the surface electron temperature decreases to ∼ 1 keV, and the region corresponding to the resonant charge state Cu22+ extends to a depth of ∼ 2.5 µm. This region remains localized near the surface and is therefore in satisfactory agreement with the measurements, although the MHD simulations implicitly assume equilibrium conditions. It is noted that, in order to best reproduce the key experimentally measured parameters—such as the heating and ionization depth—it is essential to account for the realistic peak laser intensity based on the measured spatial laser profile, as well as an appropriate preplasma profile. These are the most critical initial conditions for the PIC simulations in constraining the basic plasma parameters and are discussed in detail in the Methods section “Effect of Peak Laser Intensity and Preplasma Profile”.

Methods
X-ray setup and parameters

The online calibrated HIgh REsolution hard X-ray single-shot (HIREX) spectrometer installed in the photon tunnel of the SASE2 undulator beamline was used to monitor the SASE spectrum [43] that ensured the central X-ray photon energy fixed at 8.2 keV during the entire beam time. Fitting the measured X-ray spectrum with a Gaussian function gives the FWHM bandwidth of ∼18 eV. The photon energy was cross checked by the elastic X-ray scattering signal on the test Cu samples measured by the von Ha´mos X-ray spectrometer inside the interaction chamber [28]. The X-ray pulse energy was measured via an X-ray gas monitor (XGM) located in the photon tunnel and an intensity and position monitor (IPM) installed at the HED instrument [44]. The XFEL beam was focused on the sample to a spot size with a full width at half maximum (FWHM) of ∼ 10 µm, using the compound refractive lens (CRL) configuration comprising arms 3, 6, and 10 of CRL3, located in the HED optics hut chat a distance of ∼962 m from the source and ∼9 m to the target chamber center (interaction point) [17]. The XFEL spot size was characterized by the edge scan of the test samples via X-ray transmission using Zyla detector located at 6.31 m downstream to the target chamber center.

ReLaX optical laser setup and parameters

The ReLaX optical laser is a 3 J, 30 fs, 10 Hz Ti:sapphire based system, irradiating the Cu wires at normal incidence. The laser intensity profile measured by a 20× APO PLAN microscope objective, showed that only a fraction of the total energy was contained in the central focal spot, deviating from a perfect Gaussian profile, as shown in Fig. 5. A statistical analysis of 618 ReLaX pulses yielded mean FWHM focal sizes of 3.9 µm (horizontal) and 3.6 µm (vertical), with relative standard deviations of 12% and 11%, respectively. The fraction of energy within the central focus was 0.44, with a relative standard deviation of 9%. Fluctuations in laser energy and pulse duration were negligible compared to other sources. Accounting for all these factors, the peak intensity was estimated to be 2.5×10^20 W/cm^2, with a relative standard fluctuation below 25%, corresponding to a range of (1.875–3.125)×10^20 W/cm^2. The temporal contrast of pulse intensity was measured by the offline diagnostics package consisting of single-shot temporal pulse diagnostics (SHG cross-correlator, a WIZZLER 800 for the spectrally resolved phase and intensity), a scanning third-order intensity autocorrelator (Sequoia HD) and a spatial phase sensor (SID4) in combination with full beam adaptive deformable mirror, see our earlier work [19]. It is noted that the microscope objective was used only to generate a magnified image of the focal spot for focus-quality characterization during alignment. Because the objective was positioned downstream of the target chamber center (TCC), any dispersion it introduced would not affect the laser–matter interaction. Moreover, it was retracted during high-energy shots to prevent damage to the optics. Therefore, the microscope objective did not alter the laser pulse duration or the intensity on target.

Synchronization between optical and X-ray lasers

The timing and synchronization between optical and X-ray laser were measured by the optical encoding spatial photon arrival monitor (PAM) [45]. The measurable timing window by the PAM is within 200 fs, that gives the up limit of the uncertainty of XFEL probe time delay relative to the ReLaX laser presented in this work.

Bremsstrahlung and self-emission background subtraction of RXES data

The approach of removing the Bremsstrahlung background subtraction of RXES data has three steps. First, we fit the off-axis background for each pixel coordinate along the dispersive direction. Then we use the fit and construct an on-axis background including error. At last, the background is subtracted under the condition that the result is strictly non-negative (marginalising over the error). The error on the spectrum is a combination of Poisson observation error, dark image root-mean-square (including multiple gain stages) and background correction error. Finally, to obtain the net resonant X-ray yield, the self-emission around 8.2 keV is subtracted by fitting the Bremsstrahlung-subtracted emission yield to the He\alpha yield from shots with negative delays, which are analogous to the laser-only shots.

Justification criteria of of high-quality shots

To minimize the initial uncertainties in the coupling conditions among the optical laser, XFEL beam, and wire target, we analyzed the statistical distributions of K\alpha and He\alpha emission yields, the XFEL transmission spatial profiles, and the total transmitted intensity for justification of high-quality (“good”) shots. It is noted that here the He\alpha is defined as the 2p→1s transitions in Cu26+ and Cu27+ ranging from 8.28 to 8.42 keV. The K\alpha emission yield is found to be saturated, being limited by laser absorption and the resulting hot electron population as seen in Fig. 6. In contrast, the He\alpha yield serves as a more reliable indicator of plasma heating. Based on these statistics, high-quality ReLaX shots were selected by applying a threshold: He\alpha emission yields greater than 0.7×10^10 photons per steradian. These selected good shots were further filtered by requiring a total XFEL transmission below 0.9, suggesting good spatial overlap between the XFEL and the target. This overlap is also confirmed by examining the corresponding XFEL spatial profiles as seen in Fig. 7. The streaks observed in the good shots result from X-ray scattering at the edges of the wires. In contrast, when the XFEL transmission exceeds 0.9, the edge-scattering streaks are no longer apparent, indicating that the XFEL beam likely only partially hit the wires.

PIC simulations

In this work, all the 2D3V PIC simulations are performed with PICLS code [36], employing the realistic laser and target parameters as used in the ReLaX laser pump-XFEL probe experiment. To quantify the impact of the laser parameters on the PIC simulations, the p-polarized laser pulse with the laser wavelength λ = 0.8 µm and peak intensities ranging from 1.875×10^20 W/cm^2 to 5×10^20 W/cm^2, is modeled using Gaussian profiles in both space and time with full width at half maximum (FWHM) spot size w_FWHM = 4 µm and duration τ_FWHM = 30 fs respectively. The laser irradiates the solid copper (Cu) wire target of 10 µm diameter at normal incidence. In order to take account the effect of leading edge of ReLaX laser pulse, the density profile of preplasma predicted by the MHD simulations is added to the front surface of the Cu target. The mass density of Cu target is 8.96 g/cm^3, corresponding to the number density of Cu ions being 48.27 n_c, where n_c = 1.74×10^21 cm^-3 is the plasma critical density. The cell size Δx = Δy = 5.3 nm and time step Δt = 0.0178 fs are set to resolve the plasma wavelength (21.4 nm) and frequency (0.071 fs) in fully ionized case that the free electron density reaches 1400 n_c. The simulation box consists of N_x × N_y = 7500 × 5000, corresponding to the real space size 40 µm × 27 µm. The axes x and y represent the directions of laser propagation and polarization respectively. The initial charge state of Cu ions is 1+ and the computational Cu1+ ion number per cell is 5, corresponding to 145 electrons per cell for fully ionized case. The choice of fine cell size, time step and particle numbers ensures the elimination of numerical heating in our simulations. All the PIC simulations use the absorbing boundary and start with an initially cold neutral plasma. The collision ionization is treated either by the LTE based Thomas-Fermi pressure ionization model or NLTE based direct impact ionization model [8]. The field ionization and plasma heating is treated by the Landau-Lifshitz field ionization and the relativistic binary collisional operator respectively [36]. The large scale simulations using the realistic plasma density including both ionization and collision processes require huge computational resources to illuminate the numerical heating. Due to limited computational resources, the PIC simulations were performed up to 100 fs after the peak laser intensity reached the front surface of the target.

MHD simulations

To assess the sensitivity of the predictive capability to the choice of equation-of-state (EOS) library, MHD simulations using the FLASH code [38] with the SESAME [46] and IONMIX [47] EOS are performed to simulate the preplasma formation driven by the rising slope of the ReLaX laser pulse ranging from -80 ps to -1 ps prior to the arrival of the peak ReLaX laser pulse, corresponding to the laser intensity rising from ∼10^12 W/cm^2 to ∼10^16 W/cm^2. Figure 8 compares the spatial density profiles of preplasmas obtained using the SESAME and IONMIX EOS respectively. Up to 1 ps before the arrival of the peak laser intensity, the preplasma density exhibits a short scale length near the initial solid target surface, extending into a much lower-density region with a longer scale length in both cases. While the scale lengths in the very low-density region are comparable, the near-surface scale length is slightly larger for IONMIX (∼100 nm) than for SESAME (∼60 nm). The predicted density profile is used as the input to the kinetic PIC simulations during the main pulse solid interactions. Then the PIC predicted spatial distribution of the plasma electron and ion temperatures at 100 fs are coupled to the FLASH MHD simulation to investigate the late time hydrodynamic compression and expansion driven by the shock waves from direct laser ablation and transient surface return current up to 150 ps after the laser matter interactions. The adaptive mesh size and time step are set to satisfy the Courant–Friedrichs–Lewy (CFL) conditions to ensure the convergence of the simulations. The combination of kinetic and MHD simulations enables us to explore the complex dynamics of electron transport during the entire relativistic laser solid wire interactions.

Effect of peak laser intensity and preplasma profile

At present, predictive understanding of the complex dynamics in ultra-short, relativistic laser–solid interactions relies primarily on PIC simulations. However, for comparison with experimental data, PIC simulations have typically assumed a peak laser intensity corresponding to the full laser energy contained within an ideal Gaussian focus, together with a preplasma described by a simple exponential density profile [21]. As we discuss below, these simplified initial conditions can lead to significant discrepancies between simulated and measured plasma heating and ionization dynamics. Figure 9 shows how variations in the peak laser intensity and preplasma profile strongly affect the predictive capability of the PIC simulations. In the case of a MHD-simulated preplasma density profile with the SESAME EOS and a peak laser intensity of 5×10^20 W/cm^2, assuming that the full ReLaX energy is contained within ideal Gaussian profiles in both space and time, the front surface temperature at the interaction point rises to ∼ 12 keV and decreases to above 1 keV near the rear surface of the target. It results in the nearly full strip of L-shell electrons of Cu ions near the target surface and 5 ∼ 7 µm in-depth ionization for the resonant charge state. This significantly overestimates plasma heating and ionization—most significantly at the surface, but also at depth, compared with the experimental observations. In contrast, using a more realistic peak intensity in the central focus, 1.875×10^20 W/cm^2, which corresponds to the lower-bound peak intensity accounting for the non-negligible fraction of energy distributed outside the central region, the surface temperature is reduced to ∼ 5 keV and declines rapidly to ∼ 1.5 keV within a depth of 1.5 µm. From the measured X-ray emission spectrum, no Ly\alpha lines are observed, indicating that the temperature in the solid region should remain below 1.5 keV based on SCFLY atomic simulations. Therefore, even with the corrected peak intensity, the simulation still overestimates the heating. By further adjusting the preplasma density profile based on the MHD simulations using the IONMIX EOS, the surface temperature is reduced to ∼ 2.5 keV, falls to ∼ 1.5 keV within a depth of 0.2 µm, and decreases below 1 keV throughout the target bulk. Correspondingly, the predicted resonant charge-state of interest is populated near the surface, consistent with the resonant emission and absorption imaging of highly charged Cu ions observed in the experiment, which reveals localized surface heating confined to the laser spot size. Even when the peak laser intensity is increased to the measured upper bound of 3.125×10^20 W/cm^2 within the standard deviation, the simulated resonant charge state remains predominantly confined near the surface, extending only to ∼ 2 µm into the target, still agrees with the experimentally inferred localization. Thus, the systematic simulations and adjustments clearly show that the realistic peak laser intensity and the preplasma density profile constitute the most critical initial conditions for reliably predicting the plasma heating and ionization dynamics observed experimentally.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript reports an experimental investigation of the spatiotemporal evolution of the temperature and ionization state in intense laser–irradiated copper wire targets. These quantities underlie key plasma properties — temperature, density, resistivity, and opacity — that are central to both fundamental high-energy-density physics and a wide range of applications. The topic is timely and relevant. Laser-driven plasmas remain exceptionally challenging to characterize because they feature rapidly evolving, strongly nonequilibrium conditions, steep gradients, and relativistic electron populations. Extracting reliable, time-dependent information on atomic excitation, ionization, and relaxation in such regimes is particularly difficult and remains a bottleneck for validating theory and simulation. The authors present simultaneous time-resolved resonant X-ray emission spectroscopy and X-ray absorption imaging of Cu wires, employing a coherent XFEL probe tuned to the 1s → 2p resonance of highly ionized copper ions. The methodology is appropriate and represents an ambitious coupling of laser-driven plasma generation with XFEL-based pump–probe diagnostics. By scanning the delay between the infrared drive laser and the XFEL (8.2 keV), the authors track the resonant emission from Cu^22+, observing a ∼10 ps rise-and-fall behavior, peaking near 2.5 ps, in inverse correlation with the X-ray transmission. From these data, they infer the temporal evolution of the population in this charge state, and relate it to the evolution of the plasma temperature and opacity. The observation of off-resonant line emission arising from Auger and collisional relaxation is noteworthy. Although similar signatures have been reported in XFEL-only experiments, their appearance in a laser-driven, highly inhomogeneous plasma with a non-thermal electron distribution (including a relativistic tail) is challenging to interpret. The comparable intensities of non-resonant features on both sides of the XFEL photon energy suggest a balance between ionization and recombination processes. The modeling framework is extensive: MHD simulations to characterize the pre-plasma; PIC simulations with collisional–radiative atomic physics to describe the laser interaction, ionization dynamics, relativistic electron transport, and isochoric heating; and subsequent MHD modeling of the hydrodynamic evolution. This multi-stage approach is ambitious, but also introduces significant sources of uncertainty. The PIC simulations that incorporate nonequilibrium collisional processes produce ionization-state predictions closer to experiment than LTE-based models, but still systematically overestimate plasma heating—most significantly at the surface, but also at depth. This mismatch points to limitations either in the assumed pre-plasma conditions, the treatment of non-thermal electrons, or the collisional–radiative rates under warm-dense-matter conditions. The manuscript would benefit from a more explicit discussion of these uncertainties, including their potential impact on the inferred charge-state distributions. The need for improved characterization of the laser temporal contrast is clear, as it would enable more realistic modeling of pre-plasma density gradients and thereby reduce uncertainty in the PIC–MHD chain. Similarly, advances in non-LTE collisional–radiative modeling in the warm dense matter regime remain necessary for truly quantitative comparison. Despite these limitations, the study presents a meaningful advance relative to the existing literature. Its key strengths include: i) The use of XFEL radiation simultaneously as a pump and probe, achieving sub-picosecond temporal and sub-micrometer spatial resolution; ii) The generation and diagnosis of warm dense matter under relativistic-laser conditions coupled to an XFEL environment; iii) The use of thin cylindrical targets, which effectively mitigate uncertainties from XFEL spatial and temporal jitter. Finally, the longer (∼10 ps) and stronger resonant emission observed in Cu wires, compared to previously studied Cu foils, is a valuable result. It highlights enhanced laser-energy coupling due to reduced target mass and mitigated hot-electron divergence, and further validates the experimental design. In summary, while certain aspects of the modeling and interpretation require refinement and clearer quantitative justification, the experimental approach is innovative and the results are both original and scientifically relevant. Overall, the manuscript constitutes a significant and publishable contribution to the field of high-energy-density physics, and it is suitable for publication after minor revision.", "reviewer_2": "This study reports on time-resolved plasma temperature diagnostics using an XFEL. The use of resonant absorption measurements is highly novel, and the selection of high-quality data yields clean and reliable results. The manuscript is well written and easy to follow. However, the experimental results themselves are quite basic and largely as expected, lacking impact or surprise. Therefore, I do not recommend this manuscript for publication in Nature Communications. My specific comments are as follows: 1. The physical implications of these experimental results for the field should be carefully discussed. In particular, if the simulations do not reproduce the measurements, the reasons for the discrepancies should be quantitatively analyzed. 2. The authors state that the 2D-PIC results do not agree with the experiment. However, they should present the spatially weighted X-ray spectrum or transmission calculated from the simulation and compare it directly with the experimental data. 3. The correlation between the resonant X-ray emission yield and the XFEL transmission shown in Fig. 2(c) requires a clear physical discussion, ideally supported by comparison with theoretical or simulation results. 4. The distinction between the present diagnostic method and those in previous studies is weak. The authors should quantitatively describe the advantages of their approach compared with existing techniques. 5. The manuscript mentions that a microscope objective was used in the final optical system. Has it been verified that the pulse duration was not stretched due to geometric path length differences or group-velocity dispersion (GVD)? Such stretching could significantly alter the laser intensity. 6. Figure 2 in the Methods section is not referenced anywhere in the main text. In addition, the spatial scale should be indicated on the image."}, "author_response": "We sincerely acknowledge the referee for their careful review of our manuscript and for the positive feedback that our experimental approach is innovative, the results are both original and scientifically relevant, and the work constitutes a significant and publishable contribution to the field of high-energy-density physics. We also thank the referee for their constructive comments, noting that certain aspects of the modeling and interpretation require refinement and clearer quantitative justification. To minimize uncertainties in the multi-stage modeling framework, we examined the experimentally measured spatial profiles of ReLaX laser intensity and re-performed MHD simulations with different equation of state (EOS) libraries to characterize the preplasma, which served as input for the subsequent hybrid PIC-MHD simulation chain. We found that the 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, and preplasma conditions, and NLTE collisional processes. Firstly, we examined the experimentally measured spatial profiles of ReLaX laser intensity and found that only a fraction of the laser energy is contained in the measured central focal spot, as shown in Fig.1. In the original manuscript, the simulations used a peak intensity of 5e20W/cm^2, assuming a Gaussian ReLaX laser profile in the transverse plane and in time, with a 4 µm FWHM spot size and a 30 fs FWHM pulse duration, respectively. However, the actual laser focus deviates from a perfect Gaussian profile, with a non-negligible fraction of the energy distributed outside the central region, as shown in Fig. 1. A statistical analysis of 618 ReLaX pulses shows mean FWHM focal sizes of 3.9 µm (horizontal) and 3.6 µm (vertical), with relative standard deviations of 12% and 11%, respectively. The fraction of energy contained within the central focus is 0.44, with a relative standard deviation of 9%. Fluctuations in laser energy and pulse duration are very low and thus negligible compared to other sources. Combining all of these factors results in a reduction of the peak intensity by a factor of 2 relative to the value used in the original manuscript, yielding 2.5e20W/cm^2, with a relative standard fluctuation of less than 25%. Figure 1: (a) A typical example of the spatial intensity profile of ReLaX laser beam. Panels (b) and (c) show the shot-to-shot statistical fluctuations of the FWHM size and the energy fraction within the central focus, respectively. Secondly, in addition to the MHD simulations using the SESAME equation of state (EOS) [SESAME1994] presented in the original manuscript, we re-ran the MHD simulations using the IONMIX EOS [IONMIX1989] to characterize the preplasma density profile generated by the intrinsic laser rising edge or prepulse, and to assess the sensitivity of the results to the choice of EOS. Figure 2 compares the spatial density profiles of preplasmas obtained using the SESAME and IONMIX EOS. Up to 1 ps before the arrival of the peak laser intensity, the preplasma density exhibits a short scale length near the initial solid target surface, extending into a much lower-density region with a longer scale length in both cases. While the scale lengths in the very low-density region are comparable, the near-surface scale length is slightly larger for IONMIX (~100 nm) than for SESAME (~60 nm), which plays a crucial role in laser absorption at the arrival of the peak laser intensity. Using the nanometer-sensitive small-angle X-ray scattering (SAXS) diagnostic, our recent work demonstrates that the MHD-predicted preplasma density profile from IONMIX agrees better with the experimental SAXS measurements [Huang2026], providing strong validation for the choice of IONMIX EOS in the simulations. Figure 2: Comparison of the spatial preplasma density profiles obtained using the SESAME and IONMIX EOS up to 1 ps before the arrival of the peak laser intensity. Based on a detailed assessment of the PIC simulation initial conditions, we re-performed hybrid MHD–PIC simulations using the lower-bound peak laser intensity in the central focus (2.5e20W/cm^2*0.75 = 1.875e20W/cm^2) and varied preplasma density profiles, comparing the results to those in the original manuscript in the side view of a wire target (flat geometry). As shown in Fig. 3, the simulation using a peak intensity of 5e20W/cm^2 overestimates the plasma heating and ionization—most significantly at the surface, but also at depth. In contrast, when using the more realistic peak intensity in the central focus, 1.875e20W/cm^2, the surface temperature is reduced from ~12 keV to ~5 keV and falls to ~1.5 keV within a depth of 1.5 µm. From the measured X-ray emission spectrum, no Ly lines are observed, indicating that the temperature in the solid region α should remain below 1.5 keV based on SCFLY atomic simulations. Therefore, even with the corrected peak intensity, the simulation still overestimates the heating. By further adjusting the preplasma density profile using the MHD prediction with the IONMIX EOS (instead of the SESAME EOS), the surface temperature is reduced to ~2.5 keV, drops to ~1.5 keV within a depth of 0.2 µm, and then decreases below 1 keV in the target bulk. Correspondingly, the resonant charge-state of interest is populated near the surface, consistent with the measured resonant X-ray emission yield and the XFEL absorption which reveal the small scale length of the resonant feature and localized surface heating confined to the laser spot size. Even when the peak laser intensity is increased to the measured upper bound of 3.125e20 W/cm^2 within the standard deviation, the simulated resonant charge state remains predominantly confined near the surface, extending only to ∼ 2 μm into the target, and remains in satisfactory agreement with the measurement. In conclusion, we examined the experimentally measured spatial profiles of the ReLaX laser intensity and re-performed the MHD simulations using different EOS libraries to obtain more accurate preplasma conditions for the hybrid PIC–MHD simulation chain. This systematic adjustment shows that the realistic peak laser intensity and the preplasma density profile constitute the most critical initial conditions for reliably predicting the plasma heating and ionization dynamics observed experimentally. Figure 3: Longitudinal lineouts of (a) the plasma temperature and (b) the average ion charge state for the side view of a wire target (flat geometry), with the initial solid target region indicated by the light green background. In the revised manuscript, we have added Fig. 1 and Fig. 2 to the subsections “ReLaX optical laser setup and parameters” and “MHD simulations” within the METHODS section. In addition, we have introduced a new subsection, “Effect of initial laser and target conditions on the plasma heating and ionization,” which includes Fig. 3. This new subsection highlights how the choice of initial conditions critically influences the simulation results and, consequently, the quantitative comparison with the experimental data. Furthermore, the hybrid PIC–MHD results shown in Fig. 4 of the original manuscript have been updated with new simulations incorporating the corrected peak laser intensity and preplasma density profile, showing good consistency with the experimental measurements. The updated simulation results are also presented below. In conclusion, we found that the 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, and preplasma conditions, and NLTE collisional processes. Correspondingly, we have substantially revised the discussion of the simulation results and their comparison with the experimental data in the main text. In addition, we have included further simulations that systematically scan the initial interaction conditions, including the laser peak intensity and preplasma density profiles, in the METHODS section of the Appendix. All changes in the manuscript are highlighted in red. Figure 4: Updated hybrid PIC-MHD simulations with corrected peak laser intensity and the preplasma density profile. Spatial distribution of electron temperature and ion charge state obtained from 2D PIC simulations in the case of top view of a Cu wire with 10 µm thickness, using (a) the LTE based Thomas-Fermi and (b) the NLTE based direct impact ionization models, both at 100 fs after peak laser intensity irradiation. Corresponding 2D PIC and MHD simulations for the side view of the Cu wire using the NLTE ionization model are shown at (c) 100 fs and (d) 2.5 ps, respectively. Longitudinal lineouts of the plasma temperature (e) and average ion charge state (f) of the corresponding 2D simulation maps, extracted from the initial target region indicated by the light green area. The green regions indicate the probed resonant charge sate and its corresponding evaluated plasma temperature. [SESAME1994] J. Johnson, “The sesame database,” Tech. Rep. (1994) [IONMIX1989] J.J. Macfarlane, Computer Physics Communications56, 259 (1989) [Huang2026] L. Huang, et al., Matter and Radiation at Extremes 11, 017201 (2026) Response to Reviewer #2 Reviewer #2 (Remarks to the Author): This study reports on time-resolved plasma temperature diagnostics using an XFEL. The use of resonant absorption measurements is highly novel, and the selection of high-quality data yields clean and reliable results. The manuscript is well written and easy to follow. However, the experimental results themselves are quite basic and largely as expected, lacking impact or surprise. Therefore, I do not recommend this manuscript for publication in Nature Communications. Our response: High-quality, time resolved data on charge state populations in laser produced plasmas are valuable input to benchmark simulation data, and we thank the reviewer for identifying the work that has gone into producing these novel and high-quality data, yielding clean and reliable results. We agree that the essential result of observing resonance peaking with time was expected, as its measurement was the primary goal of the experiment. However, as demonstrated by the complex modeling presented in the revised manuscript, making precise quantitative predictions of this behavior is extremely challenging. Therefore, though qualitatively expected, the novel and high-quality data is critically important for precise understanding of the physics of extreme states of matter. The detailed simulation framework needed to approximately reproduce experimental data, and their sensitivity to the ionization models and input parameters, such as the realistic peak laser intensity and preplasma profile presented in the revised manuscript – highlight that these experimental results cannot be viewed as “expected, lacking impact or surprise”. As noticed by Reviewer #1 “Extracting reliable, time-dependent information on atomic excitation, ionization, and relaxation in such regimes is particularly difficult and remains a bottleneck for validating theory and simulation,” and we therefore believe our revised manuscript (all changes in the manuscript are highlighted in red), together with the newly performed extensive and detailed comparisons against state-of-the-art simulation capabilities directly refutes this claim – highlighting deficiencies in current modelling capabilities in extreme conditions, and how overreliance on these can result in order of magnitude errors in basic quantities such as temperature , as detailed in our response below. My specific comments are as follows: 1. The physical implications of these experimental results for the field should be carefully discussed. In particular, if the simulations do not reproduce the measurements, the reasons for the discrepancies should be quantitatively analyzed. Our response 1: We fully agree with it. We have examined the experimentally measured spatial profiles of the ReLaX laser intensity and re-performed the MHD simulations using different EOS libraries to characterize the preplasma, which further served as input for the subsequent hybrid PIC-MHD simulation chain. With additional extensive PIC and MHD simulations, we found that the realistic peak laser intensity based on measured particular laser spatial profiles and appropriate preplasma density profiles are the most critical initial conditions for the simulations to correctly predict the plasma heating and ionization dynamics observed experimentally. Further details and updated simulation results are included in our response to Reviewer #1, who raised similar comments. 2. The authors state that the 2D-PIC results do not agree with the experiment. However, they should present the spatially weighted X-ray spectrum or transmission calculated from the simulation and compare it directly with the experimental data. Our response 2: The reviewer is correct that a spectral postprocessing is a logical next step in understanding the situation, which requires to connect the 2D-PIC and MHD simulation results with collisional radiative atomic code. However, we note that ultrafast relativistic laser-driven plasmas remain exceptionally challenging to characterize due to their rapidly evolving, strongly nonequilibrium conditions, steep gradients, and relativistic electron populations. To illustrate this, we performed spectral postprocessing with atomic code FLYCHK using plasma parameters from 2D-PIC and MHD simulations as initial conditions, and found that NLTE opacities and non-thermal electrons are likely essential for reproducing the measured X-ray spectra and transmission. To reproduce experimentally measured X-ray spectrum and transmission shown in Fig. 2 (b) of the manuscript, each cell of the 2D-PIC or MHD simulation was assigned a set of three spectra calculated by the FLYCHK code based on the cell’s plasma density and temperature: an absorption spectrum, and an emission without any driver and emission with XFEL as a driver. The absorption spectrum was used to evaluate a 2D absorption profile of the 8.2 keV peak, and the difference between the driven and undriven emission to show the increase of emission peak, as observed in the experiment. An example of simulation results for time delay at t=4.1 ps is shown in Fig.1 below. Figure 1: 2D spatial distributions of mass density and electron temperature extracted from PIC–MHD simulations, along with simulated total X-ray self-emission, X-ray emission and absorption at 8.2 keV with an XFEL driver, and the difference between the driven and undriven X-ray emission at 8.2 keV. We then integrated these spectra over the 2D spatial domain to reproduce the spatially weighted, experimentally measured X-ray spectrum or transmission, as shown in Fig. 2. It can be seen that in the standard atomic simulation, based on the MHD-predicted 2D temperature distribution (black lines), the peak emission and minimum absorption occur at approximately 11–15 ps, in contrast to the experimentally observed 2–3 ps. A strong difference is observed when postprocessing is performed on the MHD simulation using temperatures interpolated from charge state in the PIC code (dotted lines). In this case, the extremes of the observables (peak emission and absorption) disappear entirely because the temperatures are too low. As an indicator of the underlying mechanisms, a set of postprocessing tests using MHD temperatures scaled by different multipliers shows that the emission peak shifts to earlier times, reaching 3 ps as observed from the experiment when the temperature is reduced to about 70%. That is obviously not a realistic plasma simulation, but indicates the mechanism of probing given atomic transition. Although the postprocessing simulation is preliminary, it highlights the critical role of transitioning from PIC to MHD results, as well as the non-thermal nature of the phenomena. Including non-thermal, non-equilibrium processes in predictive atomic modeling to accurately simulate time-dependent X-ray emission or transmission is particularly challenging, due both to the different thermalization timescales of electrons and ions and to the large number of atomic configurations required to describe highly ionized plasmas. Since improving and validating the atomic code is not the main focus of this work, including all associated details, caveats, and conclusions from the spectral postprocessing would overly scatter the current article, and is therefore better suited for a separate publication. Meanwhile, publishing these high-quality experimental data in the spirit of open science will allow other groups to benchmark and validate alternative atomic codes. Figure 2: Spatially weighted resonant X-ray emission and XFEL transmission at 8.2 keV for different treatments of the electron temperature, as predicted by simulations using the atomic code FLYCHK. 3. The correlation between the resonant X-ray emission yield and the XFEL transmission shown in Fig. 2(c) requires a clear physical discussion, ideally supported by comparison with theoretical or simulation results. Our response 3: The observed correlation between the resonant X-ray emission yield and the XFEL absorption in Fig. 2(c) indicates the small-scale length of the resonant features, as otherwise absorption becomes saturated, while backward resonant emission yield is dominated by the first absorption length thickness. In this way having both resonant backscatter (sensitive to the x-ray absorption depth) and transmission (bulk) are complementary diagnostics yielding additional information from their combination. For the resonant charge state corresponding to peak absorption at the XFEL photon energy, the effective absorption length is on the order of a micrometer, Ο(µm). This implies that, for linear proportionality, the projected thickness must be smaller than this value, further indicating that the ionization is highly localized near the front surface, rather than producing a uniform charge state. This contrasts with the early simulations in the original manuscript, which predicted ionization throughout the entire wire, but is consistent with the new simulation results showing localized ionization near the front surface when accurate initial interaction conditions are used. The small-scale length of the resonant feature is further supported by data obtained from 2 μm CH-coated Cu wires (not shown in the current manuscript), for which no obvious resonant emission is observed. It is noted that although the features are smaller than the XFEL focal size, variations in direct beam overlap arising from beam jitter introduce only minor fluctuations in the total absorption signal. Forward X-ray propagation simulations show that the absorption variation is less than 0.1 assuming ±5 µm jitter, which is consistent with the experimental data shown in Fig. 2(b) at negative delays. Consequently, changes in the resonant absorption remain clearly distinguishable when the effects of beam jitter are taken into account. Thus, while resonant emission serves as an ionization diagnostic and is extensible to thicker or layered targets containing a suitable resonance due to its spectral sensitivity, the observed correlation in resonant absorption can be used here to infer an approximate scale length even without direct imaging. We have added the above discussion for Fig. 2(c) in the revised manuscript. 4. The distinction between the present diagnostic method and those in previous studies is weak. The authors should quantitatively describe the advantages of their approach compared with existing techniques. Our response 4: As per Reviewer #1 “…the study presents a meaningful advance relative to the existing literature. Its key strengths include: i) The use of XFEL radiation simultaneously as a pump and probe, achieving sub-picosecond temporal and sub-micrometer spatial resolution …”, and the present diagnostic provides quantitative information not accessible with previously established X-ray or optical techniques. Earlier ultrafast studies relied on either broadband XAS/XANES, K α spectroscopy, or integrated bremsstrahlung emission, which lack charge-state specificity, are insensitive to narrow resonances, or average over the full charge-state distribution. In contrast, by tuning the XFEL to the Cu²²⁺ 1s→2p resonance at 8.2 keV and simultaneously measuring the monochromatic attenuation of the probe and the resonantly driven emission, we isolate the contribution of a single charge state with sub-picosecond time resolution. This enables quantitative retrieval of both the transient history of Cu²²⁺ population and the resonant opacity at solid density. Moreover, the tunability of the XFEL photon energy enables charge-sensitive diagnostics capable of measuring the spatiotemporal evolution of heating and ionization dynamics for any target of interest, which is clearly a significant advantage. In our experiment, the technique achieves a high precision in transmission and emission measurements simultaneously and reveals that the hot-plasma absorption at the resonance exceeds the cold-Cu opacity by more than a factor of two. No previous diagnostic has provided simultaneous, time-resolved access to both resonant absorption and charge-state–selective emission in a highly transient, solid-density plasma. As also mentioned in the response 3, while resonant emission can serve as an ionization diagnostic—which can be extended to thicker or layered targets containing a suitable resonance due to its spectral sensitivity—the correlated resonant absorption can provide an estimate of the scale length even without imaging. Such a unique combination of diagnostic capabilities, with unprecedented simultaneous spatiotemporal resolution, allows for a comprehensive investigation of multi-scale physics by directly comparing experimental results with multi-scale simulations. We have highlighted the distinct capabilities and benefits of the combined diagnostics in comparison with current techniques in the revised manuscript. 5. The manuscript mentions that a microscope objective was used in the final optical system. Has it been verified that the pulse duration was not stretched due to geometric path length differences or group-velocity dispersion (GVD)? Such stretching could significantly alter the laser intensity. Our response 5: The microscope objective mentioned in the manuscript was used only to generate a magnified image of the focal spot for focus-quality characterization in an alignment mode. Because the objective was positioned downstream of the target chamber center (TCC), any dispersion it introduced would not affect the laser–matter interaction. Moreover, it was retracted during high-energy shots to prevent damage to the optics. Therefore, the microscope objective does not alter the laser intensity on target. We have clarified this point in the revised manuscript. 6. Figure 2 in the Methods section is not referenced anywhere in the main text. In addition, the spatial scale should be indicated on the image. Our response 6: Thank you for pointing this out. Figure 2 in the original manuscript was intended to be referenced in the subsection “Justification criteria of high-quality shots” within the METHODS section. Due to a typo, it was mistakenly referred to as Figure 6. This has been corrected in the revised manuscript, and the spatial scale has now been added to the image and clarified in the figure caption."}, {"round": 2, "reviewer_comments": {"reviewer_1": "This referee is satisfied with the improvements in the manuscript, which address the questions/criticism from the reviewers. The more realistic account of the laser intensity profile in the simulations was particularly appreciated.", "reviewer_2": "The authors have responded appropriately and thoroughly to the reviewer comments. In the revised manuscript, the experimental results are well compared with the simulation results, representing a significant improvement over the previous version. I therefore recommend this manuscript for publication."}, "author_response": ""}]

Decision letter