Currents from relativistic laser-plasma interaction as a novel metrology for the system stability of high-repetition-rate laser secondary sources

Technological and scientific advances in lasers^1,2 have led to stable short-pulse PW-class high-repetition-rate (HRR) Ti:Sa systems^3,4 that have been implemented in many new research facilities worldwide.^5–19 With laser pulses tightly focused onto matter, the resulting relativistic interaction generates secondary sources, ranging from ionizing radiation^20–24 to extreme ultraviolet (XUV) and THz pulses,^25–28 as well as current pulses.^29–33 The extension of such laser-driven secondary sources from single-shot to the full HRR capabilities of modern relativistic laser facilities is of great interest, notably in light of recent progress toward the development of HRR sources based on gas jets^34–37 solid tapes,^38–49 liquid jets,^50–52 and cryogenic ribbons.^53,54

Many schemes for producing secondary particle or radiation sources using lasers rely on efficient energy transfer between the laser and a population of hot electrons.⁵⁵ In particular, the forward acceleration of electrons²³ can trigger pulsed bright ion beams by well known mechanisms, including target normal sheath acceleration (TNSA),^56,57 radiation pressure acceleration (RPA),⁵⁸ and others.²² Such beams are of use in isotope production,^59,60 positron emission tomography,⁶¹ ion beam microscopy,⁶² particle-induced X-ray emission (PIXE),⁶³ and inertial confinement fusion (ICF).^64,65 These ion acceleration mechanisms rely on the build up of large accelerating potentials, which are also the source of ultrastrong electromagnetic pulses (EMPs).⁶⁶ For most laser-driven secondary sources, targets acquire a strong positive net charge due to laser-accelerated electrons that are able to escape the rising potential barrier.^67,68 As a result of this, kA-level discharge pulses and return currents can be produced.^69,70 Although such laser-generated EMPs and current pulses can have undesirable effects that need to be suppressed,⁶⁶ there are also aspects of the associated electromagnetic dynamics that may be directly applicable in boosting the performance of secondary sources^32,69,71,72 and for metrology of experimental setups.^73,74

The stability of secondary sources and their initial automatic alignment are of major concern for scientific studies and technological applications at a high repetition rate. Laser facilities have to provide noninvasive metrology based on indirect measurements. In this context, we have chosen to investigate the suitability of laser-generated EMPs, which cover the wide range from radio frequencies⁷⁶ to X rays.⁷⁷ Previous work has shown that EMPs in the very high-frequency band depend on the details of the macroscopic experimental geometry,^74,75 which is often changed and is therefore not ideal to diagnose the stability of a source. In this work, we present a clear relation between the laser-generated return current and certain ion beam characteristics, namely, the TNSA proton cutoff energy, number density, and temperature, which are widely referenced features of the proton spectrum. We explore the correlation of the spectral cutoff energy with the return current for variations in (i) the target positioning in the laser-longitudinal direction and (ii) the laser pulse duration as a function of opto-acoustically induced group delay dispersion (GDD).

The experimental setup is shown in Fig. 1. In this work, we made use of current pulses excited by laser–plasma interaction, namely, the discharge pulse and the pulsed return current in the regime of relativistic laser interaction.⁶⁹ The return current was measured with a target charging monitor (TCM) the operation of which was based on the principle of an inductive current monitor.⁷⁹ The TCM measured the derivative of the current between target and ground that passed through the device. Current pulses were transported via RG142 coaxial cables, with a circuit impedance Z = 50 Ω. Cable lengths were measured with 3 ns full-width at half-maximum (FWHM) voltage pulses: the target and TCM were connected with a coaxial cable of length (9.6 ± 0.2) ns, and the TCM and ground were connected with a coaxial cable of length (13.6 ± 0.1) ns. Induced signals were transported to a 2 GHz oscilloscope within a Faraday cage that provided −110 dB attenuation up to 40 GHz. Acquisitions were corrected throughout for the frequency-dependent attenuation of circuit elements. Circuit calibrations were performed using an R&S ZNH 4 GHz vector network analyzer. The effective bandwidth of the circuit was 2 GHz.

Ion acceleration was driven by the high-power VEGA-3 laser^13,80 at the Centro de Láseres Pulsados (CLPU). Ti:Sa laser pulses were compressed to τ_L = (28 ± 3) fs with a grating compressor and transported in a high vacuum of 1 × 10⁻⁶ mbar via an f = 2.5 m off-axis parabola (OAP) onto the target. Of the laser pulse energy, up to E_L = (6.9 ± 0.3) J was contained within the first Airy disk of radius r_L = (12.8 ± 1.9) μm full-width at half-maximum (FWHM). For this experiment, this laser energy corresponded to (33.9 ± 1.5)% of the total energy on target. Hotspots were also present, as reported in previous work.³³ Under the assumption of Gaussian beam propagation, the Rayleigh length was (464 ± 145) μm. Energy and focal spot size were extrapolated from measurements at low power, and the pulse duration was measured for each shot via a reflection from the debris shield of the focusing OAP that was guided into a second-harmonic autocorrelator system.

The CLPU tape target system⁷⁸ was deployed for rapid refreshment of interaction targets at 1 Hz, allowing simultaneous study of current pulses produced by the relativistic laser interaction on the solid target.³³ In this experiment, the system spooled metallic tapes of either copper or aluminum across the laser focal plane. The positioning stability of the tape surface was better than 10% of the Rayleigh length. Insulated metal rods guided the tape and extracted the return current before it could dissipate across the target frame. In the course of this study, the system performed a maximum of 1633 shots per tape, with an average of ∼1000 shots for a half-day of operation (with 150 turns of tape on a 20 mm-diameter spool for ∼1000 shots). Two different types of tape were used for this work: 7 μm-thick copper and 10 μm-thick aluminum.

To investigate the relationship between return currents and TNSA-accelerated protons, a Thomson parabola ion spectrometer (TPS)⁸¹ was positioned in the target normal direction. This spectrometer was modified for use with a single entrance pinhole, to enable it to detect low-energy proton beams down a low-energy cutoff of 0.6 MeV, i.e., with an energy resolution of 1.3 MeV at 20 MeV, 0.14 MeV at 10 MeV, and 4 keV at 1 MeV. The TPS was fitted with an active detector screen: a multichannel plate (MCP) coupled to a phosphor screen (rectangular MCP and assembly series type F2813-12P, from Hamamatsu, Japan).

After first describing a typical measurement of the time-resolved return current. We shall discuss the return current, the laser–target interaction parameters, and the spectral cutoff energy of laser-accelerated protons. In this study, the laser pulse energy was kept constant, and the focal spot size was varied by moving the target with respect to the best focus position. A commercially available acousto-optic programmable dispersive filter⁸² (the Dazzler device from Fastlite, France) was used to modify the pulse duration by adjusting the GDD relative to the optimum position. The Dazzler was installed after the last stretcher of the double CPA system and before the amplification stages.

Typical amplitudes for return current pulses are in the kA range and their pulse duration is of the order of several tens of picoseconds to several nanoseconds. The time-resolved average current for 20 full-energy shots with (6.9 ± 0.3) J at 1 Hz and a laser pulse duration of (38 ± 6) fs onto copper tape of 7 μm thickness is shown in Fig. 2.

The current with peak value ∂_tQ = (716 ± 36) A integrates to Q^Total = (755 ± 64) nC of escaped electrons. The total discharge can be modeled as a function of the temperature T_e of the laser-accelerated relativistic electron population as $QcalcTotal=AiTe$⁠, in the ponderomotive regime of laser electron acceleration and for thin targets shot at best compression and best focus.³³ Here, A_i is a fitting parameter. This scaling assumes the escaping electrons to be part of an exponential tail of the electron distribution function that extends up to a maximum electron energy E_e max, with T_e ≪ E_e max. The material- and laser contrast-dependent constant was found to be A_Cu = (256 ± 26) nC·MeV⁻¹ in a study using the same laser system³³ and notably with same laser contrast. In the present study, the ponderomotive scaling^83,84 yields $Te=mec2[(1+a02)1/2−1]=$ (3.2 ± 0.6) MeV, where m_e is the electron rest mass, c is the speed of light, and a₀ is the normalized vector potential of the laser field. Thus, one calculates $QcalcTotal=$ (819 ± 154) nC, in good agreement with the experimental value.

The measured FWHM of the current peak is (455 ± 100) ps and could be the result of a superposition of multiple reflections on the target system. Both of the titanium guiding pins of 28 mm length and 5 mm diameter were horizontally positioned at ±8 mm with respect to the laser-interaction point on the 10 mm-wide tape. The guiding pins were connected via a 4 mm-square and 18 mm-long aluminum guide to a 83 mm-long RG142 coaxial line ending in a panel connector. One of those transmission lines was used to couple the return current into the TCM and the ground; the other was left open-ended. The length of the tape between pin and spool was (75 ± 5) mm. The direct coupling into the grounded pin (at Δt = 0 ps) was followed by the first two reflections from the nongrounded pin, i.e., those coming from the interfaces between (i) the end of the pin and the aluminum guide (at Δt = 123 ps), and (ii) the respective aluminum bar and the coaxial cable (at Δt = 243 ps). The width of the tape in conjunction with the length of the pins broadened the current pulses by at least 93 ps. It should be noted that the broadened pulses might superpose to give a single measured pulse if its exponential tail had the typical order of tens of picoseconds.⁶⁹ 

The current peak contains one-half of the total charge for this sequence of shots and is succeeded by a longer tail. Successive reflections across the target system are likely creating this tail of the measurement, i.e., coming (iii) at Δt = 527 ps and (iv) Δt = 580 ps from the spools and (v) at Δt = 797 ps from the open-ended transmission line, as discussed in Ref. 33.

Correlations of peak current ∂_tQ^Peak with integrated charge are shown in Fig. 3 for different target materials (copper and aluminum) and laser parameters (the coarse variations of focusing and pulse duration are describe in further detail later in this paper), for both the integrated total charge $QTotal=∫9ns12ns∂tQdt$ and the amount of charged confined within the current peak $QPeak=∫9ns10ns∂tQdt$⁠. The latter is strongly correlated with the peak current amplitude as Q^Peak = ∂_tQ^Peak× (0.479 ± 0.003) ns with good confidence. The Pearson linear correlation coefficients between ∂_tQ and Q^Total are 0.901 and 0.939 for copper and aluminum respectively. The correlation coefficients between ∂_tQ and Q^Peak are 0.960 and 0.999 for copper and aluminum, respectively.

The total charge scales as Q^Total ≈ 4Q^Peak for peak currents lower than 300 A and evolves smoothly to a scaling of Q^Total ≈ 2Q^Peak for peak currents higher than 600 A. This could represent the transition between an impedance-mismatched reflective coupling between tape and guiding pin for low currents and a regime of breakdown for high currents.⁸⁵ Note that the lower peak currents correspond to data from a scan of the target position, i.e., the laser intensity profile on-target. The tail might contain not only reflections, but also a relatively higher contribution of lower-energy electrons to the charging of the target, which is pronounced in the late charge ejection due to a growing Debye length.⁶⁷ 

Return currents can be used as online diagnostics for optimization of laser–target energy coupling. Figure 4 compares the proton cutoff energy (in blue) with (i) the beam power (in green), which fluctuates due to changes of the laser pulse duration, (ii) the laser peak intensity (in red), which is extrapolated to the displacement position assuming a perfectly Gaussian beam propagation, and (iii) the respective peak current amplitude ∂_tQ^Peak (in magenta) for each sequence. The power of the laser beam exhibits an increasing trend, but remains comparable within measurement uncertainties. Moving the target along the laser axis reveals coinciding maxima of the return current amplitude and spectral cutoff energy of protons when the impact-side target surface is located close to the best focus position found during a low-energy laser pre-alignment. The return current amplitude exhibits a strong dependence on the target position, which is likely linked to a correlation with the laser intensity via the hot-electron temperature. For the parametric study, the laser pulse duration τ_L = (39 ± 8) fs and the laser pulse energy E_L = (6.9 ± 0.3) J were maintained constant. We collected a series of 400 laser shots separated in bunches of 20 for each longitudinal “defocusing” position.

The coinciding maxima of return current amplitude and proton cutoff energy exhibit a small difference with respect to the position of extrapolated peak intensity from the best focus position at low energy. The relative displacement amounts to ≈20% of one Rayleigh length. This could be due to a sub-Rayleigh-length variation between low-energy and full-energy focal positions, consistent with measurements at comparable laser facilities.⁸⁶ An asymmetry between positive and negative displacement can be noted when measured peak current amplitudes and proton-spectrum cutoff energies are compared. For example, coma, astigmatism, or a spherical aberration of the focused laser beam could yield an intensity pattern that is longitudinally asymmetric with respect to the best focus position.

The maximum amplitude of the return current decreases slowly with increasing displacement, reaching its half value at ≈7.5 times the Rayleigh length. The proton cutoff energy drops rapidly with increasing displacement, reaching its half value at ≈3 times the Rayleigh length. For the latter, a rim of steep decrease can be noted in the vicinity of the first occurrence of strongly reduced axial intensity due to interference effects typical of focusing of flat-top laser beams,⁸⁷ indicated by the dashed vertical lines in Fig. 4.

In the context of TNSA proton acceleration, the peak of the return current amplitude ∂_tQ^Peak has a bijective relation with the maximum detected spectral cutoff energy of the protons: see Fig. 5, where the correlation between the proton cutoff energy and the peak current ∂_tQ^Peak is compared with the correlation with the integrated total charge Q^Total. Both cases exhibit a linear relation, but with two distinct slopes delimited by a cutoff energy of 4.6 MeV. The best fit of the peak current as a function of proton cutoff energy E_p is given by ∂_tQ^Peak = E_p × (99 ± 2) A·MeV⁻¹ for E_p < 4.6 MeV and ∂_tQ^Peak = E_p × (35 ± 5) A·MeV⁻¹ + (337 ± 42) A for E_p > 4.6 MeV. The best fit of the total charge as a function of proton cutoff energy is given by Q^Total = E_p × (146 ± 2) nC·MeV⁻¹ for E_p < 4.6 MeV and Q^Total = E_p × (8 ± 3) nC·MeV⁻¹ + (618 ± 26) nC for E_p < 4.6 MeV. The relative uncertainty in the total charge is larger than that in the current amplitudes because of the required additional numerical integration. The Pearson linear correlation coefficient between total charge and cutoff energy amounts to 0.79, which is smaller than the coefficient 0.94 between maximum current amplitude and cutoff energy. It can be seen that the variation of the total charge is within its error bars for high proton cutoff energies, whereas the steeper increase in the peak current amplitude with rising cutoff energy can be used to derive bijective fitting relations with good confidence. Higher cutoff energies correspond to shots close to the best focus and lower cutoff energies to shots where the on-axis intensity interferes to give zero. The two different regimes are indicated by two distinct slopes for ∂_tQ^Peak and Q^Total.

The time-resolved nature of a return current measurement is a further advantage when compared with the use of the time-integrated total charge as a metric. Figure 6 shows the time-resolved amplitude of the pulsed return current under variations in the target position. A pronounced maximum is followed (in time) by a tail that is stable over a wider range of target positions but has a local minimum around the best focus. The fractions of total charge in the peak and tail are equal around best focus and evolve to 25% in the peak and 75% in the tail far from best focus. This is due to a more rapid decrease of the charge in the peak. The tail is concave toward best focus in the frame of displacement vs time. The evolution of the maximum peak amplitude with distance to best focus and the elongation of the tail with increasing defocusing are promising characteristic indicators that could be used to train machine learning algorithms to compensate for drifts and perform autofocusing operations.

A scan of the laser pulse duration reveals a local minimum of the return current amplitude at best compression that coincides with a local minimum of the proton cutoff energy (Fig. 7). For the parametric study, the target was positioned at the best focus position z = 0 found during low-power alignment, and the laser pulse energy E_L = (6.9 ± 0.3) J was maintained constant. A series of 190 laser shots was separated into bunches of ten for each induced GDD (the second-order term in the Taylor-expanded spectral phase $Φ̈=∂ω2Φ$⁠). The third-order dispersion (TOD) was kept constant at the initial optimum position.

Figure 7 (bottom) shows that the minima of the peak return current amplitude and proton cutoff energy coincide with the extrapolated maximum laser intensity at best compression, i.e., the shortest pulse duration. The minimum of the proton cutoff energy has slightly asymmetric rims: the respective first local maxima appear (−912 ± 21) fs² left of best compression at a pulse duration of (100 ± 6) fs and at (591 ± 21) fs² right of best compression at a pulse duration of (135 ± 8) fs. Proton cutoff energies and return current amplitudes remain at a much higher level than the respective minima beyond the rims, but a decreasing trend is clear toward longest pulse durations.

The measurement is consistent with an expected maximum spectral cutoff energy for slightly stretched pulses using thick targets, owing to an optimum electron sheath for ion acceleration. Such an optimum has been observed in previous experiments, where it has been attributed to a number of effects: (i) the degrading effect of a sweeping sheath field for shortest pulse durations⁴⁶ in cases where the incidence angle of the laser on the target $α>arctan(cτLrL−1ln⁡2/2)$⁠; (ii) an increasing absorption efficiency for longer pulses that is eventually balanced by the falling intensity;⁸⁸ (iii) an optimum target thickness d = −2λ_D + cτ_L/2 (where λ_D is the Debye length), for which refluxing electrons increase the charge in the sheath electron cloud and thus the accelerating field.⁸⁹ In the case of the present experiment, the sweeping effect (i) is unlikely, since it arises when $cτLrL−1<0.13$⁠, but for all parametric scans in this work $cτŁrL−1>0.68$⁠. Both effects (ii) and (iii) can contribute to our findings: with regard to (ii), the laser pre-pulse of the VEGA system is likely to produce a small pre-plasma scale length⁹⁰ of the order of <1 μm; with regard to (iii), the Debye length is typically small compared with the target thickness of the order of 10 μm and enhancement of the sheath density can occur for τ_L > 2 d/c = 67 fs. The origin of this effect is beyond the scope of this paper, but is discussed in depth elsewhere.⁸⁰ 

Note that these results support previous findings from single-shot experiments on the VEGA laser system⁸⁰ and are also consistent with data obtained at the DRACO laser.⁹¹ For the latter, the evolution of absorption efficiency might be the dominant mechanism, since the pre-plasma was negligible and targets were ultrathin. Note that the main goal of the work described in Ref. 91 was not a variation of GDD, but to relate a positive TOD (yielding shallow rising edges) to higher cutoff energies at an optimum off-zero GDD, which might also be related to a changing absorption efficiency.

The correlation between peak current amplitude and proton cutoff energy is clear, even when the significant measurement uncertainty is taken into account. Figure 8 shows the correlations of the proton cutoff energy with the peak current ∂_tQ^Peak and with the integrated total charge Q^Total for a Dazzler scan. In both cases, there is a linear relation. The best fits of the peak current and the total charge as functions of proton cutoff energy E_p are given by ∂_tQ^Peak = E_p × (11 ± 3) A·MeV⁻¹ + (590 ± 30) A and Q^Total = E_p × (16 ± 3) nC·MeV⁻¹ + (536 ± 34) nC, respectively The Pearson linear correlation coefficient between total charge and cutoff energy amounts to 0.699, which is smaller than the coefficient 0.792 between maximum current amplitude and cutoff energy. This remains in the range for a relevant correlation. A measurement with lower uncertainty could reveal an even higher correlation. In this work, the measurement uncertainty in the peak current amplitude is dominated by noise in the signal and could be reduced by better shielding of the measurement circuit from EMPs. The relative uncertainty could also be reduced by using a resistive return current measurement instead of an inductive one, thereby requiring fewer steps of numerical integration.

As in the case of the scan of the focusing position described in Sec. III B, the time-resolved nature of the measurement here allows us to find the range of best compression with good confidence. Figure 9 shows the time-resolved amplitude of the pulsed return current under variation of the GDD. The current peak and tail hold an equal fraction of 50% of the total charge each, for the full scan. The current amplitude (with its full temporal evolution) is approximately symmetric about a GDD of (741 ± 80) fs², which overlaps in the margin of uncertainty with the corrected GDD for best compression in the laser focus of (712 ± 21) fs².

We detect a scaling of the return current with other key parameters of the particle spectrum such as number density and spectral temperature, besides the correlated drop in the spectral cutoff energy for the shortest pulses and the rise in cutoff energy at best focus. In the following, proton energy resolved spectra are compared with each other by fitting the experimental data with a 3D Maxwellian function $A/Ti3/2Eexp(−E/Ti)$⁠, where T_i is the temperature of the spectrum.

In the parametric scan of the GDD, the ion temperature exhibits a local minimum, while the return current and spectral ion cutoff energy exhibit minima. The ion temperature and number density are shown in Fig. 10. A minimum ion temperature in the spectral range of 0.5–7.0 MeV can be noted at a GDD of ≈(1000 ± 300) fs². The Maxwellian population and the integrated flux in the corresponding spectral range exhibit a slight drop at best compression, which is correlated with the cutoff energy. Best compression yields lower ion temperatures and only slightly varying populations, and thus more limited (narrow) ion distributions. This spectral tailoring can be useful, for example, in experiments devoted to proton–boron fusion, where the fusion cross-section peaks for low ion energies.

On comparing regions far from best compression, it can be seen that Maxwellian populations exhibit a rising trend from negative to positive GDD (the blue curves in Fig. 10), which can be seen in the cutoff energy as well. This effect has been attributed to the laser pulse chirp.⁹² 

Results from scanning in the focal displacement are shown in Fig. 11. Ion numbers show an overall dip around best focus consistent with a regime where larger foci yield a net gain of heated ions.⁹³ In detail, a slight local increase in ion population is revealed in the vicinity of zero displacement (see the solid and dashed blue curves), which is well correlated with the increase in the cutoff energy (red curve) and a local minimum in the ion temperature (black squares). This small local maximum is exceeded by a large global increase in population toward positions far from best focus. Consistent with a shrinking cutoff energy for large displacements, the ion number rises in a narrowing spectrum. The latter can be of advantage for experiments devoted to proton–boron fusion or other applications that require many low-energy ions.

Overall, on comparing results at maximum laser performance (best compression and best focus), we observe lower cutoff energies for 7 μm-thick copper tape than for 10 μm-thick aluminum tape. This is in qualitative agreement with (i) the expected smaller absorption efficiency for copper targets due to a reduced pre-plasma scale length for the heavier element and (ii) the expected greater scattering of electrons inside the target due to a higher areal density and collisional cross-section for copper. The smaller absorption efficiency on copper yields fewer hot electrons and therefore a weaker accelerating sheath field, which is further reduced by the larger area due to scattering.

We have demonstrated here for the first time that auto-generated kA-level return current through the target holder can be used as metrology for the performance of laser-driven secondary sources in high-repetition-rate PW-class laser systems. This method is independent of the experimental setup around the target system and provides a promising tool for irradiation experiments where sourced beams are absorbed. A good correlation between the spectral cutoff energy of laser-driven TNSA ion beams and the return current amplitude has been shown for laser defocusing and laser decompression, with Pearson linear correlations of up to 0.94 and 0.79, respectively. The method allows for bijective mapping and can thus be used to provide a control parameter in feedback systems. The amplitude peak can be used for Bayesian optimization, i.e., minimization in the case of laser-pulse compression and maximization in the case of laser-pulse focusing, to reach a reference point around the highest achievable intensities.

The method is indirect and entirely noninvasive, which makes it an ideal candidate for online stability monitoring. The close link between the return current and the hot-electron population will allow further development of this method for use with other laser-driven sources based on relativistic electron dynamics, such as electron, X-ray, XUV, and THz sources.

Time-resolved return current measurement provides a rich supply of information regarding the performance of secondary sources and target systems. It is also promising as an indicator for future machine learning algorithms.

This work would not have been possible without the help of the Laser and Engineering Teams at CLPU, CELIA, and PALS. Special thanks for much appreciated support go to the workshops of CELIA, CLPU, and PALS. This work received funding from the European Union’s Horizon 2020 research and innovation program through the European IMPULSE project under Grant Agreement No. 871161 and from LASERLAB-EUROPE V under Grant Agreement No. 871124, as well as from the Grant Agency of the Czech Republic (Grant No. GM23-05027M) and Grant No. PDC2021-120933-I00 funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR. The work was supported by funding from the Ministerio de Ciencia, Innovación y Universidades in Spain through ICTS Equipment Grant No. EQC2018-005230-P, further from Grant No. PID2021-125389OA-I00 funded by MCIN/AEI/10.13039/501100011033/FEDER, UE and by “ERDF A Way of Making Europe” by the European Union, and in addition from grants of the Junta de Castilla y León with Grant Nos. CLP263P20 and CLP087U16. The teams involved have operated within the framework of EUROfusion Grant No. AWP-ENR-IFE-CEA-01 “Magnetized ICF.” Views and opinions expressed are, however those of the authors only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

The authors have no conflicts to disclose.

M.E. and I.-M.V. performed the data acquisition, curation and analysis. M.E. wrote the first draft of the manuscript. J.C., P.W.B., M.E., and T.B. commissioned the TCM device at PALS. J.L.H. organized the beamtime at CLPU. J.A.P.-H. implemented the “online” pulse duration metrology line and was in charge of the temporal measurements at high power and managed the laser beam optimization during the experiment. D.d.L. and R.H.M. managed implementation of the device. P.V. worked on CAD. M.E., D.d.L., and R.L. contributed to the conception and design of the study. E.F. performed the analysis and interpretation of the ion spectra. All authors were involved with the underlying experimental work. All authors contributed to manuscript improvement, and read and approved the submitted version.

Michael Ehret: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (equal); Investigation (lead); Methodology (lead); Project administration (equal); Resources (lead); Software (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Iuliana-Mariana Vladisavlevici: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (lead); Methodology (equal); Software (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Philip Wykeham Bradford: Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Jakub Cikhardt: Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Evgeny Filippov: Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jose Luis Henares: Funding acquisition (equal); Investigation (equal); Project administration (equal); Resources (equal); Writing – review & editing (equal). Rubén Hernández Martín: Investigation (equal); Methodology (equal); Resources (equal). Diego de Luis: Conceptualization (equal); Data curation (equal); Methodology (equal); Resources (equal). José Antonio Pérez-Hernández: Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Resources (equal); Writing – review & editing (equal). Pablo Vicente: Visualization (equal). Tomas Burian: Investigation (equal); Methodology (equal); Resources (equal). Enrique García-García: Methodology (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Juan Hernández: Methodology (equal). Cruz Mendez: Methodology (equal); Supervision (equal). Marta Olivar Ruíz: Investigation (equal); Methodology (equal). Óscar Varela: Investigation (equal); Methodology (equal). Maria Dolores Rodríguez Frías: Resources (equal); Supervision (equal). João Jorge Santos: Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Giancarlo Gatti: Project administration (equal); Resources (equal); Supervision (equal).

The raw data and numerical methods that support the findings of this study are available from the corresponding author upon reasonable request.