Reconstruction algorithm for the runaway electron energy distribution function of the ITER hard x-ray monitor

Hard x-ray (HXR) spectrometry in ITER can provide information about Runaway Electrons (REs) in tokamak plasmas. Non-trivial reconstruction techniques must be applied to study the Energy distribution of REs in tokamaks since the diagnostic signals are convoluted with the emission of bremsstrahlung radiation from REs reaching the detector and the detector response function. A developed tool, coupled with the PREDICT code, has been described in this report for reconstructing the Runaway Electron energy distribution function (REDF) from HXR spectrum. Bremsstrahlung emission spectra and the detector response function are utilized in a forward modelling process to generate synthetic HXR spectra for different test REDF to which artificial noise is added. These HXR spectra are utilized to reconstruct the REDFs that can provide information about the REs in the plasma. The reconstruction process has been applied to the ITER HXR Monitor configuration for the first time. The effect of reduced optical transmission efficiency is studied on the reconstruction process and the accuracy of the extracted RE parameters. The performance of the reconstruction process is also tested for different amount of photon counts to identify the minimum number of photon counts required for optimal reconstruction. Preliminary results of RE-current estimation using the reconstruction process are also presented.


Introduction
Disruptions in reactor-relevant tokamak like ITER can convert a significant fraction of the plasma current into runaway electron (RE) current when large electric fields are induced following the thermal quench [1,2]. In ITER, RE diagnostics have to be used to detect REs to assist the commissioning of the disruption mitigation system. Since the REs interact with plasma and vessel components and emit radiation through different physical processes such as bremsstrahlung radiation, synchrotron radiation over a wide range of wavelengths or energy, a variety of diagnostics are required to study RE parameters in present experiments. While there are several diagnostics for runaway electron detection, such as infrared and visible cameras, photoneutron detection, runaway electron probe, ion cyclotron emission from runaway beam etc, runaway electrons are primarily detected by HXR monitor/spectrometer in tokamaks. In ITER also, the HXR monitor is a primary diagnostic for RE detection [2,3,11,12]. When the energetic electrons interact with the plasma components or the first wall components, x-ray photons are emitted which can then be detected by using standard scintillation counters. Although direct measurement of the HXR energy distribution can be obtained by a pulse-height analysis, it does not represent the underlying runaway electron energy distribution function (REDF) . This is because the photon spectrum is convoluted by the ion charge-dependent bremsstrahlung emission by the electron energy distribution in the plasma along with the detector response function. It is also affected by the detector geometry, shielding or in presence of a filter and the solid angle formed by the field of view of the detector. Obtaining the electron energy distribution function by unfolding the Hard x-ray spectra belongs to an ill-posed linear class of problems that require non-trivial reconstruction techniques [4,5].
Such an inversion technique has been applied for the reconstruction of the source electron flux spectrum integrated over pitch-angle from experimental hard x-ray spectra. In this report, we focus on validating the reconstruction technique and checking its consistency for various realistic REDF(s) by conducting 'blind' reconstruction experiments. The developed reconstruction tool can provide additional insights into the presence of runaway electrons in ITER discharges and can aid in testing the effectiveness of mitigation systems. Previous studies on studying RE parameters using reconstruction from HXR signals have been done on other tokamaks such as DIII-D [6], JET [5], ASDEX Upgrade [7], FT-2 [8], TUMAN-3M [9]. In this report, the reconstruction process has been carried out for the first time for the ITER HXR diagnostic, considering a proposed La-GPS:Ce scintillator crystal [10]. We have shown that the developed tool can fulfil the requirement of maximum RE energy determination for ITER plasma measurements requirement [11,12] as well as help determine the total beam energy of the runaway electrons present in the plasma. The dependence of the reconstruction process on the total HXR photon counts is also tested. A threshold is obtained above which the reconstruction process can determine the maximum RE energy with the required accuracy in ITER. Preliminary results of the determination of the RE current from the reconstructed REDF have been shown. The developed tool described in this report has been coupled with the PREDICT code [3,13] for bi-directional modeling of REDF and diagnostic signals modelling.
The ITER HXR monitor has a reduced optical transmission efficiency due to the requirement of the design of the diagnostic to withstand harsh environmental conditions such as high heat and electromagnetic loads, high magnetic fields, ultra-high vacuum compatibility, and nuclear radiation loads [3,14]. Therefore, we study the impact of reduced optical fiber transmission efficiency on the reconstruction process, which significantly modifies the measured spectrum [14,15]. The reconstruction algorithm can also be applied in remote gammaray spectrometer measurements that also have to operate in harsh environments such as nuclear sites that operate with a reduced optical transmission efficiency.
The rest of the report is structured as follows: the 2nd section describes the forward modelling procedure that has been implemented for generating synthetic HXR spectra for test REDF. The 3rd section discusses the implementation of the reconstruction algorithm. The results of the reconstruction method are applied to an experimentally measured Cs-137 spectrum in the 4th section for validation. The reconstruction of REDF from HXR spectra generated from different possible shapes of test REDF are shown in the 5th section. The 6th section deals with the performance of the reconstruction process taking into account the optical transmission efficiency of the ITER HXR monitor design. The 7th section deals with various aspects of the photon counting statistics of the detector in regards to the reconstruction process. Preliminary results of RE current estimation through the reconstruction process have been discussed in the 8th section .The 9th section summarizes the report and lists prospective improvements and other applications of the reconstruction method.

Forward modeling
In the case of the thin-target bremsstrahlung from confined REs, the runaway electron energy distribution function (REDF) is an important input quantity to estimate the photon energy spectrum as measured by the detector. In this report, a synthetic diagnostic method described in [10] has been utilized. The model implemented in [3,10] can be mathematically represented by equations (1), (2) for a single Line-of-Sight (LOS) as: . A det is the projection of area of the detector that receives that emitted photon flux, W det is the solid angle observed by the detector that depends on the collimators and apertures in front of the detector. The integral ò dl integrates the bremsstrahlung photon flux over a chord of length l of a detector line of sight. n i is the plasma ion density where i denotes the plasma and impurity ion densities and n e is the free electron density.
In this report, we assumed the HXR spectrometer diagnostic configuration for ITER as reported in [10] except the diagnostic first wall thickness in the front of the detector i.e. ∼25 cm. A 2.5 cm thick stainless-steel housing is considered for a La-GPS:Ce scintillator crystal having diameter (Φ) 2.5 cm and length 2.5 cm. The detector views plasma in radial direction i.e. collimated field of view (FOV) of the detector is  90 w.r.t. toroidal magnetic field direction (B T ) as shown in figure 2.
The major radius is assumed to be = R 6.2 m, 0 minor radius, = a 2.0 m, has been chosen and the RE beam is assumed to be centred at the geometrical axis with a beam radius of = r 0.25 m RE and the optical transmission efficiency η is selected as 0.05 % [14]. The RE beam current is taken as 10 kA for assessment of the HXRM system sensitivity which is 0.1% of the 10 MA RE current expected during the plasma disruption scenario. The cross-sectional area of RE-beam is calculated from the field of view (FOV) of the detector projected on plasma through an assumed 22 mm slit corresponding to detector diameter of Φ2.5 cm and ∼25 cm thickness of DFW [10]. The transmission efficiency of photons through the Stainless Steel-316 l housing,  figure 1. The transport spectra (equation (2)) for the following parameters for several emitted mono-energetic REs and the detector response function for several incident HXR-photon energies have been shown in figure 3.
The optical path of the ITER HXR monitor design is shown in figure 4. Due to reduced optical coupling of the components in the signal path between the scintillator and the photo-multiplier tube (PMT), the deposited photon spectrum will be significantly modified [14]. This is the result of statistical fluctuations associated with collection of photoelectrons in the PMT [18]. This is taken into account in the forward modelling procedure by artificially modifying the detector response function with the following procedure. Each photon bin count in the detector response function is assumed to have a gaussian distribution with a mean of the deposited photon energy and a standard deviation calculated from the expected energy resolution of the La-GPS:Ce scintillator A crystal system shown in figure 5. The gaussian corresponding to each detector response function bin is then summed up to generate a modified detector response function. An example of the modified detector response function is shown in figure 6. This modification of the measured spectrum due to reduced optical coupling has also been observed experimentally for a prototype ITER HXR monitor experiments as reported in [3,14]. Ideally, the detector response function is normalized i.e. ( ) which implies that all the emitted photon counts will be deposited at the detector. However after the modification mentioned above, this normalization does not necessarily hold. Instead low energy deposited photons are less likely to be detected. Physically, this lower detection probability corresponds to the counts of deposited photons falling below the noise threshold level of the PMT and the electronic circuit. The noise in the PMT arises from dark pulses and is det maximum in the low energy regime [19]. This is also taken into account in the forward modelling procedure by assuming that all photons below 0.5 MeV will not be measured. Since photons having deposited energy less than 0.5 MeV are no longer considered, the detector response condition does not hold i.e. ( ) det is plotted as a function of emitted photon energy ( ) ¢¢ E in   . The cut-off at 0.5 MeV has been chosen since it was observed that the reconstruction process was not accurate for RE energies below 0.5 MeV. However, at a later stage, the estimate of deposited photon counts below the noise level can be improved by taking the measured dark pulse spectrum directly into consideration. The implications of the lower optical transmission efficiency, the modified HXR spectrum and consequently the reconstruction algorithm are discussed in section 6.
As an example, synthetic hard x-ray spectra were generated using forward modeling according to equations (1), (2) as shown in figure 7 for a single test REDF.

Reconstruction algorithm
Equation (1) can be written in the form of a simplified integral as where ( ) F E is the experimentally measured HXR spectrum and ( ) ¢ U E is the confined RE energy distribution function in the plasma. ( ) P E is the counts-dependent Poisson noise in the system that arises due to photon counting statistics [18]. The matrix ( ) ¢ R E E , relates the photon energy spectrum measured by the instrument for a given RE of energy ¢ E . It can also be written as the matrix product of the transport spectrum (equation (2)) and the detector response function as: The integral in equation (3) can be discretized as: The process of obtaining the REDF requires estimation of electron energy distribution function U for known hard x-ray spectra F and response function R. The reconstruction is non-trivial because the matrix R is often nearly singular and poorly unconditioned which can lead to unnatural fluctuations in the inverted spectra. If the matrix R is not square, direct reconstruction is not possible in the first place. A simple least square method [3] was earlier implemented which was able to invert the HXR spectra in figure 7 and is shown in linear y-scale in figure 8. However the method was accurate only if the matrix R did not take the detector response function into account i.e. ( ) , .

B
The failed result is also shown in figure 8. Instead, methods such as linear regularization [4], Singular-value decomposition (SVD) [20], Maximumlikelihood fitting by Expectation-Maximization (ML-EM) [5,7,21,22] could be used for the reconstruction process. It was shown in [4,23] that the iterative ML-EM method provided the most accurate reconstruction for gamma-ray spectrum reconstruction. The iterative reconstruction algorithm for equation (5) can be written as [5,24]: ( ) Here p denotes the iterations of the ML-EM algorithm. The algorithm is initialized using an approximate guess The initial guess utilizes the shape of the HXR photon spectrum with a shifted magnitude as shown in figure 9. The initial guess, which depends on the HXR spectrum, will have non-zero values only up to the energy bin where a single photon count is registered as shown in figure 9 but the reconstruction process requires arbitrary non-zero value to iterate upon. For this, different exponential functions were fitted to the HXR spectra for energy bins where no counts were observed. However, this scheme was later discarded since no single fit was found to provide consistently better reconstruction results. A possible reason is attributed to providing a manipulated HXR spectrum that would affect the inversion process and deviate the reconstructed REDF from the true REDF.
The iterations can be run until a pre-specified threshold residue is obtained and otherwise for a finite number of iterations. At every step of the iterative process, only non-negative values for the inverted spectra elements + U p 1 are considered which only allows physically consistent solutions of the inverted REDF. On using the reconstruction algorithm on the HXR photon spectrum in figure 7, the reconstructed REDF is found to match the test REDF with marginal error as shown in figure 11. The RE energy and HXR photon energy axes were evenly split into 256 steps between 0.5 MeV and 30 MeV.
To minimize the propagation of noise from an experimental hard x-ray spectra in the approximate guess U 0 to the final inverted spectra, a smoothening procedure is carried out every l th iterations. To find an optimal value of l and its variation with the number of iterations, both the variables were varied and the mean squared error between the reconstructed and the true REDF was calculated and is shown in figure 10.
It can be seen that an optimal value of = l 100 can be chosen for the lowest deviation. However, this value should not be considered universal since it varied for other test functions as well as the method for smoothening. Since the main role of the smoothening method was to remove noise propagation from the approximate solution, a moving-mean smoothening method was implemented for the inversion process. The smoothening process also played a secondary role in filling in values in empty energy bins which eliminated the need for extrapolating the HXR spectra by exponential fits.
An important feature of the REDF is the maximum RE energy ( ) E .
RE max While REs in the high energy end of the REDF can have a large amount of energy, they carry no physical significance as long as their population density is significantly low. Instead, we propose to define E RE max as the maximum energy bin whose corresponding RE population's contribution to the total beam energy is less than 0.1%. Here, the total beam energy is defined as The proposed cut-off provides a better threshold to test the results of reconstruction algorithm in determining E RE max relevant for experimental purposes E RE max for the test function in figure 11 is indicated by the vertical black dashed line. REs having a higher energy than E RE max won't have any significant contribution to the total RE beam energy in the plasma. The ITER RE parameter measurement requirements: maximum RE energy and RE current [11,12] are listed in table 1.

Experimental validation and benchmarking with DeGaSum
The RE energy range of interest to test the reconstruction algorithm is between 0.1 MeV and 100 MeV which covers the wide range of REs that can exist in the tokamak plasma scenarios [5,8,11,12,25,26]. REs also emit photons on Bremsstrahlung interactions over a wide range of energies as shown in figure 3. To validate the algorithm, a g photon source with a known energy was utilized. While the photons generated from bremsstrahlung emission are HXR photons, their interaction with the detector will be identical as long as they have similar energies. Hence g photon sources can be used to validate the reconstruction algorithm. In line with previous work on REDF reconstruction [5,8,22,25], we're using a Caesium source to validate the reconstruction algorithm. The results of the reconstruction are also compared with a well-established reconstruction code, 'DeGaSum' for benchmarking purposes. DeGaSum has been applied on various tokamaks' HXR signals such as ASDEX Upgrade [7], FT-2 [8], TUMAN-3M [9], JET [5], Globus-M [27] and has also been experimentally validated with different g photon sources [5,22,25]. The reconstruction process was applied to the photon spectra generated from Caesium 137 (Cs-137) source experimentally measured using a La-GPS:Ce scintillator crystal as shown in figure 12. Cs-137 has a characteristic photo-peak emission at energy 0.662 MeV which falls in the Hard x-ray photon energy regime.
The source was kept 280 cm away from scintillator crystal and counts were integrated for time period of 1000 s [3]. For the reconstruction of the emitted photon spectrum from the Caesium source, the matrix R was replaced by D det and hence the reconstruction result provided the emitted spectrum which is shown in figure 13. The reconstruction result is also compared with DeGaSum and good agreement is found in the photo-peak of the deconvoluted spectrum. The marginal deviation for the reconstructed spectrum on the low energy side of the peak is attributed to the selection of photon energy bin resolution.

Reconstruction results
In experiments, the HXR spectra will differ from the spectra obtained in figure 7 due to statistical noise and as high-energy bin photon counts cannot be less than 1. So in the next step of the forward modelling process, only photon counts greater than 1 were retained. Additionally, Poisson noise was artificially added to the spectra randomly using a randomized weight according to = D  F F F 1 [18] , where ( ) F E are the photon counts in each photon energy bin and DF is the absolute error associated with counting statistics, to simulate a realistic HXR spectra as shown in figure 14. This shows that in reality, the maximum energy of the measured photon energy, E , HXR max is significantly less than the maximum energy of the test and reconstructed REDF, E RE max and hence should not be directly taken or interpreted as a measure of the maximum confined RE energy in the plasma as also indicated in [28].
B d e t Figure 9. Test REDF (blue solid) and initial guess, U , 0 for reconstruction algorithm (red-dashed).
Finally, the reconstruction algorithm is applied to the photon-counts mean data points in figure 14 and an inverted REDF is obtained. To conduct a blind test, no prior information about the test REDF is provided to the reconstruction algorithm. The inverted REDF is compared with the original test function in figure 15 (top). On forward modelling the reconstructed and the test function, the comparison between the synthetic Hard x-ray spectra are shown in figure 15 (bottom).
The test REDF in figure 7 was selected since it has been theoretically simulated by Fokker-Planck solvers [29,30,36] as well as experimentally reconstructed [31,32] and has non-monotonic features which should be captured during the reconstruction process. It has been simulated using equation (8).
A similar procedure was carried out for different shapes of the test functions and the reconstruction results for the same are shown in figure 16. The comparison is shown in log scale to show the matching of REDF over a wide range of RE density and in linear scale to show the matching in energy regions of high RE density which primarily affect the total beam energy. The test functions in figure 16 were selected for the following reason: (B) in figure 16 corresponds to a realistic 'mono-energetic' RE beam which was also indicated in [26]. It has been simulated using equation (9). figure 16 was previously used for benchmarking purposes in [25] and has been simulated using equation (10). figure 16 corresponds to an analytical approximation of the REDF [33] that is calculated from the Fokker-Plank equation applicable during plasma disruption scenarios which are of primary concern in ITER [1]. It is calculated using equation (11) c here E is the electric field and E c being the critical electric field for the RE-generation, , is the Coulomb logarithm, p max is the maximum energy of REs and s p is the width of the REDF in the momentum space. The distribution is normalized according to: The parameters selected for figure 16(D) The 2D distribution function calculated from the analytical approximation in [33] is plotted in with respect to RE energy and pitch angle. It is then integrated with respect to pitch angle and plotted in figure 17 (right). The REDF in figure 17 (right) is also similar to the shape of the REDF that is fitted to multiple experimental diagnostic signals in [34] but with a different total RE density. The two REDFs are compared in figure 17 (right). Figure 11. Comparison of test REDF (blue, solid) and reconstructed REDF (red, dashed) from HXR spectra obtained in figure 7 using , .

det B
* Black dashed line shows E RE max estimated using the criterion described in this report.   [11,12] with the described reconstructed tool. The reconstructed E RE max may deviate within an acceptable range, either slightly overestimating (figures 16(C), (D)) or underestimating (figures 16(A), (B)), depending on the shape of the test function.

Effect of optical transmission efficiency
To study the effect of optical transmission efficiency on the reconstruction process, a comparison is carried out for the reconstruction process with optical transmission efficiency of 0.05% and 21% [14]. As mentioned in Figure 13. Measured photon spectrum (blue); Normalized reconstructed emitted photon spectrum (red); Normalized reconstructed emitted photon spectrum from DeGaSum (yellow). Figure 14. Realistic HXR spectra obtained after cutting off counts at 1 and adding error associated with photon-counting statistics. [31,32] section 2, a lower optical transmission efficiency modifies the HXR spectrum. Figure 18 shows the comparison of HXR spectra for two different optical transmission efficiency generated for the test function in figure 7.
Applying the reconstruction process to the HXR spectrum generated for optical transmission efficiency of 21%, the reconstruction results are compared in figure 19. This is an important result for ITER HXR monitor system as the optical fiber system that has been proposed [14] lowers the optical transmission efficiency to ∼0.05%. However, it is shown that a decrease in optical transmission efficiency does not affect the reconstruction process significantly and E RE max can be deduced accurately. Additionally, the reconstruction algorithm was also applied to the modified detector response function to check if the original response function could be recovered. The results of this are shown in figure 20. It can be seen that while the shape is not exactly captured, the energy peak information is recovered. Hence the reconstruction algorithm could be applied to a photon spectrometer system with a reduced optical transmission efficiency to recover more information about the deposited spectrum. These performance assessment results are important for the ITER HXR-monitor for calibration purposes and may find their possible application for calibration purposes to recover energy information using a calibration source. Additionally, this approach can also be applied to gamma-ray spectrometer measurements that are carried out in harsh environments such as nuclear sites where measurements have to be performed remotely. The measured spectrum is modified when using optical waveguides [14,15] and the reconstruction tool can enhance source information extraction when absent from direct spectral measurement.

Effect of counting statistics
The errors in photon counts due to counting statistics translates over to the reconstructed REDF as multiple REDFs can generate a HXR spectrum that can fall within the error ranges of the counts. To estimate the error in the reconstructed REDF, a Monte-Carlo analysis is done as described in [35]. It is assumed that the photon counts corresponding to discrete energy bins lie at the mean of a Gaussian probability function whose width corresponds to the experimental error for that bin. Different points are randomly sampled for all the energy bins which are used to create artificial HXR spectra. This process is carried out N times to create multiple artificial HXR spectra to which the reconstruction process is applied. 5 such artificial HXR spectra and their corresponding reconstructed REDF are shown in figure 21.
The mean of all the reconstructed spectra can alternatively be taken as the reconstructed REDF while the standard deviation ( ) s is calculated in each bin in RE energy space and forms the error bars. The results of the error analysis is applied to test REDF (A), (B) in figure 22. The test REDFs in figure 16 generate ∼5000 counts per second during the forward modelling process. In the scenario of high RE presence in the plasma, the maximum counting rate of the La-GPS:Ce scintillator crystal would reach the order of 10 6 counts per second. Beyond that, scintillation pulse pile-up events can saturate the detector. Hence the reconstruction of the REDF can be carried out every millisecond with sufficient accuracy and E RE max can be determined accurately every 1-2 millisecond which satisfies the 10 millisecond time resolution requirement of ITER. Nevertheless, the deviation in estimating E RE max is studied by changing the total counts under the HXR spectrum for the test function (A) in figure 16. Figure 23 shows the variation of determining E RE max taking into the error bars associated with the reconstruction process. It can be seen that the deviation decreases as a function of total counts in the HXR spectrum and E RE max can be determined accurately when 300  counts are accumulated.
In case of a poor resolution in the HXR photon spectrum binning process, the number of data points available for reconstruction would be reduced. The effect of variation of the number of discrete bins of RE energy ( ) ¢ E and HXR photon energy ( ) E is studied for the test function (A) in figure 14. The error in determining E RE max is used as the metric for determining the effectiveness of the reconstruction method and is shown in figure 24. It can be seen that E RE max can be determined more accurately for a higher number of RE energy ( ) ¢ E as well as HXR photon energy ( ) E bins. This result can also assist in deciding an optimal bin size if the reconstruction process is carried out in real-time for plasma control purposes. While less number of bins lead to computationally faster reconstruction, there is a loss in E RE max that should be considered.

Estimation of RE current from reconstructed REDF
The RE current can also be determined by integrating the electron flux in the reconstructed REDF as v c is the normalized RE velocity, e is the charge of the elctron, c is the velocity of light and A RE is the RE beam radius ( figure 2). Estimation of RE current from the reconstructed REDF is carried out and compared for different test REDF in figure 16 assuming a RE beam radius of 0.25 m. The RE current in the test function is calculated assuming that electrons above 100 keV energy are REs. To compensate for the lower energy cut-off in the reconstructed REDF, the RE density in the low energy region is assumed to be equal to the RE density in the lowest energy bin of the reconstructed REDF and is shown in the third column in table 4.
The results summarized in table 4 show that the types of REDFs studied herein, the percentage deviation of RE-current estimated by the present reconstruction process remains essentially <30% under the assumptions of confined RE beams with an assumed cross-sectional area A . RE Thus, based on the assumption of A , RE the tool can fulfil the required accuracy of RE-current measurement as defined under measurements requirement of RE parameters in ITER [11,12].

Summary
A tool for reconstruction of the REDF from hard x-ray photon spectra for the ITER HXR monitor design has been developed and presented in this report. The reconstruction tool was validated on an experimentally measured Cs-137 spectrum to obtain its characteristic photo-peak and the results are also benchmarked with the DeGaSum algorithm with good agreement in the photo-peak emission energy. Synthetic HXR spectra from test REDF were generated using a forward modeling technique and noise was artificially added to these spectra. The developed tool could reconstruct the REDF from the realistic HXR spectrum with minor deviations. The reconstruction process is applied to different test REDFs which have been derived analytically in literature or experimentally fitted. A criteria is proposed to define the maximum RE energy based on the total RE beam energy content. With sufficient HXR photon counts, the reconstructed REDF's beam energy is recovered with less than 5% deviation while the maximum RE energy is determined with less than 20% deviation for all REDFs. The effect of reduced optical fibre transmission efficiency, that is relevant for the ITER HXR monitor design, has been studied on the reconstruction process and is shown to not affect the process significantly. Various effects of  photon counting statistics on the reconstruction process have been studied. It is shown that above ∼100 counts, the tool can be utilized to determine the maximum energy of the confined REs in ITER plasma scenarios using the HXR monitor under assumptions of HXR photon transport processes involved in, RE-beam size and relative position, and geometrical configuration of the detector. RE-current estimation has been carried out from the reconstructed REDF and is shown to match the test RE current with a reasonable accuracy.
At a later stage, the decrease in integrated deposited photon probability will be better estimated taking into account experimental measurements of dark pulses. A similar procedure is under development to perform the reconstruction of the REDF at higher energies from the synchrotron emission spectrum emitted by Runaway Electrons. The developed tool coupled with the PREDICT code will be utilized for source-to-signal simulations of HXR signals from RE in realistic ITER plasma scenarios and also for other tokamaks.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.

Disclaimer
The views and opinions expressed herein do not necessarily reflect those of the ITER Organization, France, Institute for Plasma Research, India, and Ioffe Institute, Russia. This publication/report is provided for scientific research and academic purposes only.

Conflict of interest
The authors have no conflicts to disclose.