CR-39 track detector calibration with H and He beams for applications in the p-11B fusion reaction

The 11B(p,α)2α reaction, generating three alpha particles, emerges as a promising alternative or complementary route for clean and efficient energy generation. A comprehensive understanding of reaction dynamics, energy distribution of emitted particles, and optimization of fusion efficiency requires precise diagnostic methods. CR39 detectors, being highly sensitive to ions and neutrons while remaining transparent to low fluxes of electrons and gammas, are extensively utilized as primary Solid State Nuclear Track Detector devices in laser-plasma environments. This study presents the CR-39 track detector calibration to low-energy protons and alpha particles. CR-39 irradiation took place at INFN-LNL (Istituto Nazionale di Fisica Nucleare — Laboratori Nazionali di Legnaro, Legnaro, Italy) across a range of energies (≥ 80 keV) up to a few MeV, employing various etching times with a NaOH solution. The observed discrepancy in particle diameters, related to a specific etching time, presents a promising avenue for distinguishing alpha particles from proton contributions. This finding holds potential for future practical applications in the study of 11B(p,α)2α fusion reactions.


Introduction
The 11 B(p,)2 reaction, involving the fusion of low-energy protons (p) with an 11B nucleus, producing three alpha particles (), has emerged as a promising alternative or complementary avenue for clean and efficient energy generation.Currently, worldwide experiments have demonstrated the possibility of initiating p-11B fusion reactions through tailored laser-plasma interaction schemes [1][2][3][4][5][6].A significant yield for p-11B fusion was therefore achieved leading to the future employment of laser-plasma interaction as a powerful alpha-particle source [7][8][9][10][11].The p- 11 B, even if energetically less favourite, exhibits several advantages concerning the well-known D-3He fusion reaction: the two reagents are abundant in nature; the reaction is neutronless bringing a strong reduction of the material activation surrounding the fusion site; there are many prominent future applications apart from inertial fusion energy plants, including the possibility of realising tabletop alpha sources and potential use in medical applications (irradiations of superficial tumours, radioisotopes production, etc.).
Unfortunately, the p-11B cross-sections in plasmas are still unknown.The classical methods to determine cross-section in beam-target schemes cannot be trivially transported to in-plasma reactions.In addition, a post-acceleration of emitted alpha particles was experimentally observed as an effect of the electric field developed inside the plasma [4].The understanding of p-11B fusion reaction in plasmas is therefore still an open question that can be approached successfully by tailored laser-matter experiments.Besides the full unclear knowledge of the interaction conditions and reaction mechanism, another principal issue in experiments involving p-11B fusion reactions is the accurate detection of the fusion products.Specifically, detecting alpha particles in high-power laser-plasma experiments is inherently difficult due to the comparable deposited energy of the emitted alpha particles and the low-energy protons produced in such reaction schemes.Proper diagnostics methods are essential for understanding the reaction dynamics, the energy distribution of the emitted particles, and optimizing fusion efficiency [8].Currently, several diagnostic techniques are employed to characterize the laser-driven fusion process: Time-of-Flight (TOF) spectrometry, nuclear activation analysis, charged particle spectroscopy with Thompson Parabola (TP) spectrometer, charged particle detection with solid-state nuclear track detectors (SSNTDs) and X-ray imaging.In addition, neutron detectors are sometimes employed to measure concurrent reaction channel rates that may be opened during the fusion.All of these diagnostic tools provide valuable insights into the dynamics of the p-11B reaction and help optimize fusion conditions.CR39 detectors are extensively used as one of the primary SSNTD detectors in laser-plasma environments due to their exclusive sensitivity to ions and neutrons while -1 -remaining transparent to low fluxes of electrons and gammas.These detectors consist of a polymer matrix where exposition to ionizing radiation generates local damage caused by the breaking of the long polymer chains due to the energy deposition from the incoming radiation.Along these damaged regions, the material is more susceptible to chemical attack and thus has a much faster etching velocity than undamaged material.To detect the latent tracks after exposure to ionizing radiation, the plastic SSNTDs are typically immersed in a NaOH solution with a specific concentration and temperature, for a certain amount of time.This causes bulk etching of plastic, and because of the enhanced etching properties of the regions exposed to radiation, tracks become visible and with sizes increasing with the duration of the bath.The etched tracks can be visualised and analysed under an optical microscope, providing valuable information about the properties of the particles involved [12,13] Advantages of CR39 detectors in studying p-11B fusion reactions include: • High sensitivity: CR39 detectors can detect low-energy alpha particles produced in the p-11B reaction, even at extremely low concentrations.
• Energy response: the detectors have a predictable energy response for alpha particles, enabling accurate energy measurement and analysis.
• Insensitivity to electromagnetic radiation: CR39 detectors are not affected by electromagnetic interference, making them suitable for experiments involving high-energy particles and intense radiation fields.
• Three-dimensional track reconstruction: CR39 allows the reconstruction of particle tracks in three dimensions, aiding precise measurement of scattering angles and energy distribution.
• Cost-effectiveness: CR39 detectors are relatively affordable compared to other detection methods, making them accessible for a wide range of research projects.
With the CR39 detectors, the process of identifying individual ion species and measuring their energy involves studying the track diameter and, if applicable, the pattern formed as the incident ion propagates through the plastic structure.The track diameter is primarily influenced by factors such as ion energy, ion mass, etching time, and etching parameters (including solution concentration and temperature).Consequently, calibration of this detector with well-known ion species and in well-known etching conditions is essential to accurately identify the particles emitted during the p-11B fusion reaction in plasma [14].
In this study, we present a precise calibration of the CR-39 track detector response for low-energy protons and alpha particles.The CR-39 irradiation took place at INFN-LNL (Istituto Nazionale di Fisica Nucleare -Laboratori Nazionali di Legnaro, Legnaro Italy).We conducted measurements of track diameters, ranging from low energies (≥ 80 keV) up to a few MeV, with various etching times using a NaOH solution (6N, 70 • C).The complete etching and reading process was meticulously executed to enhance the reproducibility of the detector analysis.A significant challenge in spectroscopy utilizing CR39 detectors is the detector's high sensitivity to minor variations in the reading procedure.This is the underlying rationale behind the difficulty of directly applying the calibration results from previously published works.Minor fluctuations in temperature or an imperfect interruption of the etching process can lead to significant alterations in track diameter.In this study, we present a meticulously defined procedure aimed at enhancing the level of reproducibility.Notably, we introduce -2 -the first accurate calibration measurements at a 30-minute etching time, successfully distinguishing alpha tracks from proton tracks, which was the primary objective of the p-11B experiment.

Experimental set-up
The detectors were irradiated with proton and alpha ion beams using the AN2000 (2MV) and the CN (7MV) accelerators at the INFN-LNL in Legnaro, (Italy).Both accelerators are single-stage Van der Graaff devices and can provide proton and alpha beams with tunable energies between 0.3-2.2MeV (AN2000) and 2-12 MeV (CN).The vacuum experimental chamber and the detector positioning holder used for the experiment are shown in figure 1 and figure 2.  -3 - The energies used for protons and alpha particles at AN2000 were 500, 800 and 1500 keV.In the case of the proton beam, particles with an energy of 1000 keV were also used; additionally, some of the detectors were covered with one or two Al foils, 2.4 um in thickness, to reach energies of 320 and 70 keV respectively.In the case of CN accelerator the energies used were between 2.2 and 5.2 MeV for both protons and alpha particles.The CR-39 detectors were irradiated by ions that were backscattered from suitable thin foils of C and Au.The detectors were placed on a wheel controlled by "in-house" software provided by the INFN-LNL support team.The adopted energies for the calibration with both protons and alpha particles are reported in table 1.
Table 1.Adopted energies for both calibration with proton and alpha particles.

Etching procedure and adopted analysis
After the irradiation, the CR39 detectors were etched in NaOH solution under well-defined conditions of molar concentration and temperature.During this step, the latent tracks left by charged particles in the CR39 polymer underwent a controlled expansion and became visible (in the form of clearly visible holes) with an optical microscope.The key factors influencing the yield of the etching process (i.e. the number of discernable holes) are the chosen etchant's chemical composition and its concentration and temperature.In this work, the adopted etching procedure can be summarized in four steps: 1.The detectors were immersed in an aqueous solution of 6.25 mol/L of sodium hydroxide (NaOH) at 70 ± 0.1 • C for a variable etching time; 2. After the proper etching time, CR-39s were removed from the thermal bath and put into an aqueous solution of 2% weight/volume acetic acid (CH3COOH) for 30 minutes; 3. Detectors were then rinsed in distilled water for 1h to stop further chemical etching and reduce the risk of halos on the plastic caused by limescale or impurities; 4. Finally, CR39s were dried with a proper antistatic cloth.
-4 -After the etching process, the CR39 detectors were subjected to meticulous reading procedures to extract valuable data from the visible tracks.They were examined under a fully automated inverted optical microscope, model Nikon ECLIPSE Ni-E, allowing for precise and detailed track measurements.The images were captured using a DS-Qi 2 camera, boasting a resolution of 4908x326 and a sensitivity of ISO800-51200 mV/s.In this study, the advanced image analysis software (NIS-Elements BR Analysis 5.11.00) was employed to automate the track measurement process and efficiently manage large datasets.The image processing was based on several steps: image acquisition with the proper value of focusing and luminosity; inversion in binary-scale of the acquired image, threshold setting and track identifications based on specific parameters of eccentricity.

Results and conclusion
We conducted a comprehensive investigation of the tracks' growth trends, studying their diameters as a function of the varying incident particle energy and etching time for both protons and alpha particles.The lowest etching time was fixed at 30 minutes.This additional calibration point, different from what is reported in previous research in the same field [14,15], has turned out to be particularly valuable in the laser-driven environment, where the fluence is exceptionally high, and the saturation effect is highly probable for longer etching times.Unfortunately, the proton tracks were not visible at the 30-minute etching interval.Consequently, we present the trend in track growth within the etching time range of 60 to 480 minutes for protons, and from 30 to 120 minutes for alpha particles.The results obtained for protons and alpha particles are reported in figure 3 and figure 4, respectively, where distinct track growth patterns can be observed for each particle type.The determination of error bars was based on the statistical dispersion of the counts, with each data point being acquired from a statistical pool encompassing approximately 10 4 tracks.By incorporating multiple measurements for each data point, we aimed to account for variability and enhance the statistical reliability of our results.-5 -In our investigation, we made intriguing observations regarding the behaviour of proton track diameters concerning their initial energies.We noticed that, in general, the track diameters decrease with increasing initial energies of protons, except for very low energy values (below 350 keV), where the opposite behaviour effect occurs, in agreement with other papers [14].Notably, this observed the disparity between track diameters caused by low and high-energy protons, became significantly more pronounced as the etching time was extended.Longer etching times, hence allowed for easier discrimination between low and high-energy protons.Additionally, we observed that proton tracks are not immediately visible at the onset of the etching process.Tracks produced by protons with energies ranging from 0.07 to 0.8 MeV became, in fact, observable starting from 1-hour etching time, while tracks with energies around 1 MeV appeared only after the 2-hour etching time.As for the calibration of alpha particles, the results, depicted in figure 4, showcased a different trend compared to the findings obtained for protons.Contrary to the delayed appearance of proton tracks, alpha particle tracks have become visible already at a 30-minute etching time.In addition, a non-linear trend in the track growth was observed as a function of the energy.At energies below 1 MeV, the diameter starts to decrease, as observed for extremely low-energy proton tracks.We conclude that the etching time should become a distinguishing factor in the proton/alpha tracks discrimination and should play as a discriminant factor when, more generally, ions of different Z are involved.The calibration measurements conducted in this study could play a pivotal role in the research involving experiments on nuclear reactions initiated by laser-accelerated ions as in the case of the proton-11B reaction in plasma.where both protons and alphas, of similar LET (Linear Energy Transfer) values, are involved.While the track's diameter measurement provides valuable insights, it is alone not sufficient for a complete alpha particle identification, as their signature is close to protons at etching times between 60 to 90 minutes.
The distinction between alpha particles and protons is most pronounced within the etching time range of 120 to 180 minutes, as a result, evident from figure 5.However, it is essential to consider the potential saturation effect that may arise in the laser-driven environment when using such extended -6 - etching times.To ensure an accurate identification of alpha particles without the interference of protons, performing an etching point at 30 minutes was crucial, indeed.This short etching time was particularly effective since proton tracks did not appear in the energy range between 0.07 to 0.8 MeV, as demonstrated in figure 3.Although this study primarily focuses on the medium energy range of protons, it is worth noting that at lower incident proton energies (corresponding to a high LET), tracks may become visible even at the 30-minute etching time.Consequently, the selection of the appropriate etching time is of paramount importance to achieve reliable and unambiguous identification of alpha particles in laser-plasma fusion research.CR39 detectors have proven to be a fundamental tool in the investigation of the p-11B fusion reaction.Their unique track-etch properties and sensitivity to alpha particles can significantly contribute to our understanding of this promising fusion process.As research continues to explore the viability of p-11B fusion for energy production, CR39 detectors will remain valuable instruments in advancing nuclear fusion science and technology.Therefore, to achieve comprehensive alpha particle identification, the track diameter measurements must be complemented by other diagnostic techniques.

Figure 1 .
Figure 1.The vacuum chamber located at the end of the AN2000 beamline where the detectors were positioned for the irradiation.

Figure 2 .
Figure 2. The holder used for the CR-39 detector irradiation.The red squares indicate the place of the detectors.

Figure 3 .
Figure 3. Proton track diameter as a function of incident energy radiation for different etching times.

Figure 4 .
Figure 4. Alpha particles track diameter as a function of incident energy radiation for different etching times.

Figure 5 .
Figure 5.Comparison between proton and alpha particles track in the etching time range between 120 to 180 minutes.