Laser-initiated p–¹¹B fusion reactions in petawatt high-repetition-rate laser facilities Open Access

The interaction of intense laser pulses with matter has historically been exploited for triggering nuclear fusion reactions. Deuterium–tritium (DT) fuel is the best-known candidate for future reactors for energy production, since it needs the lowest temperature to initiate the fusion process.¹ This reaction, however, requires a radioactive combustible (T) that is extremely scarce, and it also generates energetic neutrons, in addition to alpha particles, which induce radioactivity in the materials with which they interact, leading to serious problems for the setting up and maintenance of fusion reactors. Moreover, the energy conversion efficiency of neutrons is rather low. These disadvantages of DT fuel have prompted research activity on alternative fuels. Exploiting the p–¹¹B reaction is one of the most appealing solutions proposed to date, since energy is released in the form of alpha particle kinetic energy. Both reactants are abundant in nature and are not radioactive, and, at high energies (>500 keV), the p–¹¹B and DT cross sections are comparable. This has led to increasing interest recently in p–¹¹B fusion, by both public institutions and private companies, in the context of energy production schemes,^2–4 nuclear astrophysics,⁵ clinical radiotherapy,⁶ and production of radioisotopes for medical use,^7,8 as well as other applications requiring localized sources of alpha particles.

The first demonstration of a laser-driven p–¹¹B reaction used a picosecond laser pulse at an intensity of about 10¹⁸ W/cm², directly focused onto a composite target ¹¹B + (CH₂)_n, and resulted in about 10⁵ detected alpha particles in 4π steradians.9,10 This This was then followed by similar yields from experiments at 10¹⁵ W/cm² intensity with the ABC nanosecond laser.⁵ The use of far more energetic lasers (about 500 J) with ∼300 ps pulse [full-width at half-maximum (FWHM)] at an intensity of about 10¹⁶ W/cm² on advanced targets (H–B-enriched solid Si, or BN containing H due to target synthesis) led to remarkable yields of about 10⁹–10¹⁰ alpha particles per steradian,^11–13 far higher than previously achieved, giving a strong impetus to research on cross-sections, target material optimization, and diagnostic development.^2,3,14–21

An alternative scheme involves directing protons accelerated by laser–matter interaction, either onto solid B targets or onto B plasmas, created by a nanosecond-pulse laser on a solid B target,^18,22–24 with yields of about 10⁷ alpha particles per steradian being demonstrated. This “pitcher–catcher” scheme, when recently implemented on the high-energy LFEX laser (Japan) with a BN secondary target, gave about 5 × 10⁹ alpha particles per steradian.²⁵ 

Both of the aforementioned schemes (in-target and pitcher–catcher) have been exploited with energetic lasers, with hundreds to thousands of joules per shot. This is possible on a few large installations, but is limited to very few shots. Moreover, the various forms of intense secondary radiation (X rays, gamma rays, electrons, and ions) produced with a single energetic shot imposes significant limitations on experimental diagnostics. Instead, we propose in this work the use of a complementary approach, assessing and exploiting the effectiveness of high-repetition-rate experiments in a pitcher–catcher configuration for petawatt-scale laser-triggered p–¹¹B fusion. The accumulation of results from a large number of interactions with lower laser pulse energy and at “moderate” intensity may provide better control of parameters and of the statistics of measurements. Previous experimental studies have been performed with this aim, such as on the high-repetition-rate ECLIPSE laser^14,16,26 (35 fs FWHM, 110 mJ, 2 × 10¹⁸ W/cm²), or using a kHz repetition rate at gigawatt power.²⁷ 

In this paper, we present results achieved using an upgraded setup on the VEGA III laser at CLPU in Spain. This laser has characteristics similar to those of ECLIPSE, but with significantly higher energy per pulse. Our aim was to develop, test, and compare new experimental schemes for studying and exploiting p–¹¹B reactions with high-power, high-repetition rate lasers. The main objective of the campaign was to assess any problems with the scheme, to improve alpha production efficiency, and to ensure accurate detection of p–¹¹B reactions triggered by laser–matter interactions. Therefore, we conducted a precise characterization of the interactions and employed advanced techniques for alpha yield estimation.¹⁵ 

The experimental setup employing the pitcher–catcher scheme to induce laser-driven p–¹¹B fusion reactions is qualitatively illustrated in Figs. 1(a) and 1(b). As the p–¹¹B reaction cross-section exhibits two resonances at 148 and 614 keV center-of-mass energy, respectively,²² and maintains high values up to several MeV,²⁸ we aimed at accelerating a substantial flux of target normal sheath accelerated (TNSA) protons from thin-foil targets, to increase the number of protons with energies up to a few MeV. As we did not aim at very high energies, laser focal intensities up to ∼4 × 10¹⁹ W/cm² were considered. With such moderate intensities—for the characteristics of VEGA III (nominally, 30 J maximum pulse energy, 30 fs minimum pulse duration, 800 nm wavelength, and contrast 2 × 10⁻⁵ at 1 ps before the main pulse and <10⁻⁵ at 5 ps)—it was possible to relax the laser parameters to improve shot-to-shot repeatability. This required an experimental optimization, leading to the use of long-focal-length optics, laser pulses of average duration ∼220 fs, ∼10 μm focal spot diameter on target, and a laser pulse energy (on average, during our campaign) of 27 J before the pulse compression, with about 25% energy deposition on target. These conditions, not very usual for petawatt femtosecond lasers, required a detailed characterization of the interaction and of the emitted particle flows, with the purpose of providing as thorough as possible a picture to enable effective coupling with the theoretical models that will be discussed in Sec. VII and in future work in preparation.²⁹ As a result of this optimization, the pitcher target was chosen as a 6 μm-thick aluminum foil. It was irradiated by the laser with an angle of 12° with respect to its normal, generating the laser-accelerated protons that impinged on the boron catcher. This secondary target was 2 mm thick, had a surface of 27 × 27 mm² and was carefully positioned to maximize the number of TNSA ions impinging on it. The proton-irradiated boron catcher, where p–¹¹B fusion reactions took place, ideally emits three alpha particles for each fusion reaction, and momentum conservation entails that higher energies are expected in the direction of the incoming proton beam and lower energies in the opposite direction. This will play a role of increased importance for protons with higher energies. However, we are interested in alpha particles capable of escaping the B bulk, and thus those originating at a maximum depth of the order of a few tens of micrometers from the B front surface. For instance, alpha particles with 5 MeV (i.e., the peak energy of the theoretically expected alpha spectrum at the main 660 keV resonance) are stopped by only 18 μm of B and will therefore remain inside the sample if they are generated inside the bulk. Hence, protons up to a few MeV are of interest,¹⁵ and because of the much larger mass of B, this effect of a downshifted alpha spectrum should be not extremely large. These considerations motivated the decision to tilt the B at the reasonably large (54°) angle relatively to the pitcher normal, to enhance the number of alpha particles to be revealed by the CR39 diagnostics [see Fig. 1(b)] after escaping from the B. The tilting is meant in fact to increase the component of the proton momentum tangential to the B surface, and consequently to reduce the component along its normal. In this way, for a given proton energy, the proton stopping position is closer to the B surface, and alphas produced from p–¹¹B reactions will need to pass along a shorter path in B to exit from the bulk. The choice of angle also took account of the necessity to avoid extending the interaction region too much, on one side, and to improve the feasibility of monitoring of the fusion products stemming out of the B, on the other hand. As shown in Fig. 1(b), the tilted B catcher was at a distance of ∼13 mm from the Al pitcher. The catcher was placed on a motorized stage, to be displaced during the laser shots when the TNSA proton beam was characterized, with the diagnostics placed along the target normal (which would have been blinded by the B sample). This allowed us to dedicate part of the campaign to a careful characterization of the TNSA particles.

The setup shown in Fig. 1(a) includes diagnostics both to characterize the TNSA proton beam from the Al target and to reveal the fusion products emerging from the proton-irradiated B sample. The Cartesian coordinate system in Fig. 1(a) serves here as a reference for the equatorial angle θ on the xy plane (i.e., the plane of the interaction point), with θ = 0° being the laser axis. On the Al target normal, i.e., at θ = 12°, at a distance ∼720 mm from the target chamber center (TCC), a Thomson spectrometer [indicated by TS 1 in Fig. 1(a)], equipped with a microchannel plate detector, allowed for real-time measurements of the energy spectra of the laser-generated protons and heavy ions, at a high repetition rate.³⁰ During the campaign, we also implemented multiple diamond-based time-of-flight detectors (not shown in the condensed schemes in Fig. 1), placed at various angles with respect to the Al target, for obtaining a full view of the angular distribution of the TNSA ions. This analysis, too extensive to include in this paper, is discussed in detail in Ref. 29. The laser interaction with the Al target was also monitored with electron spectrometers placed on the target equatorial plane, to characterize the TNSA mechanism responsible for accelerating ions. The first, in the laser-forward direction with respect to the target, at an angle θ = 21° (i.e., at 9° from the target normal), was at a distance of 668 mm from the TCC. The second, in the laser-backward direction, at an angle θ = −139° (i.e., at 41° from the target normal), was at a distance of 399 mm.

For revealing the alpha particles produced by the p–¹¹B reactions, which had sufficient energy to escape the B catcher, we implemented an array of CR39 detectors,³¹ horizontally aligned as shown in Fig. 1(b), at 250 mm from the B and in line with the interaction point of the proton beam with the B sample, aiming at covering part of the wide cone of emission from it. The array was ∼100 mm long, featured three detectors of dimensions 20 × 20 mm², equally spaced at three positions [indicated in Fig. 1(b) by P1, P2 and P3], and divided into regions with different filter thicknesses (as will be discussed in more detail in Sec. VII). The array was placed about 20 mm below the horizontal plane of the point of interaction. These detectors were exposed to series of multiple shots, to accumulate the fusion reaction products of several p–¹¹B interactions. In a similar position to the CR39, at a distance of ∼250 mm from the B target, we placed an additional Thomson spectrometer (TS 2),³² to support CR39 measurements, exploiting the capability of the Thomson spectrometer to discriminate protons from heavy ions. TS 2 was equipped with either a CR39 detector or imaging plate (IP) detectors, depending on the shot series, and accumulated signals of particles emerging from the B sample during several laser shots. As detailed in  Appendix C, the implementation of the Al shield (2 mm thick) shown in Fig. 1(b), was of key importance to protect the CR39 detectors and TS 2 from the TNSA ions emitted at a large angle that would have directly impinged on the detectors and entered TS 2.

Owing to the implemented pitcher–catcher scheme, exploiting TNSA protons that have energies from the keV range to the multiple MeV range, it is expected that many of the alpha particles will remain within the catcher, as discussed in Ref. 15. They will be produced inside the catcher’s bulk, owing to the high penetration of the protons, and will not have enough energy to escape the B sample. For this reason, for evaluating their overall number, we relied upon a methodology other than the CR39s. The natural B used as catcher contains about 20% of the ¹⁰B isotope and 80% of ¹¹B. Thus, the TNSA proton beam simultaneously interacted with both ¹¹B and ¹⁰B, driving, among others, the reaction p + ¹⁰B → α + ⁷Be, producing radioactive ⁷Be isotopes with a half-life of about 53 days. The number of produced ⁷Be isotopes was measured on-site with a high-purity Ge detector (HPGe), Canberra XtRa Model GX3019,⁷ via γ-spectroscopic analysis of the ⁷Be 478 keV peak. It was equipped with a CAEN DT5781 quadruple independent 16 k digital multichannel analyzer and CoMPASS acquisition software,³³ which provided a timestamp for each registered event. Further details of these measurements and of the detector and setup calibrations can be found in Ref. 7. This system allowed us to obtain off-line information about the effectiveness of interaction, accumulated over many shots.⁷ The long decay time of ⁷Be compared with the shot-to-shot delay in VEGA III allowed observation of the cumulative effect on the B. Starting from this, the characterization of the TNSA proton beam in terms of particle flux allowed us, from the number of measured ⁷Be isotopes, to estimate the number of induced p–¹¹B fusion reactions occurring simultaneously on the same B and therefore the number of alpha particles produced. The natural B catcher can be also radioactivated via the reaction p + B → ¹¹C + n − 2.9 MeV, producing the ¹¹C isotope, of importance for medical applications.^7,8 The ¹¹C has a half-life of about 20 min and a gamma peak at 511 keV, which can be useful to obtain information on the number of produced alpha particles from the p–¹¹B reactions for energies greater than 3 MeV, as discussed in Refs. 7 and 8.

A Thomson spectrometer (TS 1) was placed on the pitcher target normal [see Fig. 1(a)] and served as the main diagnostic for estimating the flux and the maximum energy of the laser-generated protons. These results were the main output used for optimizing, during the first part of the campaign, the laser features in terms of pulse duration and focal position, and the pitcher parameters in terms of target material and thickness. The B catcher was removed from the setup to allow a line of sight from the TS to the Al target. In Fig. 2, we present typical proton and carbon ion spectra (measured by TS 1, and represented here as single-shot averages from measurements of multiple shots), obtained from 6 μm Al targets, where the laser pulse energy was, on average, ∼7 J on target, and the mean pulse duration was ∼220 fs. These laser conditions were obtained after a first phase of optimization and resulted in production of the best proton beam (in terms of particle flux and cutoff energy). The spectrum of carbon ions was obtained by adding all measured ionization states coming from the relative ion parabolas of the same Thomson spectrometer (i.e., TS 1), which were individually analyzed (the high energy end of the distribution was mainly due to C⁵⁺ and C⁶⁺ ions). It was assumed that the entire contribution on these parabolas was due only to carbon ions, and the spectra obtained will be useful for the estimations discussed later in the paper. This set of laser parameters was therefore utilized during the second phase of the experiment, where multiple-shot series were used for driving p–¹¹B reactions and accumulating the fusion products with the dedicated diagnostics. However, despite the optimization process for achieving the best stable beam conditions here, the reported error bars (which represent the standard deviation of the particle flux among the shots used for the average) indicate that significant shot-to-shot fluctuations occurred during the entire experiment. The temperatures of the nonrelativistic accelerated particles were estimated by fitting the experimental spectra with Maxwell–Boltzmann distributions, which are indicated in Fig. 2 by the dashed lines. For carbon ions, the best fit is obtained with a temperature k_BT = 3.05 MeV, while for protons we find two populations with temperatures k_BT = 0.54 and 3.25 MeV, respectively. These temperatures are in agreement with what was found for the laser-accelerated electrons, as discussed in Sec. IV.

The alpha particles were emitted mainly from the irradiated surface of the catcher, and therefore different diagnostics were used for monitoring this emission area. However, as will be discussed also in Secs. VI and VII, some of the laser-accelerated particles from the Al target are expected to be scattered by the B surface. The use of a Thomson spectrometer may be very helpful for separating the alpha particles from the TNSA-backscattered protons. However, it has some significant limitations:

1. It relies on a small pinhole (usually no more than a few hundred micrometers in diameter, as in this experiment), which dramatically reduces the acceptance cone of the revealed particles, making this diagnostic tool hardly suitable for revealing low particle fluxes.

2. It is unable to separate the alpha particles produced by the fusion reactions from the C⁶⁺ ions that are produced by the TNSA acceleration at the pitcher and enter the spectrometer after being backscattered by the B catcher.

3. Alignment of the spectrometer with the most active part of the B interacting region is definitely not an easy task.

Figure 4(a) shows an averaged spectrum of the backscattered protons obtained by directing the Thomson spectrometer TS 2,^32,37 designed and used for assessing ion emission and backscattering in this type of p–¹¹B experiment, onto the catcher. This spectrum was obtained by averaging over 71 shots accumulated on a CR39 detector placed inside the spectrometer. It is related to the trace shown on the CR39 image in Fig. 4(b) and reaches up to ∼320 keV proton energy. At higher energies, i.e., at even lower particle fluxes, the signal of the parabola drops below the background-signal level of the used CR39 (i.e., the density of tracks present in the regions where no parabola is expected), preventing further information from being retrieved. No clear signature was obtained for other particle species. This information, combined with the low energy of the detected protons, indicates that the spectrometer was potentially aligned on a region of the B catcher distant from the center of the main interaction area, confirming that the third of the abovementioned limitations can be quite severe. Clear experimental information about backscattered protons was still obtained, however, albeit not at the maximum emission point. The limitations in terms of sensitivity and alignment precision of the Thomson spectrometer suggest that for estimating the contribution of scattered high-energy particles, other complementary tools must be used, such as CR39s with a large exposed area (see Sec. VI) and/or numerical simulations and analytical calculations (see Sec. VII).

As already discussed, the effective region of the B sample from which alpha particles are expected to be capable of escaping is confined within about a few tens of micrometers from the surface. According to the previous considerations, our primary diagnostic tool for detecting escaping p–¹¹B fusion products consists of the array of CR39 track detectors positioned in direct line of sight with the exposed B surface [see Fig. 1(b)]. CR39 detectors can detect single particles and have some capabilities to discern their species and energy on the basis of the dimensions of the tracks they leave in their plastic bulk, after appropriate chemical etching.¹⁵ 

To enhance detection sensitivity across different energy ranges of protons and ions, each CR39 was mounted inside a frame subdividing the exposed area in four regions, equipped with foils acting as particle filters that, depending on the specific shot series, ranged from 2 μm of PET to 40 μm of Al. Thus, the final area of each sensing region of the CR39 was 9 × 9 mm². Figure 5 shows one of the detectors in our array, with the differential filters applied to each of the exposed regions. In  Appendix D (in Table I) we provide a summary of these filter thicknesses, with the corresponding ranges for protons, alpha particles, and carbon ions, as obtained by Monte Carlo SRIM simulations.³⁸ 

During the first part of the campaign, we evaluated the background signal on these CR39 detectors, as discussed in detail in  Appendix C. In the final version of our setup, which included the thick Al shield, of key importance for allowing only particles coming from the catcher (both emitted and backscattered), we then addressed the actual capability of CR39 to discriminate protons with respect to alpha particles and heavier ions, which is based on the larger track dimension that the latter can produce^15,23 on the same CR39. The calibration curves for protons and alpha particles for this set of CR39s are presented in Fig. 6.³⁹ It is worth noting here that the features of the CR39s are known to change for different producers and for different sets from the same producer. Moreover, calibrations are also dependent on the type of track evaluation process (namely, etching or microscopy; see  Appendix B for the processing procedure) implemented. The orange dashed line on the curve of the alpha particles is added to the calibrations for some of the etching times and indicates the linear response of the detector that is assumed, conservatively, for low-energy ions.

The calibrations reveal the following features, already well known in the literature,^{11,15,23,31,39–41} which apply to both track diameter and track area, provided that circular tracks (i.e., with no ellipticity) are produced:¹⁴ 

1. For each particle species, the physics of track formation and evolution during the etching time gives no monotonic relationship between track area and particle energy, but rather a bell-shaped curve, as for all cases reported in Fig. 6. We denote the maximum areas of these curves for protons and alpha particles by T_p and T_α, respectively. Both areas depend on the etching time. It is worth noting that calibrations at low energies are indeed quite rare, and in general they are found in a limited energy range, due to procedural difficulties, especially in the case of routine calibrations. In conclusion, there is no unequivocal correspondence of particle energy with track area.

2. There is a range of areas A, with A ∈ [0, T_p], where the same A value corresponds to both proton and alpha particle curves. An example is A = 2 μm² in Fig. 6(a) (60 min etching). Therefore, we cannot discriminate protons from alpha particles in this interval of track dimension.

3. Under the conditions of the etching process adopted here, for etching times of 60 min or longer, there is an energy interval of areas T_p < A ≤ T_α where alpha particle tracks have an area that is larger than maximum achievable proton track area. We observe from Fig. 6 and from Refs. 11, 15, 23, and 39 that the difference Δ_αp(t_h) = T_α − T_p increases with increasing etching time t_h (at least for the adopted etching conditions). These ranges are highlighted in the plots of Fig. 6, where they are delimited by the red and black dashed lines.

4. For ions heavier than alpha particles, such as C ions, we can make similar considerations, since the calibration curves are bell-shaped, ideally start from (0, 0), and tend asymptotically to 0 for high energies. Thus, if we define T_c as the maximum value of the calibration curve for C ions, we may observe that T_c > T_α.^15,23 So, for A < T_c, there is no way to separate C ions from alpha particles on the basis of track area alone.

Owing to these considerations, only a subset of all the tracks recorded by the CR39 detectors during the experiment can be associated with particles that are not protons. The track dimension ranges where particles different from protons can be discriminated with high confidence are those where T_p < A ≤ T_α. Their values are defined conservatively, by considering calibration uncertainties, and are indicated in Fig. 6 by the horizontal red dashed lines. For instance, for 90 min etching [Fig. 6(b)], the threshold of T_p = 9 μm² corresponds to an energy window delimited by the vertical black dashed lines, in the ∼[0.4, 1.9] MeV interval. Here, tracks with areal dimensions between zero and ∼9 μm² can be attributed potentially to protons, alphas, and any other particle such as C ions. These energy ranges are obtained from the calibration curves of Fig. 6 for unfiltered detectors. The use of different filters modifies the energies of the particles reaching the bare CR39 and thus provides different “energy windows” of observation to the particle beam directed toward the detector array. In  Appendix D (Table II), we indicate these “energy windows,” obtained with SRIM simulations for each filter used, for the etching times of 60 and 90 min, used later.

In Fig. 7, we present an example of the distribution of detected tracks, with respect to each filter, at position P3, in terms of particle density on the detector surface. The area of the detector without filter was saturated, which prevented us from obtaining a reliable distribution. The areas of the tracks were obtained after an etching procedure of 90 min, and show a broad areal distribution, with lower values below 1 μm². Our analysis provided several pieces of information, including (i) an indication of the overall number of tracks, (ii) the number of tracks for which protons cannot be discriminated from heavier ions, i.e., with an area A < T_p, which is indicated in the plots by the blue part of the spectral curve, and (iii) the number of tracks due to ions different from protons (alphas, C, etc.), i.e., with an area T_p < A ≤ T_α, which is indicated by the red part of the spectral curve. From the latter portion of the obtained spectra, we estimated the number of potential alpha particles that impinged on the CR39 detector. It is important to mention that C, N, O, and other heavier ions share with alpha particles the ability to produce tracks larger than those of protons in specific energy ranges.^15,23 These heavy ions are laser-accelerated from the pitcher Al target and have energies in the range of a few MeV and a TNSA emission cone similar to that of protons. They can be scattered by the B catcher and, like protons, reach the CR39 detectors. Thus, the actual information that we can get from these data is the number of ions heavier than protons. We must rely on theoretical considerations, as in Sec. VII, to discriminate alpha particles from these ions, or to evaluate the percentage of alpha particles with respect to the whole set. Moreover, from the number of tracks with A < T_p (i.e., the blue part of the spectrum), we can obtain information that is complementary to the measurements of the scattered protons obtained from TS 2, shown in Fig. 4(a). From the spectrum in Fig. 7(c), we found that 4.73 × 10⁵ particles/cm² with A < T_p were detected behind a 10 μm Al filter. Assuming that the contribution to the blue curve is mainly from protons (although, as discussed, heavier ions can also provide a contribution), their energy range before the filter is from 770 keV (i.e., the cutoff energy of 10 μm Al) to ∼1.9 MeV. This energy range is obtained under the assumption that the detector has a linear response for protons with E > 1 MeV, as indicated by the blue dashed line in Fig. 6(b). Following this linear continuation of the calibration curve, we find that the minimum detectable track dimension (i.e., tracks with an area close to zero) corresponds to ∼1.6 MeV energy of protons impinging on the detector. These protons, according to SRIM simulations, had ∼1.9 MeV energy before the filter. This leads to 6.08 × 10⁶ protons · MeV⁻¹ · sr⁻¹. This proton flux (which is probably even overestimated, since the contribution of other ions is not considered in this simplified calculation), scattering from the B surface and impinging on the detector, is too low to be revealed by TS 2 (owing to the sensitivity threshold of the spectrometer, discussed in Sec. V). However, it is compatible with the exponential decay of the scattered proton spectrum in Fig. 4(a), where at 320 keV, i.e., the maximum energy that the device was able to detect, about 2.5 × 10⁷ protons · MeV⁻¹ · sr⁻¹ were measured.

The use of the HPGe detector allowed investigation of the nuclear activation of the proton-irradiated B samples. After accumulation of tens of laser shots, the gamma decays from the natural B (composed of 80% ¹¹B and 20% ¹⁰B) were measured, using the methodology of Ref. 7. The decays of ¹¹C [from the reaction ¹¹B(p, n)¹¹C] and ⁷Be [from the reaction ¹⁰B(p, α)⁷Be] were detected. The gamma spectrum showed a dominance of ¹¹C decay at shorter times (due to the shorter half-life of this isotope), whereas at longer times, only the signal from ⁷Be remained evident, having a much longer characteristic decay time. The number of reactions that were obtained experimentally is between 5 × 10⁷ and 10⁸ for ¹¹B(p, n)¹¹C and 2 × 10⁸ for ¹⁰B(p, α)⁷Be, considering the concentrations of B isotopes in the irradiated sample. This provides a robust feedback for the analytical model that was proposed in Ref. 7, which allows an estimate of the number of induced ¹¹B(p, α)⁸Be reactions to be calculated, giving 2.2 × 10⁸ overall fusion events of this type. Using the proton beam measured by TS 1 (see Fig. 2) and assuming that it is almost entirely directed onto the B catcher [as also indicated by the microscope image in Fig. 10(a),  Appendix A], the analytical model provides the expected spectrum of produced alpha particles, which is presented in Fig. 8. This spectrum (red plot) represents the fraction of alpha particles that escape the catcher and reach the location of the CR39 detectors, among those that are produced in the bulk or on the surface of the B catcher and have sufficient initial energy to exit the B bulk, according to their point of origin inside it. These were calculated considering the penetration depth of the protons driving the reaction. In particular, the number and energy of the alpha particles were estimated for each proton energy. The energy loss of alpha particles in the B catcher, and later in different filters that were used in the experimental CR39 configurations, were estimated using SRIM. Different alpha channels were estimated using the experimental cross sections for both the ¹⁰B and ¹¹B components. While the ¹⁰B case involves simple two-body kinematics, alphas produced from the ¹¹B were estimated assuming also two-body kinematics with ⁸Be. We followed the approach of Kimura et al.¹⁰ and assumed a main contribution for this channel, denoted by α₁, where ⁸Be is in its first excited level. A Breit–Wigner distribution with the experimental width of 1.5 MeV was used to randomly generate the alpha and ⁸Be* excited state kinetic energies. The ⁸Be* fragment subsequently decays into two alphas. The particles that are emitted toward the direction of the CR39, and are energetic enough to pass through the filters, are eventually detected. The first peak, at around 2.5 MeV energy observed in the theoretical distribution of Fig. 8, is due to the decay of ⁸Be* from the excited level. More details will be given in a subsequent paper.

Also in Fig. 8, with the green curve, we show the spectrum of protons that are scattered by the surface of the B catcher and are deviated toward the angular position of the CR39 detectors, i.e., with an angle of ∼54° with respect to the B surface [see Fig. 1(b)], according to Rutherford’s scattering model.⁴² For C ions, which are slightly more massive than B, Rutherford’s scattering formulas give a maximum deflection angle of ∼26° from the B surface. Therefore, they cannot reach the CR39 array [as one can see from Fig. 1(b), remembering that distances are not in scale with each other]. However, if the catcher atoms had a mass slightly larger than B, the scattering angles would change significantly. This is the case, for example, for BN catchers (often used in p–¹¹B experiments^8,13,43) or, alternatively, in the case of impurities deposited on the B surface, which alter the effective atomic mass of the scattering surface material. The latter effect is one of the typical drawbacks of accumulating numerous shots on the same B catcher and requires a detailed analysis of the deposited materials and the thickness of the deposition, which is beyond the scope of the present paper. Instead, we consider here the simple case of a BN catcher, with effective ion mass A = 12 like the incoming C ions, although it should be noted that this represents a scenario in which, compared with our experimental conditions, the number of scattered C ions is overestimated. The results are shown by the brown curve in Fig. 8. As reference, we have added in Fig. 8(a) the measured TNSA spectra from Fig. 2, which served as input for these analytical calculations. In Fig. 8(b), we present the low-energy part of these spectra, for the two cases of 2 μm PET and 10 μm Al filters, which were among those implemented on our CR39 detectors. The particle flux, especially for the C ions, as expected, decreases compared with the filter-less case. For the 10 μm Al case, owing to the higher stopping power and thickness of the foil, the orange curve representing the C ions is decreased by about two orders of magnitude. The distribution of alpha particles (red curves), owing to the deeper penetration depth that remains, suffers much less of a decrease. This analysis allows us to evaluate the contribution of scattered C ions from BN on the CR39s, which is important, since their signals (i.e., track dimensions) are similar to those of the alpha particles.²³ Even though, as mentioned before, this scenario overestimates the number of scattered C ions, we find that their contribution does not significantly influence the measurements obtained by the CR39s. If we consider the detected alpha particle energy range in the typical case of 90 min etching, i.e., from 0.38 to 1.91 MeV, then only in in the case of the 2 μm PET filter (i.e., the thinnest filter of our set, representing only the first point of the spectral curve that we will discuss in Sec. VIII), is the number of C ions comparable to the number of predicted alpha particles. For this filter thickness, the contributions of alpha particles and C ions on the detector are estimated to be 40% and 60%, respectively, which might therefore lead to overestimation of the obtained alpha particle flux. In the case of the thicker filters, such as the 10 μm Al filter shown in Fig. 8(b), the contribution of C ions is more than an order of magnitude lower than the number of expected alpha particles and therefore is negligible.

The primary number of alpha particles that this model predicts will be detected, compares very well with those experimentally revealed in the CR39, as will be discussed in Sec. VIII. Similar agreement is found for the production of ¹¹C and ⁷Be, as discussed in Ref. 7. The model agrees quite well and its results are complementary with the measurements obtained for scattered protons from the Thomson spectrometer TS 2 [Fig. 4(a)]. As shown in Fig. 8(a) by the purple curve [which represents the spectrum measured by TS 2, as in Fig. 4(a)] and green curve, i.e., the model and the measurement from TS 2, coincide for the proton energy E ≈ 300 keV (i.e., at the higher limit of detection of TS 2). For lower energies, the analytical and experimental results diverge: the model might be underestimating the scattering of low-energy protons from B, since it uses the TNSA spectrum measured by TS 1 as input [shown in Fig. 8(a) by the blue curve], which has an intrinsic low-energy detection threshold of about 300 keV for protons. Moreover, the proposed model is also consistent with what was found by the CR39s, in terms of the number of tracks that were not associated with alpha particles. As discussed in Sec. VI, from the spectrum in Fig. 7(c) (i.e., the spectrum obtained from the tracks recorded by the irradiated CR39 covered by 10 μm Al), we obtained a flux of $∼6.08×106$ protons · MeV⁻¹ · sr⁻¹ in the range 0.77–1.9 MeV. By integrating, in the same energy range, the curve of scattered protons provided by the analytical model, we obtain $∼9.4×106$ protons · MeV⁻¹ · sr⁻¹, which is in good agreement with the experimental measurement.

By discriminating the protons using the method of Sec. VI for the different filters on the CR39s, we obtained spectral information about the distribution of particles, other than protons, that impinge on our detectors. In Fig. 9, we present data obtained by integrating the number of track counts of the red part of the obtained distributions of track density, like the example in Fig. 7. The different energy windows, indicated by the horizontal bars around each point, were obtained by adapting the highlighted energy ranges of the calibration curves of Fig. 6 to the thicknesses of the filters used in front of the detectors (see  Appendix D, Table II). We then used these numbers for estimating the original spectrum of the incoming particles, before they pass through the filters. To do so, we made the assumption that all those particles were alpha particles, and then performed SRIM simulations to account for energy loss on the several filters, and thus obtained the initial energy of the alpha particles when they left the catcher. The values of particle number shown in Fig. 9 were obtained by normalizing the track density (expressed as number of tracks per unit of area on the detector) to the solid angle intercepted by the exposed area of the CR39s and normalized by the width of the energy window to which they refer. They were then averaged to the number of cumulated shots. In this way, we are able to provide an experimental estimate of the spectrum of alpha particles reaching the CR39 array. A strict integration of these curves gave the total number in these specific energy intervals as ∼(2.1 ± 0.7) × 10⁶ alphas/sr for the first shot series (black dots) and ∼(1.5 ± 0.6) × 10⁶ alphas/sr for the second series (green dots). The values indicated by the red diamond markers were obtained from the analytical model of Sec. VII. We integrated the analytical curve of the generated alpha particles [the red curve in Fig. 8(a)], which takes account of the particle flux escaping from the B catcher and impinging on the CR39 detectors, over the energy ranges of the experimentally obtained points of the black dataset of Fig. 9. By integration of these values, the total number of alpha particles predicted by the model in the range from 1.6 to 5.4 MeV is ∼2.2 × 10⁶ alphas/sr.

The purpose of this work was to assess the features and potential of the pitcher–catcher configuration for driving p–¹¹B nuclear fusion reactions with high-repetition-rate petawatt lasers. We therefore took particular care in the characterization of the laser-matter interaction and the accelerated/scattered particles. Our findings confirm that this scheme is suitable for producing alpha particles using petawatt class high-repetition-rate laser systems. We have discussed here a methodology for effectively evaluating the performance of such laser-driven alpha sources and have addressed the challenges of implementing an experimental setup of this type. The proposed methods, which can be adapted to experiments that make use of similar setups, essentially rely on (i) careful characterization of the TNSA beam (addressing both protons and heavy ions) that drives the fusion reactions, (ii) analytical and numerical modeling and/or additional measurements that allow estimation of the flux of produced alpha particles that escape the B catcher, with respect to the flux of protons and heavy ions that potentially produce a similar signal on the implemented detectors, and (iii) analysis of the signals obtained from CR39 detectors that allows distinguishing the contribution of protons from the one of heavier ions, which produce tracks compatible with those of alpha particles.

The TNSA beam was monitored by multiple diagnostics to obtain a full characterization of the accelerated particles. The measurements, routinely performed throughout the campaign, allowed tuning of the laser parameters to provide an optimal interaction with the Al target. Moreover, exploiting the high repetition rate of the laser allowed typical proton and carbon spectra to be obtained from a statistical analysis of tens of dedicated shots. These spectra thus provided a statistically sound input for the analytical model that aimed to predict the flux of produced alpha particles.

First, clear information that a significant number of p–¹¹B → 3α fusions occurred in the B was provided by the measurements of activation by the HPGe detector. As discussed in Sec. VII, an estimate of the overall number of alpha particles produced in the B catcher was obtained: 6.6 × 10⁸ alphas/shot. However, as was also observed from the experimental data, owing to the broad spectrum and high energy of the proton beam impinging on the B, the alpha particles were produced in the entire bulk of the B catcher. Only protons with a few MeV energy at most trigger fusion reactions generating alpha particles close enough to the surface to escape from the front side of the boron bulk. Thus, our analytical model predicts an alpha spectrum that is strongly modified with respect to the original one, produced within the bulk. This has been described in Sec. VII, where the effect of different filter thicknesses on the particle spectra (alpha particles and scattered particles) has also been analyzed. This analytical approach has allowed us to interpret the results obtained from the detectors used to reveal the alpha particles, since the our observations indicate that they were indeed produced by both p–¹¹B fusion reaction products and particles scattered by the B sample.

The main diagnostic tool for revealing the alpha particles emerging from the B catcher was an array of CR39s placed in line of sight with the irradiated B surface. During the first part of the campaign, we optimized the positions of these detectors and routinely performed preliminary analysis on-site. This allowed us to estimate the maximum number of shots to be accumulated on the detector before saturating it, namely, between 35 and 50 shots. Moreover, we performed a careful estimation of the background signal that was produced on the detectors, leading to implementation of the protecting Al shield [see Fig. 1(b)], which allowed the removal of a significant background signal generated by direct irradiation by the TNSA beam (see  Appendix C). As discussed in Sec. VI, the calibration curves of the CR39 detectors can be used to obtain threshold values of the track dimensions that allow the contribution of protons to be discriminated from other contributions. This approach, in combination with equipping the CR39 array with differential filters and appropriate time-step etching, can give a suitable estimate of the impinging alpha spectrum, if information on particles heavier than protons that reach the array (such as TNSA particles scattered from B) is supplied. As obtained from Fig. 8, in the alpha particle energy range of interest, from 0.38 to 1.91 MeV, in the case of 90 min etching of the CR39 and a 2 μm PET filter in front of the detector, the estimated number of C ions is comparable to the predicted number of alpha particles, for the example case of a BN catcher. A possible overestimation of the alpha flux due to the contribution of C ions is limited to just this case, since the use of thicker filters to protect the detector leads to a significantly reduced contribution of C ions, by more than one order of magnitude, in the case of 10 μm (or thicker) Al filters. This shows that the C ion contribution is negligible in the spectrum of Fig. 9, representing the alpha particles reaching the CR39 array. The total flux of measured alpha particles, considering the black dataset of Fig. 9 (i.e., that over the widest range of energy), obtained after a 90 min etching procedure, is estimated to be ∼(2.1 ± 0.7) × 10⁶ alphas/sr, which compares very well with the theoretical flux of alphas (∼2.2 × 10⁶ alphas/sr) calculated from the red dots in Fig. 9 in the same energy range. Considering a uniform alpha emission from the overall number of estimated fusion reactions, obtained from HPGe measurements, it is possible to obtain a reference number for the estimated alpha density flux originating within the B bulk over the whole alpha spectrum: 5.25 × 10⁷ alphas/sr. The number of alpha particles detected by the CR39 in the limited energy range of the black dataset of Fig. 9 are about 4% of the latter, which are instead related to the full spectral emission. This gives us an estimate of the minimum transmission ratio of alpha particles produced in the B bulk that are capable of passing through it and reaching the CR39 position in this experiment. The shape of the theoretically expected alpha particle distribution and consequently the obtained red dataset in Fig. 9, although predicting a comparable integrated particle flux, differ somewhat from the experimental data. The likely reasons for this are as follows: (i) the theoretical model calculates the alpha particle spectrum starting from the measured proton energy spectrum, which (as shown in Fig. 2) exhibits significant fluctuations; (ii) the analytical curve is based on models (concerning, for example, the cross sections for the fusion events and the penetration range of the accelerated protons and generated alpha particles) that assume the B catcher to be solid and at room temperature; (iii) the effects on the B surface of impinging X rays, hot electrons (Fig. 3), and high-energy protons are not considered (these include heating and plasma formation, damage to the catcher surface during a large sequence of consecutive shots, and ion implantation on the catcher surface). Future work in this direction needs to include the development of an even more accurate theoretical model for predicting the experimental measurements in a real-case scenario of high-repetition-rate laser–matter experiments.

The methodology developed here for the CR39 analysis is capable of effectively accounting for the contribution of incoming protons, which is a well-known issue with this type of detectors, by using both proton and alpha calibrations of the CR39. In some cases, estimates of the number of detected alpha particles can be obtained using only the alpha particle calibration of the CR39s.^{13,15,25,43–45} This inevitably introduces an increased uncertainty in the estimates, the magnitude of which depends strongly on the specific experiment performed, owing to the non-monotonic calibration curve for alpha particles (see Fig. 6). In such cases, the contribution of low-energy alpha particles might be erroneously attributed to particles with higher energy. In a subsequent experiment performed on this facility by most of the authors of the present paper,⁴¹ we have found by comparison that for the scheme investigated here, a minimal increase in uncertainty was produced, which did not significantly affect the overall measurement uncertainty.

One of the main purposes of this work, as also shown in the Appendixes, is to reveal the significant issues to be taken into account for a suitable use of this setup. We have proposed effective solutions for these, which have been fruitfully used in subsequent experiments of the same type on the same facility.^8,43 This scheme can thus be effectively applied to high-repetition-rate petawatt-scale laser facilities with higher energy and intensity to exploit its full potential. Hopefully, future experiments will further improve both the fusion reaction process, by optimizing and stabilizing the laser–plasma proton beam even more (especially in the range 0.2–5 MeV, where the p–¹¹B cross-section is higher²⁸) and developing even more accurate and sensitive diagnostic methodologies. In this regard, an experimental campaign of this type has been recently performed at ELI-Beamlines with the L3 laser by some of the present research group, and the results are now under preliminary assessment.

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Program (Grant Agreement No. 101052200—EUROfusion). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. The involved teams have operated within the framework of the Enabling Research Project: ENR-IFE.01.CEA “Advancing Shock Ignition for Direct-Drive Inertial Fusion.”

This work has been carried out within the framework of the COST Action No. CA21128-PROBONO “PROton BOron Nuclear Fusion: From Energy Production to Medical Applications,” supported by COST (European Cooperation in Science and Technology, www.cost.eu).

The research leading to these results has received funding from LASERLAB-EUROPE (Grant Agreement No. 871124, European Union’s Horizon 2020 Research and Innovation Program).

This work was supported in part by the United States Department of Energy under Grant No. DE-FG02-93ER40773.

We also acknowledge support from Grant No. PID2021-125389OA-I00 funded by MCIN/AEI/10.13039/501100011033/FEDER, UE and by “ERDF A Way of Making Europe” by the European Union and Unidad de Investigación Consolidada of Junta de Castilla y León UIC 167.

This work was supported in part by the National Natural Science Foundation of China under Grant No. 12375125 and the Fundamental Research Funds for the Central Universities.

This work was performed with the support of the Czech Science Foundation through Grant No. GACR24-11398S.

We thank the Laser Division, Engineering, Radioprotection, and TIC areas, as well as the Managing area of the CLPU, for their valuable support.

The authors have no conflicts to disclose.

M. Scisciò: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – original draft (equal). G. Petringa: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal). Z. Zhu: Data curation (equal); Formal analysis (equal); Investigation (equal); Software (equal); Writing – review & editing (equal). M. R. D. Rodrigues: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). M. Alonzo: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). P. L. Andreoli: Investigation (equal); Writing – review & editing (equal). F. Filippi: Investigation (equal); Writing – review & editing (equal). Fe. Consoli: Investigation (equal); Writing – review & editing (equal). M. Huault: Data curation (equal); Investigation (equal); Writing – review & editing (equal). D. Raffestin: Data curation (equal); Investigation (equal); Writing – review & editing (equal). D. Molloy: Data curation (equal); Investigation (equal); Writing – review & editing (equal). H. Larreur: Investigation (equal); Writing – review & editing (equal). D. Singappuli: Investigation (equal); Writing – review & editing (equal). T. Carriere: Investigation (equal); Writing – review & editing (equal). C. Verona: Data curation (equal); Investigation (equal); Writing – review & editing (equal). P. Nicolai: Investigation (equal); Writing – review & editing (equal). A. McNamee: Investigation (equal); Writing – review & editing (equal). M. Ehret: Data curation (equal); Investigation (equal); Writing – review & editing (equal). E. Filippov: Data curation (equal); Investigation (equal); Writing – review & editing (equal). R. Lera: Investigation (equal); Writing – review & editing (equal). J. A. Pérez-Hernández: Investigation (equal); Methodology (equal); Writing – review & editing (equal). S. Agarwal: Data curation (equal); Investigation (equal); Writing – review & editing (equal). M. Krupka: Data curation (equal); Investigation (equal); Writing – review & editing (equal). S. Singh: Data curation (equal); Investigation (equal); Writing – review & editing (equal). V. Istokskaia: Data curation (equal); Investigation (equal); Writing – review & editing (equal). D. Lattuada: Data curation (equal); Investigation (equal); Writing – review & editing (equal). M. La Cognata: Investigation (equal); Writing – review & editing (equal). G. L. Guardo: Investigation (equal); Writing – review & editing (equal). S. Palmerini: Investigation (equal); Writing – review & editing (equal). G. Rapisarda: Investigation (equal); Writing – review & editing (equal). K. Batani: Investigation (equal); Writing – review & editing (equal). M. Cipriani: Investigation (equal); Writing – review & editing (equal). G. Cristofari: Investigation (equal); Writing – review & editing (equal). E. Di Ferdinando: Investigation (equal); Writing – review & editing (equal). G. Di Giorgio: Investigation (equal); Writing – review & editing (equal). R. De Angelis: Investigation (equal); Writing – review & editing (equal). D. Giulietti: Investigation (equal); Writing – review & editing (equal). J. Xu: Investigation (equal); Writing – original draft (equal). L. Volpe: Investigation (equal); Writing – review & editing (equal). M. D. Rodríguez-Frías: Investigation (equal); Writing – review & editing (equal). L. Giuffrida: Investigation (equal); Writing – review & editing (equal). D. Margarone: Conceptualization (supporting); Investigation (equal); Writing – review & editing (equal). D. Batani: Investigation (equal); Resources (supporting); Writing – review & editing (equal). G. A. P. Cirrone: Conceptualization (supporting); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). A. Bonasera: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing – original draft (equal). Fa. Consoli: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal).

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

During the experiment, different nominally identical B samples were used as catcher targets and were irradiated by multiple-shot series. The accumulation of many shots onto the same B left, on the irradiated surface, an area where debris coming from the pitcher (mainly Al) was deposited after being sputtered by the laser hitting the target. This gave information on the aging/spoiling of the B surface after many shots, which is important when exploiting high-repetition-rate interactions. In Fig. 10(a), we show a microscope image of the irradiated boron. The horizontal and vertical lineouts (Gaussian-like) of the gray values of the image (indicated in the figure by the red dashed lines), provide a good estimate of the elliptical area that is marked by the debris (as expected, since the B sample had an inclination of 54° with respect to the pitcher), for which we obtained an area A ≈ 42.2 mm². Both vertical and horizontal lineouts in Fig. 10(b) indicate that the peak of the gray values is on the irradiated target, indicating that the sample was well aligned with the Al target.

After being exposed to the particles and the radiation produced during the laser–plasma interactions, 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. This process aimed at providing comprehensive insight into the evolution of track diameter over etching time, thereby enhancing the potential for particle discrimination, at the expense of increased throughput of data. After the etching process, the CR39 detectors were analyzed to extract valuable data from the visible tracks, using a Nikon ECLIPSE Ni-E fully automated inverted optical microscope, enabling precise and detailed track measurements. Pictures were acquired with a DS-Qi 2 camera, having a resolution of 4908 × 326 and a sensitivity range of ISO 800–51 200 mV/s.

In the present campaign, the CR39 detectors revealed particles stemming from the catcher, over tens of laser shots. Given the expected low number of alpha particles, during the first part of the campaign, special attention was paid to estimating the background on the CR39 detectors, also obtained in shot series without catcher and related holder. This estimation considered two main aspects:

1. Latent tracks due to natural background on the CR39, caused by environmental radiation.¹⁵ 

2. Particles reaching the detectors via scattering off the surfaces of the TNSA target frame and off the various objects in the chamber.

Concerning the first point, the frame where the detectors were placed was made of 2 mm-thick Al, capable of providing an effective shield for any of the particles meant to reach the CR39. Thus, the etching of the unexposed regions of the CR39 supplied appropriate information on the background, which turned out to be very low for this brand new set of CR39s, at just about 10 tracks/cm².

We estimated the second type of contribution by analyzing some CR39s in the absence of both the catcher and its holder. We found that a surprisingly large number of ions were able to reach them. The upper image in Fig. 11 is from one exposed region of a CR39 placed at position P2, obtained after a series of 86 shots and chemical etching. It is evident that this region of the CR39 is heavily polluted by particles with different areal dimensions. We found that the careful positioning of a protecting Al screen (shown in Fig. 2) was an effective solution to this problem. The lower image in Fig. 11 is of a CR39 etched after 20 shots with the Al screen in place. The use of the thick Al plate clearly prevented any obvious pollution of the detector and thus served well at stopping all the stray particles observed in the upper image. This showed that one significant contribution to the pollution comes from the pitcher structure and indicates that appropriate care must be taken in the future implementations of this pitcher–catcher scheme for p–¹¹B interaction.

For more detailed observation, a thick pitcher frame was constructed with a conical hole on the back side of the 45° half aperture angle, and the CR39s were placed at about 90° from the normal axis of the pitcher [see Fig. 1(b)]. Thus, no direct line of sight was provided from the latter to the three CR39s. Nevertheless, potential lateral straggling of ion flows, interacting with the frame edges, should have produced an important scattering component leading to stray ions reaching the CR39s. In fact, the Al shield was effective in protecting the detectors at the P2 and P3 positions of the CR39 array [see Fig. 1(b)] and partially mitigated the pollution on the detector at P1. These observations showed that ion scattering was a significant effect that needed to be taken into account, and therefore we wanted to minimize potential contributions from scattering of the TNSA ions emitted from the pitcher on the B frame holder. We did this by considering in the analysis of the CR39 images the selection of tracks that had zero or very small (0.9) ellipticity and thus came from the B surface and its close neighborhood, rather than from other nearby objects.¹⁴ 

Table I shows the cutoff energies of protons and heavier ions provided by the different filters that were used for covering the exposed regions of the CR39 detectors.

Table II shows the energy ranges of alpha particles that met the conditions for tracks on the CR39 detector with a calculated area T_p < A ≤ T_α.³⁹ These ranges are listed for the different filter thicknesses and materials used in the experiment. The range in the case of no filter was obtained from the calibration curves of Fig. 6. The ranges for the filtered regions were obtained by SRIM simulations.