Proton spectroscopy for 11B(p,α)2α fusion reaction with RCF films: calibration and unfolding procedure

The reaction occurring between protons and 11B isotope (p+11B → 3α+8.7 MeV) has recently attracted attention as a possible candidate to overcome the generation of high-energy neutrons via the more studied Deuterium-Tritium fusion reaction. Since the early 2000s, several experiments have been carried out to investigate the viability of triggering this aneutronic reaction in laser-target interaction schemes. During these experiments, the total number of escaping α particles is measured to infer fusion reaction efficiency. However, the accurate detection of α particles in such experiments poses a real challenge. In this scenario, RadioChromic Films (RCFs) arranged in a stack configuration can be used for the fluence and energy spectra reconstruction of generated protons, being this mandatory information in both “pitcher-catcher” and “in plasma” p-11B irradiation schemes. Nevertheless, RCF response exhibits a dependence on Linear Energy Transfer (LET), which leads to an underestimation of the response in high-LET conditions. This can result in dosimetric errors if not properly taken into account. In this work, an analytical procedure able to reconstruct the incident energy spectra in an RCF stack was developed and validated thanks to a calibration procedure that was established for high and low proton energy (4–60 MeV) beams to properly reconstruct the incident spectra in the “pitcher-catcher” irradiation scheme.


Introduction
Inertial Confinement Fusion (or ICF) is an energy production approach consisting of initiating a fusion reaction by compressing and heating a target filled with thermonuclear fuels (usually Deuterium and Tritium) [1].The fuel is compressed using many energetic laser beams, to more than 1000 times density of liquids within the time interval in which mass inertia keeps the burning fuel together.The required densities can be obtained by imploding spherical shells with radiation pressure, delivered by an external driver as X-Rays, ion beams, or high-power laser radiation [1].Recently, a renewed interest in ICF came from the major advance announced in August 2021 at the National Ignition Facility (NIF) of the Lawrence Livermore National Laboratory (LLNL) in the U.S.A. [2], where researchers were able to convert 70% of the laser energy (used to compress the fuel) into products of the Deuterium-Tritium (DT) fusion reactions, reaching the so-called burning-plasma condition.On the other hand, the Deuterium-Tritium approach face many technological and sustainability challenges: low availability of the Tritium itself and radiation damage and huge radioactivity induced in the reactor by the produced high-energy neutrons [3].Hence the scientific community is looking for the possible alternatives and neutronless fusion reactions.These are considered the Holy Grail for what is called the "third generation fusion power plants": they do not require radioactive reagents (as Tritium in the DT reactions), there is a high abundance of reagents, and they neutrons as the main channel.Among these neutronless fusion reactions [1], the proton-Boron nuclear reaction p + 11 B → 3 + 8.7 MeV is particularly attractive, being highly exoenergetic and because of the abundance of reagents in nature, neither of them being radioactive.Moreover, its only output is given by alpha particle radiation.These features make the p- 11 B reaction appealing for possible future fuels for nuclear fusion reactors as the recent interest of private companies also demonstrates [4,5].
It is also worth mentioning that the interest in the use of such a reaction, using a laser-triggered scheme, lies not only in the energy production but also in the possibility of developing a table-top, high-brilliance source of  particles that could be exploited for multidisciplinary applications [6][7][8][9][10][11][12][13] as, for example, irradiation station for radioisotopes production.
Nowadays, several groups have tried different laser-driven approaches, irradiation set-ups, and target materials to improve the alphas yield of the reaction with recent experiments, and have -1 -demonstrated the possibility of reaching up to 10 10 particles/sr/shot [14,15].Recently, the Europeanfunded COST Action "PROton BOron Nuclear fusion: from energy production to medical applicatiOns" (PROBONO) [16] has been established, with more than forty institutions participating worldwide.The major goal and ambition of the Action is to consolidate knowledge in the burgeoning field of laser-driven pB fusion to facilitate basic science studies, maximize the production of new knowledge, and achieve breakthrough discoveries.
One of the most challenging tasks in p- 11  fusion experiments is the capability to make an accurate quantification of the fusion products.The diagnostic of the generated plasmas and the produced radiation is, in fact, fundamental for the reaction characterization and the quantification of p-11  reaction rates.Here, the main problem consists in the correct discrimination of the generated protons and alphas [17] since protons are always present with stopping power values often overlapping with the alphas ones.Many diagnostic strategies have been developed, based on the use of solid-state detectors in time-of-flight (TOF) configuration, CR-39 track detectors, and Thomson-like spectrometers coupled with CR-39 [17,18].Other groups have proposed and are currently investigating the possibility of using gamma and/or neutron detection from other reaction channels [17,19] to retrieve information on the reaction and exceed the problem of alphas/protons discrimination.
Recently, researchers suggested the possibility of investigating the reaction not only with highenergy (MJ order) and low-repetition rate lasers, but also exploiting the characteristics of short-pulse (tens of fs), lower-energy (tens of Joules order), and high-repetition-rate laser systems [20,21].In this case, in addition to having diagnostics that work properly at the Hz level, having instruments capable of reconstructing the more energetic (up to tens of MeV) proton spectra present is critical, since this knowledge may aid in the identification of  ℎ particles.
Radiochromic Films (RCFs), arranged in a stack configuration, represent in this framework an essential diagnostic tool.When properly calibrated, they allow for the measurement of the proton energy spectrum by implementing the so-called unfolding (or deconvolution) procedure [22,23].The reduced Water Equivalent thickness (WET) of RCFs (hundreds of μm) enables the spectrum to be derived with an energy resolution of up to 200 keV (for 70 MeV protons and HD-V2 film).An important aspect to consider is that RCFs are not sensitive to the ion species and that they offer the possibility of isolating the proton component of the radiation field produced by laser-target acceleration systems [22].There are other advantages related to the use of these devices in the laser-driven acceleration and proton-Boron fusion context.First of all, RCFs are insensitive to the electromagnetic pulse (EMP) produced in the laser-target interaction region [23].For this reason, they can be located very close to the interaction point, allowing for the acquisition of the whole beam in a single shot.As a result, a 3D description of the beam can be obtained.By analyzing the 2D image of the particle distribution, it is possible to resolve angular distributions of proton energy as well.
Moreover, RCFs show a very large sensitivity range, spanning typically from 10 −3 Gy up to 10 5 Gy [22,24], and their response can be considered independent from the dose rate within 5% [25,26].On the other hand, RCFs exhibit a dependence on the Linear Energy Transfer (LET) of the radiation, showing an underestimation in the detected dose reaching the 20% near the end of the proton range [24,[27][28][29].
In this work, the validation of the unfolding procedure applied to a stack of RCFs irradiated with a laser-driven proton beam was performed.To quantify the impact of the LET dependence -2 -on the result of the unfolding procedure, a preliminary dose calibration of different RCF films (HD-V2, EBT3, and EBT3-Unlaminated type) with beams at different LET (in water) was performed.Irradiations were conducted at the Italian Institute of Nuclear Physics (INFN) in Legnaro (4 and 5 MeV proton beams, LET > 8 keV/μm), at the CATANA proton therapy facility of Catania (60 MeV proton beam, LET ≃ 1-4 keV/μm) and at the Policlinico Universitario "G.Martino" of Messina (6 MeV photon beam, LET ≃ 0.2 keV/μm [30]).These calibration curves were then used to estimate the energetic spectrum of a laser-driven proton beam acquired through an HD-V2 stack irradiated at the Eli-Beamlines laser facility [31].

Radiochromic films
RCFs are two-dimensional self-developing devices consisting of one or more active layers containing a microcrystalline monomeric dispersion deposited on a clear plastic substrate [22,23].Upon interaction with ionizing radiation, the active layer undergoes polymerization and changes its color from nearly transparent to blue [23,32].The extent of coloring depends on the absorbed dose and is characterized in terms of Optical Density (OD), defined as: where  0 is the light intensity detected for a non-irradiated film and  is the residual light intensity after passing through the irradiated one.The films must undergo digitization to extract quantitative data.In this context, both  0 and  are assessed in terms of pixel intensity values, specifically measured within a selected color channel chosen to enhance measurement sensitivity.The chosen region on each film for evaluating  and  0 is typically referred to as the Region Of Interest (ROI).
In this study, we employed three distinct RCF types: HD-V2, EBT3, and EBT3-Unlaminated (EBT3-U).Comprehensive specifications for each model are reported in table 1.In figure 1 the layer configuration of each different RCF is shown.
The RCF reading and analysis were carried out following the protocol outlined in [27].The scanner for detector reading had a resolution of 600 dpi and a dynamic range of 16-bit grayscale.The  and  0 measures were performed reading the signal in the red channel, following the manufacturer's recommended guidelines [26].

The unfolding procedure
As previously stated, an accurate measurement of the proton energy spectrum can greatly aid in predicting alpha particle emissions resulting from the 11 B(p, )2 fusion reaction.RCFs serve as valuable diagnostic instruments in this context.When appropriately configured, these devices enable the reconstruction of both the depth dose distribution and the energy spectrum of the incident proton beam by employing the unfolding (or deconvolution) method [22,23].For the reconstruction of the depth dose distribution, RCFs are used in a configuration known as a stack arrangement, where a series of  films are arranged consecutively [23,32].In this configuration, the incoming radiation hits perpendicularly the  films and each RCF acts as a filter for the following one.The total dose response  ( ) tot of the  th RCF ( = 1, . . ., ) along the stack is due solely to the protons that have enough energy to reach it.This comprehends protons that stop inside the  th RCF (called primary protons to the  th RCF), but also protons having enough energy to continue their path inside the stack.The primary objective of the unfolding procedure is to extract the dose contribution  ( )  prim originating from primary protons by employing a weighted subtraction method as described with the following formula: where the coefficients  sufficient to reach and stop inside the  th layer ( <  ≤ ).Once  ( )  prim is determined, it is possible to obtain the number of primary protons  ( )  using the expression: where  ( )  pr represent the dose released in the  th layer by a single primary proton.Thus, by repeating this procedure for each RCF of the stack and dividing the equation (2.3) by the area of the selected ROI, the beam spectrum for the incident proton beam is obtained.
An automated MATLAB-based routine was implemented for the execution of the unfolding procedure.The algorithm's performance and accuracy were tested using conventional proton beams spanning energies from 30 MeV to 60 MeV, as documented in the references [31].

Dose calibrations
To establish a correlation between the measured optical density with the released dose it is imperative to conduct a thorough calibration procedure for each RCF type.Detector calibration plays a crucial -4 -role in the reconstruction of proton energy, performed by employing the described unfolding procedure.Additionally, the calibration procedure is essential due to the evident dependence of the RCF response on the incident particle energy (or LET).
To examine the correlation between the RCF response and the LET of the incident radiation, a comparison was conducted among calibration curves obtained with radiations at various LET values.Specifically: 1. HD-V2 and EBT3 films were calibrated by means of a 60 MeV proton (LET = 1 keV/μm) beam delivered at the CATANA (Centro di AdroTerapia e Applicazioni Nucleari Avanzate) proton therapy facility of INFN-LNS (Catania, Italy) [34].
2. EBT3 and EBT3-U were calibrated by means of a 6 MV photon beam (LET = 0.2 keV/μm) delivered at the Policlinico Universitario "G.Martino" (Messina, Italy) using a LINAC PRIMUS dedicated to clinical treatments.
Table 2 provides a summary of the adopted irradiation setup, encompassing RCF type, employed particles, energy, and released dose.The first two facilities are clinical centers, where the RCFs' irradiations followed the customary beamline calibration procedures, typically adopted for patient treatments.This procedure was repeated before each experimental session to minimize overall uncertainty.Notably, the variation in beam calibration observed across the various experiments remained within a 3% margin.
In the third facility, not clinical, the calibration session involved the use of a pulsed proton beam (with a beam flux of 4•10 7 pps and a pulse duration of 0.3 seconds).In this specific case, a non-standard dosimetric procedure was adopted to perform the beamline calibration procedure.A Faraday Cup (or FC) for absolute dosimetry and a Secondary Emission Monitor (or SEM) for relative dosimetry [31] were employed.A schematic description of the experimental setup is provided in figure 2.
Here, the proton beam, accelerated and transported in a vacuum, initially interacts with the SEM before reaching the FC.In such a way, the SEM was adopted as an in-transmission dosimeter properly calibrated in dose through the FC. Figure 3 illustrates the SEM calibration curve: its response (in charge) was fitted as a function of the administered doses, which were measured using the FC while keeping the beam current and energy constant.After the SEM calibration, the RCFs were precisely placed at the entrance of the FC representing the reference irradiation point.

Results
RCF calibrations were carried out by exposing the films to various doses in all the aforementioned configurations.The measured optical density was fitted as a function of the released dose using a third-order polynomial curve, following the guidelines outlined by the manufacturer [26].The outcomes of this procedure are depicted in figure 4 and figure 5, showcasing the comparison among calibration curves acquired using varying LET radiations.Error bars were calculated by propagating uncertainties linked to beam calibrations and optical density measurements.
The LET-dependence is evident looking at the curves of figure 4 and figure 5: fixed a dose value, the optical density at high-LET (4 MeV and 5 MeV protons) is lower than at low-LET calibration curves (60 MeV protons and 6 MeV photons).Additionally, it is observable that the difference in optical density values among the various calibration curves becomes more pronounced as the corresponding dose increases.This phenomenon can be attributed to the local saturation of the polymerization -6 -  For each data set, the trend line obtained by applying the best-fit procedure with a third-order polynomial curve is reported ( 2 = 0.999).
process along the particle tracks.Specifically, when the LET of the radiation is such that ionization events along the tracks occur at very close distances, the local polymerization becomes saturated.Consequently, a portion of the deposited energy remains unconverted into a measurable signal, leading to an underestimation of the response [23].
The calibration process stands as the primary prerequisite for executing and validating the unfolding procedure using a stack of RCFs irradiated within the context of laser-plasma interactions.After establishing the RCF response as a function of the released dose across a broad spectrum of incident LETs, the energy spectrum was reconstructed.This was accomplished within a stack of HD-V2 films exposed during a pre-commissioning campaign at the ELI-Beamlines laser facility [31].RCFs were coated with a 40 μm aluminium filter to eliminate background contributions arising from gamma-ray exposure.It was irradiated in the experimental room E4 using the E3 laser.The emission of protons resulted from the interaction of a 10 J laser power on an aluminium solid target with a thickness of 15 μm.
In figure 6 the pictures of the nine radiochromics that formed the stack are reported.It is possible to note how the degree of blackening varies depending on the depth at which each RCF is located.
-7 - The first RCF of the stack (number 35 in figure 6) exhibits a greater degree of blackening as it has a high background due to the high gamma rays component emitted during the laser-target interaction.From layer number 35 to layer number 29, it is evident that the degree of darkening decreases with increasing depth, this being ascribed to the fluence reduction of the low-energy proton component.In the examined stack, the kinetic energy of the primary protons ranges between 2 MeV and 11 MeV as the stack depth changes: this corresponds to a variation of the LET within the 4-16 keV/μm range, as depicted in figure 7.As previously stated, RCFs response exhibits an evident dependence on LET.As a result, multiple calibration curves are required to account for the incoming particles' varying LET.
Considering the given variation, we opted to employ three distinct calibration curves in the unfolding procedure to accurately reconstruct the incident energy spectra in the RCF stack: • for the energy range between 2 MeV and 4 MeV, we applied the calibration curve obtained with the 4 MeV proton beam; • to measure the dose at 5 MeV, we employed the calibration curve obtained at LNL with 5 MeV proton beams; • in the energy range between 6 MeV and 10.5 MeV, we utilized the calibration curve at 60 MeV.
In figure 8, the incident proton energy spectrum reconstructed using the unfolding method is presented.The total uncertainty in fluence is computed by propagating errors throughout the entire unfolding procedure.To underscore the impact that using a single calibration curve would have in reconstructing the fluence spectrum of the incident beam, the unfolding method was applied to the entire stack by employing individual calibrations at 4 MeV, 5 MeV, and 60 MeV (grey lines in figure 8).The percentage differences in fluence for all energy components of the stack are illustrated in figure 9.
-8 - The fluence value corresponding to 5.35 MeV obtained with the 5 MeV calibration curve is 75% lower than that obtained with the 4 MeV calibration curve.When considering the fluence related to the incident proton energy of 4 MeV, the value obtained through the 5 MeV calibration curve shows an underestimation of approximately 68% compared to the corresponding value obtained with the 4 MeV case.This underestimation increases to 86% when compared with the fluence value obtained using the 60 MeV curve.-9 -

Conclusion
In this study, a dose calibration for HD-V2, EBT3, and EBT3-U films in a high and low LET regime was conducted.The calibration curves for HD-V2 were subsequently employed to estimate the energy spectrum of a laser-driven proton beam, acquired through a stack configuration, using the unfolding procedure.The comparison of the resulting spectra underscores the significance of utilizing calibration curves at different LETs to avoid substantial errors in dose and particle fluence.Based on these preliminary results, it's evident a clear necessity to establish a protocol -currently nonexistent -that enables accurate consideration of the dependence of Radiochromic Films' response on the LET of the incident radiation.
Implementing the unfolding procedure while differentiating the calibration curves according to the LET of the incident radiation, the error on energy spectra reconstruction can be reduced up to 86%.This proposed approach can contribute to refining unfolding techniques, enhancing the accuracy of spectroscopic characterization for non-monochromatic proton beams, such as laser-driven ones, especially in the context of applications in the 11 B(p, )2 reaction field.The study conducted in the E4 experimental room at ELI-Beamlines has affirmed the efficacy of this approach in reconstructing proton spectra with a high-repetition rate and short-pulse laser.This method holds promise for future fusion studies.
)  represent the energy loss in the  th layer of the stack by protons with an energy  (  )

Table 2 .
Summary of irradiation configurations implemented during RCFs calibration.The beam characteristics are specified, along with the dose ranges released on the RCFs.

Figure 2 .
Figure 2. Experimental hall at INFN-LNL laboratory.a) Schematization of the experimental setup.b) Lateral view of the vacuum chamber and FC.c) RSFs placed after an Al collimator (5 mm diameter).FC entrance is visible as well.d) Picture of SEM device.

Figure 3 .
Figure 3. SEM dose calibration curve obtained for 4 MeV proton beam.Each data point represents the mean value of 10 irradiations.The resulting curve of a linear fitting procedure is also reported ( 2 = 0.998).

Figure 4 .
Figure 4. HD-V2 calibration curves at different LET values.For each data set, the trend line obtained by applying the best-fit procedure with a third-order polynomial curve is reported ( 2 = 0.998).

Figure 5 .
Figure 5. EBT3-U calibration curves at different LET values.The comparison with the EBT3 calibration curves highlights the different behavior of these two RCF types.For each data set, the trend line obtained by applying the best-fit procedure with a third-order polynomial curve is reported ( 2 = 0.999).

Figure 7 .
Figure 7. LET trend as a function of primary proton energy for the HD-V2 stack irradiated at the Eli-Beamlines facility.

Figure 8 .
Figure 8. Incident proton energy spectrum determined by applying the unfolding procedure to HD-V2 stack obtained by differentiating the calibration curves according to the LET of the radiation (solid line).Results obtained by using different calibration curves are also shown (dashed lines).The ROI selected to perform the analysis was maintained the same for all the configurations.

Figure 9 .
Figure 9. Percentage difference between the fluence values at different energies obtained with different calibration curves.The legend describes between which fluence curves the percentage difference is calculated.For example, "5 MeV vs 4 MeV" indicates the result of the percentage difference of the fluence points obtained with the 5 MeV calibration curve compared to the fluence points obtained with the 4 MeV calibration curve.