Compact in-vacuum gamma-ray spectrometer for high-repetition rate PW-class laser–matter interaction

In recent years, advancements in laser technology across the globe have led to an increase, not only in power levels, but also in repetition rates. Presently, several facilities are capable of delivering PW class laser pulses at intervals of a few minutes to seconds.^1–5 For instance, the L3 laser at ELI Beamlines in the Czech Republic can generate 0.5 PW shots at a frequency of 3.3 Hz.¹ Similarly, the BELLA PW laser at the Lawrence Berkeley National Laboratory (LBNL) can deliver 1 PW shots at a repetition rate of 1 Hz.⁶ This surge in statistical data presents exciting opportunities for the laser-plasma community, but it also necessitates corresponding advancements in diagnostic tools.

It is crucial that detectors are compatible with the new energy ranges of produced particles^7–14 at these new intensity levels. In this range, the gamma-ray photons produced can provide insights into topics like the production of gamma-ray bursts in astrophysics,^15,16 radioactive waste management,¹⁷ and the production of matter through photon–photon collision as theorized by Breit–Wheeler.^18–24 There is also significant industry interest in the reliable and well-characterized production of high energy photons, which can penetrate matter more efficiently and be used as non-destructive probes.^25,26

While several methods exist to produce high energy photons,^17,27–31 the Direct Laser Acceleration (DLA) method^10,13,14,32 has promising laser-to-photon conversion in the range of several percent of gamma-ray emission. The described method involves accelerating electrons to relativistic speeds within a medium of near-critical density, defined as a threshold density above which the incident laser is predominantly reflected with the equation $nc=meω024πe2$ using ω₀, the laser’s frequency, m_e, the electron’s mass, and e, its charge. The ponderomotive force pushes electrons along the laser axis, generating a strong azimuthal magnetic field. This magnetic field then alters the electrons’ trajectories, bending them in the transverse direction. Such bending of the trajectories induces a synchrotron-like emission. This leads to a bright emission of high-energy gamma-rays. At PW levels, gamma-rays up to a few MeV (for 0.5 PW laser pulses) to hundreds of MeV (for 10 PW laser pulses) can be produced.^10,33

In order to conduct these experiments, we need to design a diagnostic tool suitable for these high energies. Adapting current photon spectrometer designs to this high-energy spectrum presents some challenges. For example, the design of x-ray spectrometers based on crystal diffraction^34–37 is impossible for these wavelengths (∼0.1 Å) as no crystal with sufficiently small interplanar distance exists. This necessitates the creation of a new detector type. Research in this new energy range has been ongoing for several years, leading to the development of various detectors.^38–44 These detectors usually utilize a pattern of alternating absorbers and Imaging Plates (IPs). By adjusting the thickness and material type of the absorbers, the energy spectrum can be unfolded. However, these stacking calorimeters have a significant limitation linked to the passivity of the detector. IPs must be analyzed between shots, a time-consuming process reducing the advantage of new high-repetition rate lasers without accumulating over several shots.

In response to this challenge, several research groups have developed active gamma-ray spectrometer designs.^45–48 By operating as both absorbers and detectors simultaneously, scintillators uphold the principle of energy deposition variation while also ensuring compactness and sensitivity. These spectrometers are usually located outside the interaction chamber, with the stack of scintillators placed directly behind a beryllium window or a thick aluminum flange. However, this additional obstacle can emit supplementary radiation or particles, creating difficulties in retrieving the original spectrum. Positioning the spectrometer inside the chamber helps in reducing this parasitic signal.

In addition, as interaction chambers continue to increase in size, centimeter-scale scintillators fail to cover the entire opening angle of the gamma rays, which is typically from 30° (∼500 mrad) for low energy photons to a few degrees (∼150 mrad) for the highest energy photons, as predicted for gamma flash experiments.¹⁴ Although increasing the size of the scintillators is an option, it is impractical to create very large windows due to pressure and cost constraints. In addition, this reduces the spectrometer’s adaptability, as the angular position will be only defined by the flanges and/or windows around the interaction chamber. As a result, we decided to focus on designing a spectrometer that can withstand the extreme conditions of an experimental chamber during PW-class laser shots. The chamber often houses multiple components, such as large optics, which can significantly limit the available real space for additional devices like detectors. To address this, we introduce the design of a highly compact gamma-ray spectrometer in this paper. The device has been engineered with dimensions of 20 × 20 × 25 cm³ and is particularly well-suited for high-repetition-rate experiments and adaptable to the rigorous environmental conditions characteristics of a laser-plasma interaction chamber (electromagnetic pulses, cleanliness, vacuum pressure, etc.).

This paper describes the design of the high repetition rate spectrometer suited for the extreme constraints of the PW-level interaction chamber in Sec. II. Section III elaborates on the methodology employed for unfolding the gamma-ray spectrum from the acquired spectrometer images. This process is crucial for translating the raw data into a meaningful energy spectrum. The paper follows with a discussion of the calibration process, outlining the strategies employed to align the experimental setup with the theoretical models. Finally, Sec. V reviews the installation and use of the spectrometer at the BELLA center, a PW-class level interaction facility, at LBNL (California, USA).

In this paper, gamma rays are classified as photons with energy >100 keV. To accommodate these high energies, the fluorescence properties of various materials can be used. Gamma-ray photons deposit some of their energy within these materials, thereby exciting them. The materials subsequently relax, emitting fluorescence photons generally within the optical wavelength range, which can be collected by a camera. By arranging scintillators in a stack configuration in the gamma propagation axis, the first layers act as detectors for lower energy gamma rays and at the same time serve as a filter allowing for the detection of only (ideally) higher energy gamma-rays in the deeper scintillators.

Energy deposition is primarily dependent on three factors: the energy of the incident photon, the material of the scintillator, and its thickness. As we aim to determine the photon spectra, we have two adjustable parameters: the material and the thickness of the scintillator. Different types of scintillators offer different absorption coefficients for varying gamma-ray energies. The spectrometer designed in this study is intended to be used in different experimental setups covering various energy ranges. Consequently, we employ several types of scintillators to widen the measurable energy range. The stack consists of three types of scintillators, each with different thicknesses tailored to their specific radiation lengths. Plastic scintillators, which have a high radiation length, effectively absorb low-energy photons but allow higher energy photons to pass through. Positioned behind them are YAG:Ce scintillators with a shorter radiation length, designed to detect these higher energy photons that the plastic layers do not absorb. At the end of the stack, CsI:Tl scintillators have an even shorter radiation length, making them capable of detecting the highest energy photons that have been through both the plastic and YAG layers. It is important to note that the transition in photon energy detection between each scintillator type is gradual, not a hard threshold.

The limited space within most interaction chambers led us to use a limited number of scintillators in a layered configuration adapted to the expected gamma-ray spectrum. Here, it includes two 2 cm thick SP33 polystyrene (plastic) scintillators supplied by NUVIATech Instruments, ten 5 mm thick YAG:Ce scintillators, and five 5 mm thick CsI:Tl scintillators, both provided by Advatech UK Ltd. The arrangement of the scintillators is illustrated in Fig. 1, and their properties are summarized in Table I. Note that this modular design allows for the individual scintillators to be readily interchanged, offering flexibility to accommodate a range of energy spectra as necessitated by different experimental requirements. The design prioritizes compactness to facilitate integration with various experimental setups. Nevertheless, this compactness comes at the cost of the configuration versatility. To mitigate this, one could envisage a spectrometer with a larger number of scintillators.

A critical factor in the spectrometer’s performance is the decay time of the scintillators, particularly the CsI:Tl, which has the longest one of 900 ns. This characteristic time can limit the maximum achievable repetition rate that can be used without signal overlap. Even if the scintillator hardware is far above the required characteristics, the camera becomes the limiting factor for the repetition rate achievable. As an example, the camera used here from Allied Vision, model “Manta Camera 507-B,” can only reach up to 23 fps but can be easily fixed with a high speed camera. With the current setup operating at a repetition rate of 10 Hz, the system is within the limits, ensuring clear temporal separation of detection events.

The fluorescence photons from the scintillators are collected using an optical camera combined with an f/2.8 objective to have a large field of view with a short focal distance, as the spectrometer height is only 20 cm. All faces are left ground except one polished on the crystal scintillators. Each scintillator is wrapped in Polytetrafluoroethylene (PTFE) tape, leaving the polished face exposed, to enhance photon collection toward the camera while maintaining sufficient spatial spacing for scintillator differentiation. To shield the camera from Electromagnetic Pulses (EMPs)^49,50 emitted during laser-plasma interaction, a 5 mm copper Faraday cage is installed around it. To protect the camera from the plasma self-emission (and any other parasitic light), a box composed of 2 mm aluminum sheets held by 90° clamps is positioned around the spectrometer. Using appropriate opto-mechanical elements, we meet cleanliness requirements, achieving a pressure of 10⁻⁶–10⁻⁷ mbar inside the interaction chamber and passing Residual Gas Analysis (RGA) tests. The spectrometer’s assembly, suited for installation within the chamber, is presented in Fig. 2.

Having underlined the hardware components of the detection system, attention must now turn to the process of data interpretation. The raw data captured by the camera requires a transformation to yield a meaningful gamma-ray spectrum. This transformation process, commonly referred to as “unfolding”, is essential to convert the digitized image data into a physically interpretable format. Unfolding is an important step in the experimental pipeline, as the quality of the algorithm directly impacts the accuracy and resolution of the resultant gamma-ray spectrum, thereby influencing the interpretation of the underlying physical phenomena. Given the complexity of the data and the risk for various sources of noise and distortion, the algorithm applied must be robust and meticulously validated to ensure reliable results. The method is presented in Sec. III.

In order to accurately reconstruct the energy spectrum of the particle source under investigation, several computational and data analysis techniques must be employed on the data captured by the spectrometer. These data are acquired using a camera, resulting in an image of the scintillators integrated over the interaction time. This image serves as a raw source of information and is directly correlated with the energy deposited within various scintillation materials. The latter can be calculated thanks to a Monte-Carlo code, taking as input the spectrometer’s configuration and particle’s energy spectrum.

To calculate the energy deposition in the scintillators, we employ a Monte-Carlo simulation approach using the FLUKA code.^51,52 This is complemented by the FLAIR software,⁵³ a visual interface used to effectively configure and visualize the FLUKA simulations. Together, they provide a robust framework for rebuilding the experimental setup in a virtual environment, thereby allowing us to account for material-specific interactions, scattering, and other complex phenomena that influence the observed data.

Previous articles used Bayesian statistic to unfold the spectrum. This method is reliable and very fast. However, this approach requires an initial hypothesis on the generating process, which has a quite large impact on the final unfolded spectrum. This is adequate when the photon distribution spectrum, such as that in Laser Wakefield Acceleration (LWFA), has been previously identified and validated.^54–58 However, for photon distributions that are either novel or not yet empirically verified, this method proves to be unsuitable.

Consequently, there was a need to refine the unfolding algorithm to eliminate the reliance on physical assumptions. A significant challenge arises from the numerous local minima encountered during the minimization process between the experimental data and the Monte-Carlo simulation’s energy deposition. This complexity renders traditional gradient-based optimization methods ineffective.

In order to comprehensively explore the entire variable space, stochastic methods emerge as the most viable option. These methods are better equipped to locate global minima, at the expense of increased computational time. This trade-off highlights the inherent complexity in refining the unfolding algorithm to accommodate a wider range of photon distributions without depending on predefined physical assumptions.

The covariance matrix adaptation evolution strategy operates as a stochastic evolutionary algorithm,^59,60 inspired by biological evolution, and iteratively enhances a population of candidate solutions based on natural selection and genetic variation principles. This method was, for our case, the fastest and most reliable stochastic algorithm. To give a simple idea of its working principle, a new population is created with its corresponding energy deposition pattern. The difference between the experimental data is calculated, and then a new population is created. The process is repeated until the best agreement is found.

The efficiency of an unfolding algorithm is determined by the creation of new populations from previous ones. The CMA-ES algorithm leverages the covariance matrix of each point on the unfolding spectrum to make informed guesses. Each point represents a dimension within the solution space. What sets CMA-ES apart is its emphasis on adapting the covariance matrix to capture correlations among variables in this space. This adaptation enables efficient searches for global optima by learning the shape of the fitness landscape, thereby significantly reducing convergence time.

The algorithm commences with an initial random population of candidate solutions, x_i, i = 1, 2, …, λ, where λ denotes the population size. Each candidate is a vector in the n-dimensional real-valued solution space.

To estimate the fitness function, as expressed in Eq. (1), a comprehensive understanding of two critical variables is essential: the experimental data (D) and the simulated data (S). In our experimental framework, the primary observable for the experimental data is the energy deposition. This necessitates the calculation of energy deposition from a known photon distribution, which will subsequently be utilized as our minimization variables.

The deployment of Monte-Carlo simulations at each iteration is way too computationally intensive. Each function evaluation within the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm, if reliant on direct calls to the Monte-Carlo code, could cumulatively demand several thousand CPU-hours. This high computational cost is primarily due to the intricate physics involved in the interactions of photons with the materials in the scintillators, as well as the need to accurately simulate the secondary particle generation and their subsequent interactions.

We can greatly reduce the computing time using the approximation that incident photons do not interact with the secondary particles generated within the scintillators. This assumption allows us to treat the energy deposition from a continuous photon distribution as a sum of energy depositions from individual mono-energetic photons. The response matrix (taking into account the aluminum shielding in front of the detector, which acts as a low energy photon absorber) for this detector is illustrated in Fig. 4.

The concept of the Response Matrix^38,46 (RM) emerges as a crucial tool in this simplified model. The RM encapsulates the relationship between the energy of mono-energetic photons and the resultant energy deposition in the detector. This relationship links the hypothesized photon distribution to the observed energy deposition.

Utilizing the fitness function as defined in Eq. (5), our optimization process, while convergent, gravitates toward “peak” solutions, where the spectrum exhibits high peaks with no physical meaning. To address this issue, we postulate that the measured distribution should exhibit continuity, implying it is either differentiable or, in this case, possesses a low difference at each point x_i.

Selecting an appropriate value for a_s is crucial for obtaining accurate results. If a_s is set too high, it results in overly flat solutions, whereas a too low value leads to solutions that emphasize peaks excessively. To determine the optimal a_s, we use an iterative process as follows:

1. Perform multiple unfolding procedures on a known distribution, each with a varying a_s.

2. Identify the iteration that yields the minimum mean error to determine the best a_s.

This method ensures that a_s is finely tuned to provide the most accurate representation of the underlying data distribution. Both datasets D and S are normalized to unity before applying the fitness function to maintain consistency and generalizability across different datasets. This normalization is crucial as it ensures that the impact of a_s remains consistent regardless of the scale of D and S, facilitating comparability across datasets and enhancing the robustness of our optimization strategy. As a result, a_s is set at 6.5 × 10⁻⁴. Note that this factor does not prohibit “peak” solutions, as will be visible in Sec. IV on the calibration unfolding.

In order to determine if the model is accurately unfolding spectra, several tests were performed. The first is taking a known distribution, here a synchrotron one, calculating the theoretical energy deposition inside the detector, and then unfolding the result to find back the original distribution. Typical unfolding results are pictured in Fig. 5. The unfolding usually takes about 30 s on a lab-grade laptop and uses around 200 000 function evaluations.

To compute the error, we used 500 different distributions, using Gaussian, bremsstrahlung, and synchrotron distribution, and compared it to the unfolded spectrum. The mean relative error was calculated, and a 2D interpolation was used to calculate a function that takes as input the position of the spectrum point in the energy space but also its value compared to the maximum. The standard deviation was also calculated on this relative error. The gray area corresponds to three times the standard deviation on the unfolding error. The blue error bar corresponds to the mean relative error applied to the unfolding data. By applying this process to different distribution functions, we can arrive at the limitations of the unfolding/measure. One of them is linked to the total energy deposited inside the detector. If one considers a 1 MeV photon and a 100 MeV photon, with a simple picture, the higher energy photon can deposit a total energy two orders of magnitude higher than the lower energy photon. This means that if now we have 100 1 MeV photons and one 100 MeV, the difference in total energy deposition will be negligible. Meaning there is an intrinsic measurement error linked to the number of photons in the energy bin considered compared to the total energy deposition per bin. In the range of 10 keV–1 GeV, the difference in energy deposited by photons does not exceed four orders of magnitude, leading to a maximum detection of four orders of magnitude between energy bins.

The unfolded spectra on simulated data gives accurate and promising results. Section III E focuses on experimental data unfolding.

In experimental measurements, noise can often be present in the signal, affecting the accuracy of the unfolding process. To address this, our method varies the measured pixel value as part of the CMA-ES minimization. By allowing these factors to vary within a small range, we can correct potential errors arising from the RM calculation.

To test the robustness of this approach, we simulate noise by adding a multiplicative factor to each scintillator layer, as described in Eq. (7). This noise factor is randomly sampled from a uniform distribution within the limits [−P₁₀₀, P₁₀₀]. For each noise level, we perform multiple iterations and compare the resulting unfolded spectra with the true spectrum, shown in red in Fig. 6.

The calculated energy deposited inside the scintillators used in Sec. III still needs to be converted into the actual data recorded, which is the pixel value of the camera used. This conversion is performed by using a set of calibration factors.

In our specific case, we opted to use sources with activities in the TBq range. After careful consideration, a ⁶⁰Co source was selected for its suitability for our experiments. This source has an activity of 0.185 TBq and emits photons with two dominant photopeaks at energies of 1.173 and 1.332 MeV. The experimental setup was placed at a distance of 1 m from the source, which has an opening angle of 11° (∼200 mrad).

Data acquisition was executed under varying conditions of gain and exposure time to optimize the sensitivity and dynamic range of the camera. A typical scintillation image obtained from this setup is shown in Fig. 7.

Upon the successful completion of the data acquisition phase, we proceeded to start the comparative analysis between our experimentally derived data and the simulations generated from FLUKA. The beam card ISOTOPE was used along with the DCYSCORE, HI-PROBE, and RADDECAY. Then the air kerma rate was calculated using USRBIN scoring DOSE-EQ⁶¹ and compared to the calibrated air kerma rate of the facility. The number of photons hitting the detector is referred to as the theoretical number of photons in the following. This comparison was critical for the extraction of the calibration factors key metrics defined in Eq. (8).

To further refine the data and mitigate inconsistencies or inhomogeneities, we applied a statistical treatment to the acquired pixel values. Specifically, the mean pixel value was calculated for each individual scintillator in the stacked array, reducing the number of outliers, which can make comparison with simulations more difficult. The calibration factors are then calculated using the ratio of the experimental data to the FLUKA output taking into consideration the activity of the source.

These quantifications, which represent the photon-to-pixel value conversion efficiency, are crucial for the accurate interpretation of the energy spectrum deduced from the observed data. This means that every FLUKA output will be multiplied by the calibration factor specific to each scintillator before trying to compare it to the experimental data. This way it is possible to retrieve the original data using the FLUKA output and calibration factors presented in Table II.

Figure 8 presents the unfolding result. The unfolding process does not introduce any bias toward any specific feature configuration other than the smoothness of the spectrum. It begins with a completely random uniform distribution, iteratively refined as described in Sec. III. Remarkably, this method converges to a double-peak distribution, demonstrating the robustness of the algorithm. However, it is worth noting that the actual energy feature values are slightly offset. This discrepancy is due to the presence of small components in the detector, such as screws and posts, which are not accounted for in the FLUKA simulations.

To enhance accuracy, a second calibration using a simpler design was performed. The aluminum box was swapped for polyether ether ketone (PEEK), and every posts, clamps were removed. The corresponding unfolding is shown in Fig. 9.

This new calibration underlines the importance of the match between the FLUKA simulation and experimental setup. This method is the first for this design able to resolve two close photopeaks with such accuracy with this type of detector.

In order to test the spectrometer in real conditions, we participated in an experiment at the BELLA Center at LBNL. The laser was operated at ∼0.2 PW after compression with ∼0.13 PW on target after reflection from a double plasma mirror setup. Shots were performed on foam targets for ion acceleration and radiation generation.⁶² The spectrometer, using aluminum as a black box, was successfully implemented, and the corresponding acquired data are discussed hereafter.

The experimental configuration is illustrated in Fig. 10. Utilizing a ∼50 fs pulse, which was focused by an f/2.5 OAP,^2,63 we achieved a focal spot size of ∼3 μm at $1e2$ and delivered an energy of ∼4 J onto foam targets of density ∼20 mg/cc and ∼40 μm thickness. Foam targets⁶⁴ specifically manufactured such that the total density is close to the critical density while maintaining solid properties. The shots resulted in the emission of photons, which were directed along the laser axis where the spectrometer was positioned. The experiment yielded multiple images; an example is shown in Fig. 11.

These images demonstrate that it is feasible to acquire gamma-ray data within a PW-class interaction chamber using active elements, even in the presence of EMPs and strict cleanliness requirements. However, the experiment utilized relatively thin shielding (2 mm of aluminum), and no electron spectrometer was employed. Consequently, the detected signal may contain contributions from both electrons and photons, necessitating certain assumptions to interpret the measurements accurately.

In Fig. 12, an example of the energy responses of various particle types is compared with the experimental data. It is evident that, to reproduce the first peak observed on scintillator 2, photons with an energy of 100 keV must have been measured. This feature cannot be replicated by electrons above 100 MeV, as lower-energy electrons are deviated by the magnets. The second peak, observed on scintillator 12, presents a more complex scenario. The response of 140 MeV electrons (which can hit the detector due to the short distance between the magnets and the scintillators) is similar to that of 4 MeV photons, suggesting that this peak could be the result of contributions from both particle types. Note that, if 140 MeV electrons were produced, the bremsstrahlung process would inevitably generate photons with energies of at least several MeV.

These results highlight the importance of employing an electron spectrometer when using this type of detector for both deviating and precisely measuring the electron energy distribution. The experimental configurations must be first simulated to ensure that the distance between the magnets and scintillators is large enough to deviate up to 500 MeV electrons (for a 10 PW class laser shot).

In this paper, an active gamma-ray spectrometer suited for use inside a PW-class laser interaction chamber is presented for gamma-rays detection from 100 keV to 100 s MeV. This spectrometer offers several advantages in its design. First, by using a stack of different scintillators, it can reach a high repetition rate of up to 10 Hz, which can be easily increased by upgrading the camera model to a faster one. This design is modular, meaning each scintillator can be easily replaced for maintenance or swapped to meet the needs of energy analysis or precision.

The spectrometer’s compatibility with the extreme conditions of a PW-class laser interaction chamber, such as electromagnetic pulse (EMP) resistance, vacuum pressure tolerance, and maintenance of cleanliness, is ensured through a careful selection of materials and design.

This spectrometer has undergone a calibration process utilizing a radioactive source of ⁶⁰Co. We used the observed data compared to simulations to calculate the calibration factors used as conversion factors between simulations and real-world data. Even if the configurations can be easily adapted to the experimental needs, due to an unavoidable variation in the photometric response, surface sanding, and efficacy of wrapping, when scintillators are interchanged or move locations within the diagnostic, new calibration factors are needed to accurately interpret data from laser experiments. The simulations performed thanks to the Monte-Carlo code FLUKA allow us to calculate the energy deposition of any spectrum shape.

The unfolding performed thanks to a stochastic algorithm, the Covariance Matrix Adaptation Evolution strategy (CMA-ES), leads to the discrimination of two close photopeaks of the calibration source, a first with this type of detector.

The spectrometer has been successfully deployed during an experimental campaign at the BELLA Center of LBNL. The obtained results demonstrate the feasibility of recording gamma-ray data inside a PW-class interaction chamber with active elements, which had not been, to the best of our knowledge, performed yet. Then, by benefiting from high-repetition rate operation at state-of-the-art facilities, the errors and uncertainties of the measurement will be iterated down by recording more datasets for different experimental conditions and stack configurations. This possibility, impossible with low-repetition rate lasers and diagnostics, will allow us to compare 3D PIC simulations to the experimental data and lead to a better understanding of the physics that is at play during DLA and other gamma-ray generation processes.

We would like to acknowledge Hansen et al.⁶⁰ for the creation of the py-cma library used for this work. We would like to acknowledge V. Istokskaia, L. Giuffrida, B. Lefebvre, R. Versaci, and C. Lacoste for fruitful conversation regarding the design and unfolding method. We wish to acknowledge the support of the National Science Foundation (NSF Grant No. PHY-2206777) and the Czech Science Foundation (GA ČR) for funding on Project No. 22-42890L in the frame of the National Science Foundation–Czech Science Foundation partnership. The work conducted at BELLA was supported by the U.S. DOE Office of Science Offices of HEP and FES (incl. LaserNetUS) under Contract No. DE-AC02-05CH11231, the Defense Advanced Research Projects Agency via Northrop Grumman Corporation, and the U.S. DOE FES Postdoctoral Research Program, administered by ORISE under Contract No. DE-SC0014664.

The authors have no conflicts to disclose.

G. Fauvel: Conceptualization (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). K. Tangtartharakul: Investigation (equal); Writing – review & editing (equal). A. Arefiev: Writing – review & editing (equal). J. De Chant: Investigation (equal); Writing – review & editing (equal). S. Hakimi: Investigation (equal); Writing – review & editing (equal). O. Klimo: Writing – review & editing (equal). M. Manuel: Investigation (equal); Writing – review & editing (equal). A. McIlvenny: Investigation (equal); Writing – review & editing (equal). K. Nakamura: Investigation (equal); Writing – review & editing (equal). L. Obst-Huebl: Investigation (equal); Writing – review & editing (equal). P. Rubovic: Writing – review & editing (equal). S. Weber: Project administration (equal); Writing – review & editing (equal). F. P. Condamine: Conceptualization (equal); Investigation (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal).

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