During a high-intensity laser interaction with matter, copious amounts of X-rays and laser-accelerated charged particles are produced. In the case of solid targets, the currently most extensively researched regime of particle acceleration is target normal sheath acceleration (TNSA)^[1^,2^]. In this regime, the target gets ionized during the interaction, and the laser energy is transferred to the so-called ‘hot’ electrons, a high-energy population of electrons that can escape from the target rear side. As a result of this charge separation induced by electron escape, an electrostatic sheath field is formed, which is strong enough to accelerate ions from the rear target surface up to the energies of tens of MeV^[3^], depending on the laser parameters. Most plasma electrons remain ‘cold’, that is, they have relatively low kinetic energy, and thus are trapped refluxing inside the target. While electrons propagate through the medium, bremsstrahlung radiation is produced as a result of their deceleration in the Coulomb field of other charged particles^[4^,5^]. The bremsstrahlung emission from the ‘cold’ and ‘hot’ electron populations is expected to form a two-component X-ray field following a bi-Maxwellian distribution^[6^–10^]. For laser intensities below approximately 10²² W/cm², the bremsstrahlung mechanism is typically considered the predominant source of hard X-rays emitted from the laser–plasma interaction^[11^,12^].

In recent years, the concept of efficient laser-driven ion accelerators has evolved into reality, as has been demonstrated in several facilities around the world^[13^–15^]. Various possible applications of such accelerators range from radiobiology to cultural heritage studies^[16^–19^]. One such beamline is ELIMAIA (ELI Multidisciplinary Application of laser-Ion Acceleration)^[15^,20^,21^] at the ELI Beamlines facility of the Extreme Light Infrastructure ERIC^[22^], focusing on ion acceleration up to the energy of tens of MeV at a high repetition rate (>1 Hz). As state-of-the-art facilities operate at increasingly high repetition rates, the demand for efficient and real-time diagnostics becomes more pronounced, in contrast to single-shot experiments. Real-time (or ‘online’) monitoring of the fluctuations in the generation of the main laser–plasma byproducts, such as ions and X-rays, on a shot-to-shot basis is crucial not only for granting a stable accelerator output and timely detection of possible issues but also for fundamental research of the physics underlying the acceleration processes.

Shot-to-shot measurements of hard X-rays in such facilities remain challenging due to the high radiation fluxes emitted in a short time, causing saturation of common single-photon diagnostics. Differential filtering spectrometers relying on passive detectors, such as radiochromic films (RCFs) or image plates (IPs)^[23^–25^], are not suitable for real-time detection due to their time-consuming handling and post-processing. One of the possible real-time solutions, scintillator-based calorimetry, inspired by field of high-energy physics, is based on the measurements of the energy deposited in a material by the impinging radiation. When irradiated, scintillators produce visible light that can be recorded by different means, for example, using a charge-coupled device (CCD)/complementary metal–oxide–semiconductor (CMOS) camera, and, given that the signal decay time is usually quite short (from 1 ns to 1 μs), scintillator-based detectors have become promising candidates for high-repetition-rate experiments. Various scintillator devices have gained interest in the last years, often being implemented in a stack configuration, where each scintillator acts as a layer for scoring the deposited energy^[26^–29^]. In this work, we used two advanced scintillator stack detectors located at different angles from the target to monitor the hard X-ray fluctuations in real time.

Although real-time ion detection methods, such as online Thomson parabola spectrometers or semiconductor detectors, are more established^[30^–32^], laser-driven ion accelerator facilities like ELIMAIA often allocate ion/proton beams for various applications, such as sample irradiation. In such cases, the beam cannot be measured by these disruptive diagnostics, as it would prevent its propagation towards the irradiation station downstream. However, gaining insight into the shot-to-shot fluctuation of key ion beam parameters, such as proton maximum energy, is paramount for understanding the overall characteristics and stability of the interaction. Since the generation of ions, electrons and X-rays is closely interlinked, the real-time measurements and characterization of bremsstrahlung radiation might shed light on the shot-to-shot fluctuations of the proton parameters in a non-disruptive manner when direct measurements are not feasible. Moreover, in the TNSA regime, ions with higher energies are accelerated in narrower cones^[2^,11^,33^] requiring precise alignment of the diagnostics to measure the beam characteristics, including the maximum energy. Bremsstrahlung radiation, on the other hand, exhibits a significantly broader angular distribution compared to ions. Also, the measurements in this case are not limited to the vacuum chamber due to the high penetration capacity of hard X-rays, simplifying the detector positioning and design considerations.

In this paper, we will present online bremsstrahlung radiation measurements for different laser defocusing performed at ELIMAIA at sub-Hz repetition rates, followed by a comparison with proton maximum energy fluctuations for the same shot series. The paper is structured as follows: the experimental setup is described in Section 2; the simulation setup and the unfolding summary are detailed in Section 3; Section 4 summarizes the results of the bremsstrahlung analysis, in comparison with the proton signal and cross-validation of the scintillator stack detector with two other X-ray diagnostics; and Section 5 concludes the manuscript.

To measure the two-component bremsstrahlung radiation emitted from plasma upon laser interaction, the scintillator stack detector SCIS-CAL (SCIntillator Stack CALorimter), developed in-house, was used. The device operates on the principles of an electromagnetic calorimeter (hereafter EMC), that is, it absorbs the deposited energy of the electromagnetic shower induced by incoming radiation. The EMC is composed of 21 scintillator tiles of different thicknesses (from 2 to 10 mm) and scintillator materials (plastic EJ200 and inorganic bismuth germanium oxide (BGO))^[34^] with transverse dimensions of 20 mm × 20 mm. Details of the detector configuration can be found in Table 1. The usage of two materials with a large density gap is meant to provide good sensitivity to both low- and high-energy components of the X-ray spectrum. Each scintillator tile is wrapped in polytetrafluoroethylene (PTFE; Teflon), leaving one face open, and placed inside a separating three-dimensional (3D)-printed plastic holder resulting in a total stack length of 20 cm. Two lead absorbers of 10 mm thickness each are added to alternate with the last three BGO tiles in order to better attenuate the high-energy radiation component. A CMOS Manta 235B camera coupled with an 8 mm focal length lens is used to collect the scintillation light. The stack and the camera are put inside a light-proof black box to avoid signal contamination with external light. The schematic of the detector and its typical light output recorded by the camera are shown in Figures 1(a) and 1(b).

The measurements were performed during the commissioning of the ELIMAIA beamline at ELI Beamlines. The L3-HAPLS (The High-Repetition-Rate Advanced Petawatt Laser System)^[35^] laser, a PW-class laser system delivering ultrashort pulses (<30 fs full width at half maximum (FWHM)) with a central wavelength of 810 nm and (at that time) maximum energy of 10 J on target, was focused using an f/1.75 off-axis parabola (OAP) onto a solid 2.4 μm thick Al target at approximately 15° incidence angle from the target normal to the intensity slightly above 2 × 10²¹ W/cm². The laser intensity contrast at the ns/ps level was approximately 5 × 10⁻¹⁰. The Al targets were mounted onto a special high-repetition-rate target tower, which contains a matrix of conical target holes of about 1.5 mm in diameter^[36^]. The maximum laser power during the experiment was around 330 TW. The maximum repetition rate tested during the measurements was 0.5 Hz. However, the majority of the shots were performed at the shot-on-demand regime, amounting to around one to two shots per minute.

Two identical EMC detectors were installed at different locations to get insight into the bremsstrahlung radiation angular dependence: one was located in the forward direction of acceleration at 30° with respect to the target normal (hereafter the forward stack), while the second one was placed at the top of the vacuum chamber above the target at 75° from the target normal (hereafter the top stack). Both detectors were placed behind 6-mm-thick glass viewports and aligned with respect to the laser–target interaction point. The viewports were chosen rather than a chamber wall location to minimize the attenuation of X-rays and reduce the associated spectral change, especially for the low-energy component. The distances between the target and the detector were 117 and 67 cm for the forward and top stacks, respectively.

To deflect hot electrons that could potentially escape via the glass viewport in the forward direction, a 0.4 T magnet was added between the detector and the viewport (outside of the chamber) at a distance of 20 cm from the forward stack. In such a configuration, electrons with energies below approximately 40 MeV should be prevented from reaching the detector. For the top detector, it was assumed that the electron impact would be negligible due to its location (electrons are accelerated predominantly in the laser beam propagation direction according to the literature^[2^,37^], i.e., forward); therefore, no magnet was used in this case.

The ion signal was recorded by a diamond detector (DD) working in the time-of-flight (TOF) configuration and located along the target normal (at 0°). The DD was placed inside a vacuum pipe extension at 3.25 m from the laser–target interaction. The width of the sensing layer of the DD was 500 μm and the voltage applied was 300 V. The entrance to the detector was covered with a 600 μm Al foil to cut the low-energy ions. Due to its robust characteristics^[30^], the DD can efficiently differentiate between the photon-induced peak signal (a mix of visible light and X-rays) and the fastest protons/ions emitted from the laser-generated plasma. Using a deconvolution technique^[30^], it is possible to extract the ion energy spectrum from the TOF measurement, including one of the crucial parameters – the maximum energy of protons.

In addition, a single-scintillator counter was located next to the forward EMC to measure the hard X-ray flux. It consisted of a 5 mm thick BGO crystal connected to a silicon photomultiplier. It was covered with a 50 μm thick Al filter to protect it from the external light and filter the low-energy secondary electrons. Such measurements were useful to cross-check the hard X-ray measurements from the EMC detector, as will be shown in Section 4.3.

An overview of the experimental setup is shown in Figure 1(a).

Both the top and forward EMC detectors were calibrated prior to the experiment. The calibration was performed in two steps using a Cs-137 source with an approximate activity of 37 MBq: (i) individual tiles were irradiated one by one to correct for the light output variability due to the possible differences in manufacturing processes and handling; (ii) a point of view correction with respect to the camera was measured by moving test tiles (of the same geometry and material as the stack tiles) from the middle to the corners of the stack, compensating for the differences in light intensities induced by different distances and angles of individual tiles to the camera lens.

To unfold the X-ray spectral information from the scintillation light measured by the stack, the detector response to radiation of a given energy or temperature is first modelled using Monte Carlo simulations. The simulation output (or the ‘simulated signal’) makes up the detector’s response vector. A set of such response vectors, corresponding to different energies or temperatures of radiation, is used to create a response matrix, which is the core element for the subsequent signal unfolding procedure. The unfolding involves minimizing of the χ²-function, representing the difference between the measured and simulated signals. Details of the unfolding procedure used in this work can be found in the work of Istokskaia et al.^[29^] and Stránský et al.^[38^].

The simulations were performed using the FLUKA Monte Carlo code^[39^–41^] for a set of single-temperature photon distributions. The simulation model of the detector and part of the interaction chamber were created using the Flair interface^[42^]. The detector model included 21 scintillation tiles (made of BGO or EJ200), the PTFE wrapping and the 3D-printed holder made of polylactic acid. The wall of the interaction chamber is simulated as a 4 cm thick wall of aluminium alloy (EN6082). The model includes a viewport with a 9 mm thick borosilicate window of 5 cm in diameter. The relative positioning and angle of the chamber wall vary depending on the detector location (top or forward). For the forward EMC, an electron-bending magnet is added to the simulation. The simulation model of the forward scintillator stack is shown in Figure 2. The simulated particles are photons emitted from the laser–target interaction point in a cone of 90 mrad, enough to cover the entire viewport and part of the chamber wall. The simulated energy spectrum is exponential of the form ${e}^{-E/T}$ where T is the temperature parameter and E is the energy of the primary photon, as often used to estimate the bremsstrahlung spectrum tail^[43^]. The spectrum is bounded between 10 keV and 50 MeV for all simulations.

A total of 12 temperature points were simulated between 30 keV and 10 MeV. The values were chosen so as to keep the simulation error small compared to the response vector variations between temperature points that can lead to the χ²-function minimizer getting stuck at local minima. The total energy deposition in each scintillator tile is scored, thereby providing a 21-dimension response vector for each temperature point. The number of primaries is set at 48 million for each temperature point, corresponding to a simulation statistical error of approximately 1% for the tiles having a non-negligible energy deposition.

During the unfolding procedure, we assume a two-temperature (2T) photon energy distribution, a common representation found in the literature^[6^–10^]. Such energy distribution combines the hot and cold photon populations, each associated with a temperature and an amplitude, resulting in a χ²-function with four parameters: T_low, T_high and A_low, A_high. The temperatures determine the hardness of each population, while the amplitudes are proportional to the number of photons in each.

Figure 3 shows a typical comparison between the measured signal and the unfolding result for the top and forward scintillator stacks for the same shot. The measured signal originates from the analysis of the scintillation image and is given by the mean value of the pixels covering each tile after background subtraction. The error bars represent the standard deviation of the pixel values inside a region of interest (the tile image). The correction coefficients, discussed in Section 2, have been applied to the signals. The unfolded temperatures and ratio of the amplitudes are presented in Table 2. The errors stated in the table come from the nonlinear regression model (‘fitnlm’ function of MATLAB) used in the unfolding algorithm, which also provides statistical parameters p-value and adjusted R-square, amounting to less than 0.001 and more than 0.98, respectively, for both detectors, which indicates a good fit quality. The total detector uncertainty amounts to approximately 10% for a monoenergetic spectrum, as was experimentally determined during measurements with a known source^[38^]. For the Maxwellian or power-law spectrum, we expect the total uncertainty to be slightly higher; however, it has never been measured yet due to the sophisticated conditions required. The currently used unfolding algorithm can provide results for the 2T distribution within 3 s, including the initialization using an ordinary off-the-shelf PC, which is sufficient for sub-Hz operations and also capable of further optimization (e.g., using machine learning^[44^]).

As can be seen from the signal peak heights in Figure 3, the detector response is stronger in the forward direction than in the top one, despite the larger distance from the laser–target interaction in this case, which is in agreement with expectations (more radiation is typically produced in the direction of the laser propagation). Nevertheless, the best-fit temperatures agree well for both locations. We anticipate angular dependency for the bremsstrahlung spectrum to be far less directional than the distribution of hot electrons due to the ‘randomization’ of the bremsstrahlung emission direction in the target. According to some theoretical and experimental findings, the higher energies are likely to be found around the laser propagation axis rather than in its perpendicular direction. While the fit for the top detector matches well the measured signal, in the case of the forward stack, there is a discrepancy in the plastic (EJ200) part. Such discrepancy was observed in shots with the highest laser intensity and can be attributed to the deposition of secondary electrons and photons scattered from the detector surroundings (mainly from the magnet) caused by the impact of forward-accelerated hot electrons. These particles reach the front side of the forward EMC but are then fully absorbed in the low-density plastic part, leaving the high-energy X-ray deposition pattern deeper in the stack undisturbed. This explanation is supported by dedicated FLUKA simulations of the forward detector using electron primaries with exponential spectra. The simulations showed that, given a similar number of photons and electrons are emitted from the laser target, the contribution of electrons to the signal in EJ200 is comparable to that of photons for temperatures larger than 1 MeV. The electron contribution is negligible in the BGO part for the temperatures considered in this work. Consequently, the first five plastic tiles were not considered during the unfolding of the forward stack signal. The two elevated final points in Figure 3 correspond to the signal from the tiles located after the lead absorbers. We suspect that the observed discrepancy could be attributed to inaccuracies in simulating the energy deposition within the lead, possibly stemming from the suboptimal quality of the lead material used in the experiment.

During the experiment, the laser focal spot size was systematically changed to study the respective changes in the properties of the accelerated particles and radiation induced by the respective change in laser intensity and laser spot size. The systematic exploration of the laser focal spot around the best focus configuration is a commonly employed procedure in laser–plasma experiments^[45^–47^] since it offers the possibility to tune the interaction and optimize the experimental outcomes (e.g., maximize proton energy and/or number of products from the interaction). During the ELIMAIA campaign, the defocusing was performed by shifting the position of the OAP in both the negative and positive directions relative to its initial position (shift = 0), corresponding to the laser beam being tightly focused on the target surface. Negative OAP shift values correspond to the focus location in front of the target (between the target and the OAP), while positive ones correspond to the imaginary ‘in-target’ focus location. For both negative and positive shifts, the physics behind the laser–plasma interaction can differ, mainly due to the preplasma effects^[48^,49^] and also due to the slight asymmetry of the focal spot. The OAP shift scan ranged from –31 to 31 μm with steps of 8 μm, with several shots (from four to six) being fired at each position, providing statistics for each experimental condition. This corresponds to the laser intensity range between 3.5 × 10²⁰ and 2.0 × 10²¹ W/cm². The conversion from the OAP shift to the intensity value was done through the analyses of the images of the laser focus taken at several OAP positions. Subsequently, an interpolation between the measured points was applied.

The unfolding procedure described in Section 3 was applied to all the measurements recorded by the forward and top EMC detectors during the laser focus scan. Figure 4 shows average values of the best-fit temperatures of the ‘hot’ bremsstrahlung component per given OAP shift for the two detectors. The error bars arise from the standard deviation of the values per corresponding OAP shift. The temperatures fall approximately within the range from 1.7 to 2.3 MeV for the top detector, and from 2.1 to 2.4 MeV for the forward one. The temperatures peak at the OAP shift of around –8 μm for both detectors (which corresponds to the laser intensity of 1.4 × 10²¹ W/cm²), decreasing with larger defocusing. The calculated laser intensity corresponding to each OAP position is also shown in the plot. While the maximum temperatures measured with the top and forward EMC detectors agree within the error bars, the values begin to slightly diverge after 20 μm OAP shift in both negative and positive directions. The values measured by the top detector tend to decrease more than those measured by the forward one for large defocus values, although the results are still close within the detector uncertainty. Future dedicated studies can provide insights to better understand the underlying reasons for this difference.

Since the high-temperature bremsstrahlung radiation is assumed to be generated by the hot electrons, their temperature was estimated for the scanned laser intensities using the theoretical ponderomotive^[50^] and Beg’s scaling laws^[51^] in order to benchmark the experimental results. To the best of our knowledge, there is no established relationship between the temperatures of the hot electrons and bremsstrahlung radiation, since the mechanism of bremsstrahlung generation is sensitive to experimental conditions. However, we would anticipate the bremsstrahlung temperature to be a fraction of the temperature of the hot electrons. In general, the bremsstrahlung temperature cannot exceed the electron temperature due to the laws of energy conservation. The hot electron temperature predicted using the ponderomotive law ranged from 6 to 16 MeV for the studied laser intensities and appeared to significantly overestimate the experimental measurements. Beg’s scaling law, on the other hand, aligned closely with the measurements. The green curve shown alongside the unfolded photon temperatures in Figure 4 represents the hot electron temperature range predicted by Beg’s scaling law (the ponderomotive scaling is omitted from the figure as it is beyond the scale and does not effectively describe the data). The values for the electron temperature predicted by Beg’s law span from approximately 1.5 MeV for large OAP shifts to 3.0 MeV for the tight-focus case. The uncertainties of the electron temperatures are shown as a green shaded region and come mainly from the OAP position and laser intensity conversion uncertainties. Except for the points at the edges of the OAP shift distribution, the unfolded bremsstrahlung temperature is equal to or less than the hot electron temperature prediction, which is in accordance with expectations. It is worth noting that the scaling laws depend solely on laser intensity, given that all the other laser and target characteristics remain the same; hence they do not account for, for example, potential preplasma-related effects. These effects can cause slight differences in the electron and photon temperature distribution for different OAP shifts.

The temperature of the ‘cold’ bremsstrahlung component was found to be between 60 and 85 keV and did not show strong dependence on the laser focus position. This is expected since the cold electron component does not undergo a direct laser energy coupling as opposed to the hot electrons, and is mostly caused by the collisional heating processes in plasma^[52^]. However, the cold electrons may be significantly influenced by the refluxing effect, wherein electrons recirculate within the target volume due to the presence of strong sheath fields that prevent their escape^[53^]. In such cases, the bremsstrahlung spectrum may deviate from the Maxwellian distribution^[54^], as utilized in our unfolding technique. Consequently, the unfolded temperature may be shifted away from the ‘true’ value. One potential strategy would involve conducting specific simulations, akin to those in the work of Borm et al.^[54^], to employ a different function for describing the distribution of low-energy bremsstrahlung, rather than the Maxwellian distribution currently utilized. It is important to note that the high-energy bremsstrahlung generated by the hot electrons should remain largely unaffected, as these energetic electrons are capable of escaping from the target.

The two remaining unfolding parameters, the relative amplitudes of the low- and high-energy bremsstrahlung radiation components, are shown in Figure 5 as the averaged ratios A_high/A_low for different OAP shifts. For both detectors, the trend is very similar. The maximum values are distributed between –16 and 0 μm, suggesting that a larger fraction of the hot photons (hence hot electrons) was produced for the OAP positions closer to the tight focus. A larger defocus leads to a larger ablated area; therefore, more electrons eventually become thermalized, increasing the number of the ‘cold’ population versus the ‘hot’ one. It is important to note that extensive defocusing corresponds to lower laser intensities, leading to a less efficient acceleration mechanism. Furthermore, the A_high/A_low ratio is asymmetric for the negative and positive shifts for both detectors, indicating a more efficient hot electron generation for the negative defocus. This phenomenon can be explained by the preplasma effects: for the negative defocus, the focal plane is located in the preionized preplasma region, where, depending on the preplasma scale length and density, different effects enhancing the laser absorption may occur (e.g., self-focusing^[55^]). In contrast, for the positive shift, the tight focus is never achieved and the laser intensity received by the material is lower.

The four unfolded values described in this section can provide important insights into the laser–target interaction physics in terms of laser absorption, hot electron transfer and bremsstrahlung radiation generation^[56^,57^].

During laser-driven ion acceleration experiments, the so-called ion/proton cutoff energy is one of the most crucial parameters of the beam since it enables one to immediately understand the effectiveness of the acceleration process. In Figure 6, the proton cutoff energy extracted from the TOF measurements by the DD is compared with the bremsstrahlung radiation parameters measured by the EMC detector. Figure 6(a) presents a comparison between the proton cutoff energy and the total light yield (LY) from both the top and forward EMCs for different OAP shifts. The LY of the EMC is calculated as the sum of mean pixel values from all the scintillation tiles. It is a direct measurement of the X-ray flux that is evaluated in real-time during shots, akin to the proton cutoff energy. In the energy range we consider (50 keV–3 MeV), the scintillation LY can be assumed to be proportional to the bremsstrahlung yield at the detector’s front. The shown LY values are normalized to the maximum measured value for each detector for the purpose of comparison, given that the top signals were generally weaker than those in the forward direction. In Figure 6(b), the proton cutoff energy is compared with the unfolded temperatures of the high-energy bremsstrahlung radiation T_high for both EMCs for the same OAP shift scan as in Figure 6(a). The average values of the proton energy and bremsstrahlung parameters, derived from several shots performed per OAP position, are shown in the figures. The measurement error bars arise from the standard deviation of parameters from the shots per corresponding OAP shift.

The highest proton cutoff energy was measured to be around 24 MeV when the laser pulse was focused at –8 μm in front of the target. Again, this can be attributed to the preplasma effect described in Section 4.1; the same effects are responsible for the bremsstrahlung LY and temperature asymmetry around the tight-focus case. The proton energy gradually decreases below 10 MeV as the OAP moves further away from the optimal focus position. This decline is primarily attributed to the reduction in the corresponding laser intensity associated with increased defocus, similar to the decline of the bremsstrahlung radiation parameters in this region, as was described in Section 4.1.

As can be seen from Figure 6(a), the scintillation LY is in excellent agreement with the proton cutoff energy fluctuations. The strong positive correlation can be quantified by the Pearson correlation coefficient, which exceeds 0.94 for both the top and forward detectors. Since the LY is evaluated online for each shot, it can be used to obtain immediate feedback about the laser–target interaction and to monitor the fluctuations in laser-driven products (protons and bremsstrahlung radiation).

The unfolded temperatures or the high-energy bremsstrahlung radiation follows the same trend as the proton cutoff for different OAP shifts, as can be seen from Figure 6(b). This aligns with expectations since the high-energy bremsstrahlung component is assumed to be generated predominantly by the hot electrons, which in turn are responsible for the ion acceleration. A consistent trend between the hardness of the bremsstrahlung spectrum and the energy cutoff was observed also for foam targets, as described by Prencipe et al.^[58^]. The Pearson coefficients between the photon and proton datasets are 0.86 and 0.71 for the forward and top detectors, respectively. The correlation differences are probably given by the detectors’ locations: the forward stack was at the same plane and direction of the acceleration as the DD, as opposed to the top one. Therefore, the forward EMC is more sensitive to the bremsstrahlung radiation generated by electrons with a large momentum component parallel to the beam axis – specifically, those transferring the most energy to the ions. The maximum values of both photon temperatures and proton energies indicate the same optimum in the OAP shift.

Based on the data comparison from Figure 6(b), it is possible to calculate the ratio between the proton cutoff energy and bremsstrahlung radiation temperature for different laser defocusing. The average values of the resulting ratios are shown in Figure 7. The error bars are calculated using error propagation. In the optimal region, the proton maximum energy is approximately 10 times larger than the bremsstrahlung temperature, while for the rest of the points, the average can be estimated around 5. Such a relation can be useful for ELIMAIA experiments where the proton maximum energy cannot be determined directly without disrupting the beam from propagation to the sample irradiation station. Moreover, the ratios are very close for the both top and forward EMCs, suggesting that angular variations for the detector location can be disregarded for experiments where the setup space is limited. This stands in contrast to the currently available ion diagnostics, which often require precise alignment along the target normal. It is worth noting that theoretical predictions of the ratio are scarce, although according to one of the models formulated by Passoni and Lontano^[59^], for a similar experiment, one would expect the scaling to be E_cutoff ≈ 6T_h, where E_cutoff is the maximum ion energy and T_h is the hot electron temperature. It is worth noting that based on the ion cutoff energy measurement and its relation with the hot electron temperature resulting from the ion-hot electron scaling laws^[59^,60^], the ponderomotive scaling mentioned in Section 4.1 seems to significantly overestimate the results. This holds true for both ion and bremsstrahlung radiation measurements.

To cross-validate the EMC detector’s response to the bremsstrahlung radiation signal on a shot-to-shot basis, the LY (described in Section 4.2) was compared with other X-ray measurements provided by two independent diagnostics: (1) the integrated photopeak from the TOF spectrum recorded during proton measurements by the same DD (the photopeak is typically composed of a broad spectrum, including visible light and soft and hard X-rays; in our case, the visible light was cut by the Al filter in front of the detector, as mentioned in Section 2) and (2) the integrated signal from the single-scintillator counter. The comparison was done only for the forward stack since the DD and the counter were located in the forward direction of ion acceleration. Figure 8 summarizes the normalized photon yield measured by the three detectors for the same list of shots presented in the OAP study. The Pearson correlation coefficient for all the detectors is better than 0.9, indicating that the EMC LY is indeed a good predictor of the intensity of the integrated photon radiation field.

In this paper, we have studied the performance of a scintillator stack detector for measuring the two-component bremsstrahlung radiation accompanying laser-driven particles produced in the TNSA regime. The measurements were done in real time during a sub-Hz repetition rate shot series using the L3-HAPLS PW-class laser system reaching the intensity on target of about 2 × 10²¹ W/cm². The laser focal position was scanned in the positive and negative directions by shifting the OAP, allowing the study of the laser–plasma interaction under different conditions (laser intensity, focal plane position). Two identical scintillator stack detectors were installed, viewing from the forward direction of acceleration and from above the interaction, providing a glimpse into the bremsstrahlung angular distribution. During the experimental run, the bremsstrahlung radiation yield was evaluated online for each shot via the calculation of the total scintillation light output measured by each detector. The measurements allowed the monitoring of the laser–plasma interaction quality on a shot-to-shot basis through the fluctuations of the bremsstrahlung radiation characteristics. The specially developed unfolding process performed at the shot post-processing stage revealed temperatures of approximately 2.4 MeV and 85 keV for the high- and low-energy bremsstrahlung populations, respectively, at the optimal OAP position.

Moreover, the measured scintillation LY and bremsstrahlung temperature were compared with the proton maximum (cutoff) energy (as measured by the TOF DD), as the physics behind ion acceleration and bremsstrahlung radiation generation is closely linked through hot electrons. Remarkably, the LY from the EMC has proven to be in excellent agreement with the fluctuations in the cutoff energy of laser-driven protons depending on the OAP position. Furthermore, the temperature of the bremsstrahlung component generated by the hot electrons also followed a consistent trend with the proton cutoff, decreasing as the OAP moved farther from the optimal laser focus position. Given a thorough calibration for the given laser parameters, a more precise relation between the proton maximum energy and bremsstrahlung radiation temperature could be obtained in the future. Future steps would also include obtaining more statistics per specific experimental conditions to derive the confidence level for such a relation. Thus, the detector is a promising tool for potential non-disruptive estimation of the proton energy and its fluctuations during high-repetition-rate experiments for cases when direct proton measurements are not feasible (e.g., the beam is intended to be used for sample irradiation).

The measurement and analysis results were very similar for both scintillator stack detectors located at different positions, proving valuable flexibility for experiments with limited space available for the bremsstrahlung measurements. Finally, the forward EMC’s shot-to-shot fluctuations were cross-checked with the integrated X-ray signal from the DD and the single-scintillator counter.

Real-time measurements, reliable response and flexible location requirements make this developed scintillator stack detector of the bremsstrahlung radiation a promising tool for the online monitoring of ultrahigh-intensity laser–plasma interaction and fluctuations of the laser-driven secondary sources.