A Methodology for the Discrimination of Alpha Particles from Other Ions in Laser-Driven Proton-Boron Reactions Using CR-39 Detectors Coupled in a Thomson Parabola Spectrometer

Solid-state nuclear track detectors (CR-39 type) are frequently used for the detection of ions accelerated by laser-plasma interaction because they are sensitive to each single particle. To the present day, CR-39 detectors are the main diagnostics in experiments focused on laser-driven proton-boron (p 11 B) fusion reactions to detect alpha particles, which are the main products of such a nuclear reaction, and to reconstruct their energy distribution. However, the acceleration of multispecies ions in the laser-generated plasma makes this spectroscopic method complex and often does not allow to unambiguously discriminate the alpha particles generated from p 11 B fusion events from the laser-driven ions. In this experimental work, performed at the PALS laser facility (600 J, 300ps, laser intensity 10 16 W/cm 2 ), CR-39 detectors were used as main detectors for the angular distribution of the produced alpha particles during a p 11 B fusion dedicated experimental campaign. Additionally, a CR-39 detector was set inside a Tomson Parabola (TP) spectrometer with the aim to calibrate the CR-39 response for low energetic laser-driven ions originating from the plasma in the given experimental conditions. Te detected ion energies were ranging from hundreds of keV to a few MeV, and the ion track diameters were measured for etching times up to 9 hours. Te goal of the test was the evaluation of the detectors’ ability to discriminate the alpha particles from the aforementioned ions. Within this study, the calibration curves for protons and silicon low energy ions are accomplished, the overlapping of the proton tracks and alpha particles is verifed, and a methodology to avoid this problem is realized.


Introduction
Nowadays, the interest of the scientifc community involved in the study of the laser-driven nuclear reactions is growing because of the possible multidisciplinary applications.Although the fusion reaction between tritium and deuterium is still considered the most interesting among other fusion reactions considered for power generation [1], the one between hydrogen and 11 B nucleus, called proton-boron nuclear fusion reaction (p 11 B) [2], represents a complementary and potentially alternative solution in future advanced schemes.In fact the possibility to generate three alpha particles per single reaction, with a negligible generation of neutrons, makes this type of reaction of interest in many felds of research (for a futuristic nuclear plant [3], in space applications [4], in cancer treatment [5,6], in radioisotope production [7], or in material science).
As reported in the literature, this nuclear reaction has a main resonance occurring at 670 keV of proton energy in the center of mass frame, with the cross section of 1.2 barn and a secondary resonance peak at 170 keV energy in the center of mass (0.1 barn).Te generated alpha particles have a broad energy spectrum with the main peak at around 4 MeV and a cut-of energy at 7 MeV [8,9].
Since 2005, the p 11 B reaction has been triggered by the use of ultra-high intense laser systems [10][11][12][13][14], and despite the impressive progresses in the alpha particle rate enhancement [15], an extensive systematic investigation of laser-based p 11 B fusion and deep understanding of the underpinning physics is still missing [16].
As of today, in the experimental study of the p 11 B fusion reaction, one of the critical experimental bottlenecks is the defnition of a trustable detector allowing to discriminate the alpha particles from the other charged particles produced from the plasma source.Tis issue is related with the clear understanding and interpretation of the experimental results [17].
In this direction, solid-state nuclear track detectors, CR-39 type, have proved to be a reliable diagnostic tool for the characterization of the energy distribution of alpha particles generated by the laser-driven proton-boron fusion.In fact, they are extremely sensitive to a single incident particle and are not afected by the intense electromagnetic noise produced in the laser-target interaction [18].
One of the issues related with the use of such as passive diagnostic is that a calibration is needed to correlate the diameter of the tracks created by the particles caught in the detector surface during the irradiation to the corresponding incident energy and to the ion species.Te calibration curves can be produced by the irradiation of the CR-39 detectors with monochromatic ions that can be generated by accelerators or radioactive sources.Although the use of CR-39 detectors appears to be straightforward, the major difculty of their application relies on the fact that the same size of a track can correspond to two diferent energies of the same particle or to two diferent ions with diferent energies.
Within this study, we propose an alternative calibration technique for the CR-39 detectors and a simple method to discriminate the alpha particles generated in a p 11 B reaction from concurrent protons and other ions at given experimental conditions.

Materials and Methods
Te current experiment was realized during a p 11 B nuclear reaction experiment at the Prague Asterix Laser System (PALS) in Czech Republic [19].Te PALS laser is an iodine laser working at the fundamental wavelength of 1315 nm, ∼800 J maximum laser energy on the target, and sub-ns pulse duration (0.3 ns FWHM).Te laser was focused on the sample with an incidence angle of 30 °to the target normal reaching an intensity of 1•10 16 W/cm 2 .
A Tomson Parabola spectrometer (TP) was placed at 0 °along the target normal and 1.58 m away from the target.Te laser-driven ions were collimated by a 200 μm diameter pinhole before entering the TP as sketched in Figure 1.
Te produced ions are defected when they pass through electric and magnetic felds mutual parallel and perpendicular to the beam axis.Te electric feld causes a defection in one direction (x axis) that it is proportional to the E i /Z ratio, where E i is the energy of the ion and Z is the ion charge.Te magnetic feld defects the ions proportionally to the m i / Z ratio in a perpendicular direction (y axis), where m i is the mass of the ion.Terefore, the ions with higher charge and lower kinetic energy will defect more and ions with the same mass over charge ratio will group on the same parabola [20,21].
Te parabolas are usually recorded by an imaging plate.Within the current experiment, the electric and magnetic felds applied were 500 kV/m and 168 mT, respectively, and the parabolas were partially recorded by CR-39 nuclear track detectors that were placed on top of the imaging plate.Te energies of the detected ions calculated by the analytical formulas of the parabolas were crosschecked by simulation using the SIMION software [22].
Within this study, we present results originating from the CR-39 used as focal plane detector in the TP detecting ions from the interaction of the laser with a SiHB target.
Te operation of the CR-39 detectors is based on the damage of the molecular chains of polymers by the passage of charged particles that leave tracks on their way.Te irradiated detectors are placed in a sodium hydroxide (NaOH) or a potassium hydroxide (KOH) solution at a certain temperature (ranging from 60 to 90 °C) to be etched.Afterwards the etched detectors are analyzed with a highresolution optical microscope to measure the diameter of the recorded tracks and their number.
Te track diameter is related to the energy of the impinging particle, thus allowing reconstructing the energy distribution of the ion beam, as well as its fux [23].Many studies describe the dependence of the track diameter with the energy of the diferent ions, mostly referred to protons, alpha particles, and carbon ions [23][24][25][26][27][28][29][30][31][32][33][34][35].However, the calibration of CR-39 for other species such as boron and silicon ions is almost missing in the current bibliography.
Te dependence of the track diameter on the ion energy can be described as follows: in the low energy region, the diameter of the track grows rapidly with the energy until a threshold is reached, after which the diameter decreases as the energy of the ion increases.Tis behavior follows the stopping power shape of the ion inside the materials [25,36] and at the same etching conditions and etching time: (a) ions with higher stopping power values create bigger tracks and (b) ions of the same species but with diferent energy cause bigger tracks when their energy is closer to the stopping power maximum.
Te detectors energy calibration can be performed by irradiating them with monochromatic ion beams at conventional accelerator facilities or by using radioactive sources.Te laserdriven ion beams are not monoenergetic and therefore cannot be used as an ion source to precisely calibrate the CR-39 detectors unless a control spectral dispersion is used.In [26,30,37], CR-39 detectors have been calibrated for protons, carbons, deuterons, and nitrogen ions in laser facilities, and in the current experiment, we used a similar confguration.
Te SiHB targets presented in this paper were realized in a complementary metal-oxide-semiconductor (CMOS) fabrication pilot line, the class-10 clean room for device microfabrication at the micro and nanofacility of the Fondazione Bruno Kessler in Trento (Italy) [38][39][40].So, the developed process is compatible with standard CMOS processing, which allows a direct transfer of the technology.Targets were made starting from 6-inch standard CZ (Czochralski) <100> silicon wafers with a thickness of 300 μm.By silicon microfabrication technological processes, a series of free-standing membranes of about 2 microns of thickness has been realized.Tese last were subsequently doped by boron ion implantation (D � 10 17 cm −2 ; E � 50 keV) and enriched by hydrogen atmosphere for 3 hours at a temperature of 420 °C by using a thermal annealing furnace.Even if the natural isotope abundance of the boron is 80% for 11 B and 20% of 10 B, the ion implanter utilized in that experiment (like all systems worthy of the name) they possess an analyzing magnet selecting the right mass on charge ratio (m/q), in our case for the p 11 B we need 11 B. Te possible presence of the boron 10 inside the target is certainly in a negligible concentration.
After the laser-target interaction, protons, silicon, boron, carbon ions (originating from surface contaminations), and alpha particles, emerging from the p 11 B nuclear reactions, were generated and detected by the CR-39 detectors located inside the TP.
After the irradiation, the CR-39 were etched for 9 hours in a NaOH 6.25 M solution at 70 °C.Te tracks were recorded after every hour of etching with an optical microscope [41].An example of an irradiated detector with tracks of diferent ions, after 8 h of etching is presented in Figure 2. Te signal less defected in the vertical direction originates from the protons that are the most energetic, followed by the diferent charge states of heavier ions (silicon, boron, and carbon).
Te detection of B and C ions was not possible due to their parabolas are very close to Si ones as it is determined from their Z/m ratio.In Table 1, we shortened the Z/m ratios of each produced ion from the smallest ratio to the biggest one.From this, it is evident that the following pairs of B and Si ions have parabolas that are very close: (B +1 , Si +3 ), (B +2 , Si +6 ), (B +3 , Si +8 ), (B +4 , Si +11 ), or completely overlapped (B +5 , C +6 , He +2 , Si +12 ).Additionally, the boron element being a dopant inside the SiHB target has lower concentration than Si resulting to fewer production of B ions with respect to the Si ones.For these reasons, the detection of B ions was not possible.Te C ions, being present as a contaminant from the surface are produced in smaller amounts (with respect to the Si ones) only C + was possible to detect and only at 9 h of etching because the tracks were not well defned from the early etching times.Regarding the He ions, He +1 parabola overlaps with C +3 and Si +7 ones making their detection impossible.
Unfortunately, the detection of alpha particles was not realized as well due to the production of Si +14 and B +5 ions that overlap the parabola of alpha particles having the same Z/m ratio.Additionally, it should also be noted that the number of the produced alpha particles is negligible with respect to the other ion signals, and therefore, their tracks can easily be "hidden" inside the common parabola.Tis is supported from a previous p 11 B experiment at PALS [15] where the number of the produced alpha particles from a hydrated Si target was estimated at 10 9 p/sr/shot.Tis fux would result to an entrance of 13 alpha particles/shot inside the TP.
A summary of the detected ions and their energy at the CR-39 is presented in Table 2, together with all information about the target and laser parameters used during this test.Carbon ions (C +1 ) were recorded only at 9 h of etching because the tracks were not well defned from the early etching times.
Te proton and silicon parabolas were fully documented by taking subsequent pictures moving the microscope vertically on the sample from the upper area (away from the pinhole) to the bottom (closer to the pinhole).Each picture corresponds to diferent vertical positions without overlapping or gaps between the images.Ten, the pictures were grouped in groups of ten (squares in Figure 3(a)) and were analyzed using the ImageJ [42] software.
Figure 3(a) presents the proton signal from the TP of the frst shot here under study.Te squares in Figure 3 With this method, we correlated the energy of the analyzed tracks with respect to the diameters of the tracks and accordingly we produce the calibration curves.In Figure 3(b), the colors of the Gaussians correspond to the same-colored areas (squares) from Figure 3(a).In this example, the diameters are becoming wider in the direction from the top of the CR-39 (away from the pinhole) to the bottom (i.e., from the black area to the purple one).Tis means that the tracks from the particles with higher energy are bigger; this is correct in this case because the detected energies are less than 0.5 MeV, which is lower than the expected maximum (in diameters) in the calibration curve.Terefore, the track diameters increase with the energy increment.Figure 3(c) presents the calibration curves for protons as it was produced from all three diferent shots and for diferent etching times (2-9 hours).
For the sake of completeness, a comparison between the calibration curve obtained from the TP in this work, the calibration from a previous study, done using a conventional accelerator at INFN in Catania, and one from reference [25] is presented in Figure 4. Tese calibrations were performed using the same etching conditions and the same etching time, 8 h.Te graphic shows that the TP results (here referred as "current work" and presented in black circle) are in excellent agreement with the literature results from [25], (red circles), while exhibit at least 30% diference (if we take into account the errors in diameters and energy) with the previous results from INFN, (blue circles).However, we should also point out that calibration curves that are carried out in diferent laboratories even if they are produced from the same experimental campaigns might vary due to the use of a diferent setup (microscopes, etching baths, software for the analysis of the tracks, and mainly because of a diferent operator).
From the parabolas, it was possible to extract useful information for the calibration of CR-39 for the Si + in the energy range between 0.5 and 1.9 MeV. Figure 5 presents the  calibration curves of Si + from 2 h up to 9 h of etching.Te results show that, in this case, the diameter of the tracks increases with the increment of the energy.Tis behavior was expected since the energy of the ions is small, away from the maximum in stopping power.
In Figure 6, the diameters of the tracks of Si +1, +2, +3, +4, and +12 are also included for 9 h of etching.Te analysis of the rest of the silicon ions was not possible since their parabolas were either too close one to the other causing saturation or they contained more than one ion track species, which were not discernible.However, the analysis of these parabolas would not provide more data since they correspond to energies that are already reported (the minimum and the maximum energies are determined by the energies of Si +1 and +12, respectively) and therefore would not improve the graph in Figure 6.A ftting procedure of the experimental data was introduced to determine the energy dependence of the diameter of the tracks.Te diameter (D in μm) exhibits an exponential grow dependence with the energy (E in MeV) of the Si ions within the specifc energy range (0.5-14 MeV).Te ftting relation is as follows: where A � −21.1341 ± 0.51717, b � −3.39641 ± 0.27833, and C � 27.07478 ± 0.59134 A comparison between the calibration curves of protons, silicon, and carbon ions at 9 h of etching is presented in Figure 7. Te diameters of the diferent ions have similar sizes at the low energy region (below 2 MeV) suggesting that the discrimination of the particles is not always possible.Te inset in Figure 7 shows a zoom in the energies below 2 MeV where we can see that the protons with energies between 0.2 and 0.7 MeV correspond to diameters 9.6-14.8μm, which also correspond to silicon and carbon ions with energies between 0.7-1.4 and 0.46-1.34MeV, respectively.Furthermore, protons with energies between 1.24 and 1.75 MeV form tracks with diameters between 7.3 and 4.6 μm, which correspond to silicon and carbon ions with energies less than 0.7 and 0.3 MeV, respectively.However, this situation is valid only for the specifc etching time, and therefore, the results must be evaluated case by case.
Figure 8 shows that the tracks of Si + are distinguishable from the ones of the proton tracks for the frst three hours of etching (Figure 8(a)).From 4 to 6 hours the Si tracks that correspond to energies below 1 MeV have similar sizes with the protons tracks (Figure 8(b)).Ten, up to 8 hours, the Si tracks that correspond to energies below 1.2 MeV are not distinguishable from proton tracks (Figure 8(c)) and fnally at 9 hours Si tracks up to 1.8 MeV have similar sizes with the proton tracks (Figure 8(d)).
Tis can be explained by the diference of the tracks etching growth.Figure 9 shows the evolution of the diameters for protons and Si +1 of 0.5 MeV through etching time.Although proton tracks exhibit a linear growth with time, Si ion tracks stop growing after 3 h of etching.Te diameters of Si ions from 4 h to 9 h of etching have a mean value of 5.8 ± 0.9 μm.Although the respective diameter at 4 h of etching has a lower value, it also includes a big error and fts inside this interval.Tis behavior of the etching growth can be attributed to the fact that the Si tracks are superfcial (1 MeV Si ions is stopped at 2 μm inside the CR-39), and consequently, after 3 h of etching the exposed surface of the detector has reached the damaged zone resulting in slow growth.Tis is analytically described in [36] where the depth dependence of track etch rate and of the restricted energy loss (REL) are presented.Te track etch rate and the REL reach a maximum at the same depth of the detector and then the etch rate decreases rapidly.Consequently, the evolution of a track almost stops when the etched surface of the detector nearly matches the bottom of the track.Tis means that although Si ions form tracks that have bigger diameters from the proton ones; after some hours of etching (in our laboratory 4 h), the diference in their growth result to similar sized tracks.For this reason, we believe that long etching hours should be avoided.
Finally, we evaluate the potential of the CR-39 detectors to discriminate the alpha particles from protons and silicon ions during a p 11 B experiment.We coupled the alpha particle track calibration curve with the experimental ones (from TP) of protons and silicon ions at 2 h of etching, as shown in Figure 10.Te calibration of CR-39 for alpha particles was realized at LNL-INFN accelerators (AN2000 and CN) in Legnaro, Italy [43], but the detectors were analyzed in our laboratory.Tis graph shows that the tracks of alpha particles overlap mostly with the ones from silicon ions in the range of diameters between 3-4.8 μm (red area in the graph).Terefore, the alpha particles with energies between 0.5 and 3.15 MeV form same sized tracks with the Si ions with energies between 0.5 and 1.25 MeV.Additionally, the alpha tracks overlap with the proton ones in the range 1.7-2.6 μm; black area in the graph that correspond to protons with energies 0.39-0.87MeV and alpha particles with energies 4-4.8 MeV.However, the lower limitation in diameters (and consequently the higher detected energies) in our calibration curve is not absolute.Te trend of the calibration curves shows that alpha particles with energy higher than 4.8 MeV should create tracks with diameters less than 1.7 μm.Tis means that the alpha tracks with energies above 4 MeV have the same size with all the protons in our   Laser and Particle Beams calibration curve (above 0.39 MeV).Apparently, the alpha tracks overlap fully with Si and proton tracks at 2 h of etching.Nevertheless, in the case of silicon ions, their discrimination from the alpha particles can be achieved by the use of proper fltering that can be placed in front of the CR-39 that would prevent their passage on the detectors' surface.For example, in our case, an Al flter with thickness 6 μm would exclude all silicon ions with energies below 13 MeV and alpha particles and protons with energies below 1.7 and 0.6 MeV, respectively.A diferent approach should be adopted for the discrimination of alpha particles from protons since a thicker flter would exclude frstly the detection of alpha particles.with results from INFN and from [20].Te diameters calculated from TP (black circles) are in excellent agreement with the ones from bibliography (red circles).However, there is a big diference (more than 30%) from the INFN results (blue circles).

Laser and Particle Beams 7
Te proposed methodology relies on the fact that the tracks of protons and alpha particles start to appear at diferent etching times due to their diference in size and energy.Te tracks of the same ion with diferent energy also appear at diferent etching times.Te tracks that correspond to higher energies form smaller and deeper tracks that appear later on during the etching procedure.Terefore, we propose that the minimum etching time where the alpha particles are detected without the appearance of the proton tracks should be determined experimentally.With our microscope and the current experimental conditions, we clarifed that the proton tracks are visible but not well defned in the frst hour of etching.In Figure 11 we can see the tracks of 500 keV protons after 1 h of etching, revealing that the proton tracks are barely noticeable and below the resolution of our microscope.Tis is the reason why we present the calibration curve of protons for etching times above 2 h.At 1 h of etching, the diameter of the alpha tracks varies between 1.5-2.8μm, for energies between 0.6 and 3.7 MeV, which is just above the resolution of our microscope (protons have diameters below 1 μm).Concluding that after 1 h of etching and by the use of the specifc magnifcation, we are able to detect tracks that correspond to alpha particles with energies between 0.6 and 3.7 MeV without the interference of the proton tracks.However, this does not mean that we cannot measure alpha particles with higher energies using this calibration curve.Te use of appropriate flters in front of the CR-39 detectors during an experiment results to Te measured energy corresponds to an initial energy (before the flter) by the addition of the energy loss inside the flter, which can be easily calculated by SRIM or LISE software [44,45].In this way, the calibration curve can be extended to the detection of higher energies.
Additionally, flters of diferent thicknesses of materials could be used in front of the CR-39 detector or the IP inside the TP spectrometer during the calibration procedure.Within this methodology (diferential fltering), the diferent flters are placed along the parabolas in order to exclude O, C, and other heavier ions [46,47].Laser and Particle Beams 9

Figure 1 :
Figure 1: Scheme of the experimental setup, CR-39 detector was placed on top of the TP imaging plate, covering part of its surface.

Figure 2 :
Figure 2: Image of ion parabolas recorded on the CR-39 detector after the irradiation of SiHB target as obtained after 8 h of etching.

Figure 3 :
Figure 3: (a) Stitched images showing the full proton parabola from the TP as registered on the CR-39.Te colored squares represent diferent regions analyzed.(b) Te analysis of each group (of 10 pictures) resulted a Gaussian-like distribution of the diameters of the detected tracks.Te colors of the Gaussians correspond to the same colored rectangular form (a). (c) Dependence of the diameter of protons at a function of the proton energy for diferent etching times.

Figure 4 :
Figure 4: Comparison of our experimental results (current work) with results from INFN and from[20].Te diameters calculated from TP (black circles) are in excellent agreement with the ones from bibliography (red circles).However, there is a big diference (more than 30%) from the INFN results (blue circles).

Figure 5 :Figure 6 :
Figure 5: Calibration curves of Si + ions from 2 h up to 9 h of etching time.

Figure 7 :
Figure 7: Diameters versus energy for protons, Si and C +1 ions for 9 h of etching.Te inset presents a zoom in the energy region below 2 MeV.Te results suggest the discrimination of protons from Si and C ions is not possible for energies below 2 MeV.

Figure 8 :
Figure 8: Diameter versus energy of protons and Si +1 ions at diferent etching times: 3 h (a), 6 h (b), 8 h (c), and 9 h (d), revealing that the particles are fully discriminated only in the frst 3 h of etching.

Figure 9 :Figure 10 :
Figure 9: Te track size of Si + and protons of 0.5 MeV through all etching times reveals the diference in their etching growth.

Table 1 :
Te charge over mass ratio of each produced ion.

Table 2 :
Detected ions and their energy at each CR-39 detector.