Univocal Discrimination of α Particles Produced by 11 B(p, α )2 α Fusions in Laser-Matter Experiments by Advanced Thomson Spectrometry

Te energy problem is an open issue becoming increasingly pressing. Te possibility to use nuclear fusion as an alternative energy source is thus acquiring progressively more importance and many investors are pushing to achieve the goal of an electric plant based on fusion. Te most studied reaction is the deuterium-tritium one, but this poses several technical issues related to the handling of the radioactive fuel and neutron generation. In this frame, the aneutronic 11 B(p, α )2 α fusion reaction has attracted the interest of many researchers. Despite a fusion reactor based on pB is still a long-term goal, the study of this reaction is important both for astrophysics research and for its possible employment in schemes of high brightness source of α particles for applications, as for instance in medicine. Nevertheless


Introduction
Te aneutronic fusion reaction based on the synthesis of a proton with a Boron-11 nucleus [1][2][3] has attracted the interest of both researchers and investors [4,5]. Indeed, despite the lower cross section, the 11 B(p, α)2α fusion reaction presents some non-negligible advantages with respect to the more studied deuterium-tritium one, such as the abundance of the reactant, the use of nonradioactive fuel, and the lack of neutrons as products. Even though fusion reactors based on p+ 11 B reaction are still a long-term goal, the study of this process is relevant both for astrophysics research [6] and for its possible employment as high brightness source of α particles for important applications, such as medicine [7,8]. To trigger the reaction, two main schemes involving high energy and intensity lasers have been studied: the "in target" scheme [2,[9][10][11][12][13], where a highintensity laser pulse is focused on an hydrogenated boron target, and the "pitcher-catcher" scheme, where a beam of laser-accelerated protons is directed onto a boron target or a preformed boron plasma [14][15][16][17][18]. Both geometries showed a progressive increment in the yield of p+ 11 B fusion reactions along the experiments that were carried out during the last years [2,10,11,14]. Nevertheless, aiming at further progresses in this feld, the understanding of the process needs to be deepened. To pursuit this objective, a detailed characterization of the laser-matter interaction and of the fusion products must be achieved. Given the environment in which these experiments are conducted, the latter is anything but a simple task [19]. Indeed, along with the fusion reactions, several other processes are triggered inducing electromagnetic ionizing radiation spanning over a broad spectrum, particle radiation, and radiofrequency-microwave emission [20][21][22]. Hence, a non-negligible background is produced, hindering the detection of the fusion products characterized by a low yield. Moreover, the emitted electromagnetic pulses (EMPs) in the radiofrequencymicrowave regime can lead to the malfunctioning of some of the deployed diagnostic systems, especially when located near the interaction point [21,23].
Te diagnostic techniques commonly used in this feld are solid state nuclear track detectors (SSNTDs) [24,25], time-of-fight method [26] and Tomson spectrometers [27]. Each of these presents some specifc advantages and drawbacks for this context [19].
In the SSNTD, the impinging radiation damages the flm in localized spots and an etching procedure is used to reveal the tracks. A detailed analysis of the track characteristics allows to infer information on the impinging radiation [18,28,29]. However, the background due to the detection of all other emitted radiation produced during the laser-matter interaction hinders the efective discrimination of α particles. Tus, the flm is usually covered by a thin plastic or metal foil to cut the contribution of low energy and heavy ions while allowing for α-particle detection. Nevertheless, protons are more penetrant than alphas; hence, the presence of the flter does not cut their contribution from the signal [19].
Te time-of-fight technique is an efcient way to obtain information on the energy of the detected particles once their type is known. Its working principle relies on the measurement of the time needed by the particle to travel through a known distance, i.e., from the source to the detector. Te arrival time of the particle must be detected together with the reference of the laser-matter interaction time, which is usually retrieved by the detection of the emitted UV and X-rays. Te main issue in this kind of diagnostic system is the simultaneous detection of alphas and other ions. As for SSNTD, the contribution coming from low energy and heavier ions can be cut by the employment of flters of proper material and thickness. However, also in this case, the use of flters is not efective in excluding the proton contribution [19].
Te discrimination of particles having diferent mass-tocharge ratios can be achieved by employing Tomson spectrometers. Tese devices exploit the action of parallel electric and magnetic felds, both orthogonal to the direction of propagation of the incoming charged particles. As a result, particles reaching the detector plane leave diferent parabolic traces, each associated to a specifc mass-over-charge ratio. As shown in Figure 1, ions entering a Tomson spectrometer will frst traverse an entrance pinhole, whose dimension determines the energy resolution as well as the capability of discriminating the diferent ion traces. Ten, there is a region where both an electric and magnetic feld are applied. Here, the charged particles are defected and afterwards they travel over a proper drift space, while increasing their mutual separation until they reach the detector site. Tis could either be a passive detector [30], such as imaging plates [31] and SSNTDs, or an active one to allow on-line measurement [32].
A strong efort has been required to design Tomson spectrometers resistant to the electromagnetic pulses (EMPs) produced during the interaction and being thus capable to work near the interaction point, for enhancing the device sensitivity by the increase of the solid angle covered. Tis allows to employ a small entrance pinhole while maintaining a high signal-to-noise ratio even for the products of low-rate nuclear fusion reactions. For this purpose, it was necessary to have an optimized shielding for EMPs otherwise they can couple to the spectrometer and cause an unwanted modulation, and thus superimposition, of the traces [11,33,34]. An optimal EMP resistance was achieved by keeping the defector compact, the spectrometer has indeed only one defecting unit providing both electric and magnetic defection. Tis grants that the residual EMPs entering the device act on the particles only for a limited amount of time. Te employment of a single defecting unit also reduces the overall spectrometer dimension allowing to place it near the interaction point without blocking the line of view of other diagnostics.
Te main advantage of Tomson spectrometers is that the proton trace is well separated from all the others. Hence, using this diagnostic, the issue related to the superimposition of proton to alpha particle signal is solved, easing the procedure for alphas univocal discrimination. However, the limitations in employing this technique come from the fact that the trace due to α particles is superimposed to those left by all other ion species with the same mass over charge ratio such as C 6+ , N 7+ , or O 8+ , that are routinely detected during laser-matter interaction experiments [19,20].
One possibility in achieving the univocal characterization of the produced α particles consists in the simultaneous characterization of the interaction by means of several diferent diagnostics placed in close proximity and providing complementary information [19,35]. Nevertheless, this is not always a viable solution due to space limitation in the experimental chamber. In this article, we intend to analyse in detail the possibility of employing a Tomson spectrometer with an adequate diferential fltering system [36] to obtain univocal identifcation of alphas produced by the fusion reaction. We will also investigate the feasibility of using a TOF line coupled to a Tomson spectrometer to discriminate carbon ions from alpha particles for the energy ranges where the diferential fltering methods cannot be used.

Differential Filtering Method
Te motion of a charged particle moving along the z direction with velocity v z entering a Tomson spectrometer characterized by an electric feld E � | E → y | and a magnetic feld B � | B → y | applied for region of length L followed by a drift space of length L D can be described by the following equations (37): where Z is the atomic number, q e is the electronic charge expressed in Coulomb, A is the atomic mass, m p is the proton mass expressed in kg, and E k is the ion energy expressed in Joule. A B and A E are the integral coefcients of the magnetic and electric feld along the longitudinal direction z that includes the nonuniform feld. Tey include both the feld integral I B and I E [38] as well as all the dependences from the distances as follows: where L 1 is the distance from the target to the pinhole and L 2 is the distance from the pinhole to the electrodes and magnets, as labelled in Figure 1. A B and A E are thus expressed in Tm 2 and Vm, respectively. From these relations, the following equation of the parabolic traces detected by the chosen imaging system can be retrieved: Tese expressions do not consider relativistic efects of the particle motion, assumption which is reasonable for the typical energies of laser-accelerated ions (in the range of a few tens of MeV at most). Te equations also assume the case where (L/R) ≪ 1 (being L the length of the dipole and R the bending radius of the particles travelling through it) condition that is often satisfed given the dimensions of the dipoles implemented in TS devices (usually a few centimetres long). As expected, the traces have a parabolic shape: each parabola is related to a specifc mass over charge ratio and each point on the parabola corresponds to a diferent ion energy. Te capability of resolving diferent traces and energies is related to the strength of defection of the magnetic and electric feld, as well as to the pinhole projection size [32,39]. In general terms, to improve both the energy and the charge resolution, small pinhole sizes and large defecting felds are preferred, according to the specifc energy ranges of interest and the expected ion fuxes [39]. Identifying the size of the pinhole projection on the detector plane as s, the energy resolution along a parabolic trace for any A/Z can be expressed as follows [40]: where the A and Z appear in the expression of x, from equation (1). Te charge resolution is limited by the capability of separating the traces left by ions having diferent mass over charge ratios on the imaging system. In general, the separation between the diferent traces decreases as the ion energy increases, i.e., getting closer to the pinhole image projection. For each couple of parabolic traces, it is possible to identify their merging point and the corresponding energy here, it is called merging energy. Tis is the maximum energy over which ion specie discrimination is no more achievable due to the intersection of the traces. Te mentioned merging energy E m is strongly related to the electric feld defection as well as to the pinhole image size. For a pair of two ion species, it is possible to write the following equation: the subscripts "1" and "2" are two generic indexes referring to the two diferent ionic species considered, and E m defnes the merging energy of the ion with charge Z i q e [40].
For instance, taking as reference the parameters of the Tomson spectrometer labelled as "BIG" described in Giorgio et al. [33] and assuming to have s � 1.5 mm the superimposition of the alpha trace with the one of protons happens for E α ≃88 MeV, whereas the superimposition of the alpha trace with the one of C 5+ happens for E α ≃24 MeV.
As mentioned in the introduction, the trace of the α particles will be superimposed to those of other fully stripped ions such as carbon, oxygen, and nitrogen, each having A/Z � 2. In each point (x, y) of this specifc parabolic trace, from equation (1), it results that all ions contributing to the signal have the same velocity, thus the same energy per nucleon. Being E α the energy of α particles, for each (x, y) point, it is possible to write Because of the higher stopping power of heavier ions, the action of a foil of suitable thickness placed in front of the imaging system can be exploited to cut out the contribution of heavier ions from the trace, while allowing Laser and Particle Beams alphas to pass through it. Nevertheless, given the expected broad spectrum of the emitted alphas, the employment of a single flter is not suitable to recover a complete information since it would be too thin to cut the contribution coming from heavier ions having higher energies or too thick for the alphas of lower energy. For instance, according to simulations performed with the Montecarlo code SRIM [41], a 15 μm of aluminium foil allows to detect alphas free from any other ion contribution in the energy range (3.9-5.7) MeV. But for E α < 3.9 MeV, the flter is too thick, and alphas are not able to cross it, whereas for E α > 5.7 MeV, carbon ions of 17.1 MeV start to pass through the flter contributing to the trace generation, as highlighted in Figure 2 where the ranges of alphas and carbon ions are depicted as a function of energy per nucleon.
A similar issue has been discussed and addressed by Alejo et al. [36] for the univocal characterization of deuteron ions emitted during the irradiation of a deuterated plastic. Te author suggests the possibility of employing a set of diferent flters along the energy dispersion axis, tailoring the material and the thickness of each to cut the contributions of all other ions but deuterons. A similar approach can be used for our purpose: for each energy interval, delimited by (x 1 , x 2 ) coordinates, the chosen flter must cut the contribution coming from heavier ions while allowing alphas with energies within the range (E α (x 2 ), E α (x 1 )) to reach the detector.
In Figures 3(a)-3(d)), the ranges of alphas and carbons for diferent foil materials are reported as a function of the energy per nucleon. Te data are obtained from the SRIM [41] tables.
Terefore, it is possible to determine the proper flter thickness to use in each energy region just by comparing the ranges of the ions.
Once the ideal flter material and thickness has been found, it is necessary to translate the energy interval into the corresponding spatial region where the flter has to be placed. Tis can be performed by exploiting equation (1), which allows to calculate the spatial range (along the horizontal direction x) that corresponds to a given energy range.
Te discussed methodology is now applied taking as reference the Tomson spectrometer labelled as "BIG," described in detail in Giorgio et al. [33]. Te mentioned spectrometer was expressly designed to detect low-rate fusion reaction products. It is supplied with a double entrance pinhole drilled in lead with the smaller one having a 0.35 mm diameter. Te spectrometer works with magnetic feld B ∼ 4 kG and electrostatic potential V � 7 kV. Te length of the electrodes and magnets is of 25 mm. Te gap between the magnets is 5 mm and the drift space before reaching the imaging system (either an imaging plate or a CR-39) is 197 mm long.
Te values reported in Table 1 have been retrieved according to the ion ranges provided by the SRIM tables and depicted in Figure 3  section, as reported in Kimura et al. [42], and also to investigate if alphas of slightly higher energies are detected. From Table 1, the ∆x values for the specifc confguration of the TS in use appear to be rather small. To guarantee the stability and precision in mounting such thin stripes of few μm thick flters avoiding issues related to their disruption as well as to their jagged sides (originated by the cutting procedure), an ad hoc holding structure made of stainless steel was designed and it is here shown in Figure 4. Te physical dimension of the holder although, does not allow to use the set of the three mentioned flters, since the width of the structure will be covering a portion of the imaging system. Te set of flters is thus reduced to two and we found convenient the employment of the 10 μm and 30 μm one. Tese will allow to investigate the energy region where the maximum alphas yield is expected and to explore what happens for energies higher than 6.4 MeV, beyond the current alpha energy cut-of.  x 1 and x 2 are the coordinates on the detector plane corresponding to the maximum and minimum alpha energy able to cross the flter (x � 0 corresponds to the pinhole image position).

Tomson Spectrometer Integrated with Time-Resolved Detector.
As it is possible to see from the graphs in Figure 2, the diferential flter method cannot be used for low energy particles. Indeed, for energies/nucleon lower than ∼300 keV (i.e., E α ∼ 1.2 MeV), the spatial extension of the energetic region free from ions contribution would either be too small or cannot be defned. For this energy region, we need to fnd some other method. We here investigate the possibility of integrating a time-of-fight (ToF) methodology in the Tomson spectrometer assembly. Te general idea is to discriminate the diferent species according to their diferent time of arrival by placing a time-resolved detector after the region where the particles are subjected to the electric and magnetic feld of the Tomson spectrometer. Te detector will be placed along the trajectory of the particles having an A/Z � 2, so to exclude the contribution of protons and other ions to the signal generation. Since the ions contributing to each (x, y) point in this parabola trace have the same velocity, the simple TOF technique does not work for particle discrimination. Nevertheless, if a thin metal or plastic foil is placed in the particle path, the diferent species may undergo to a different energy attenuation and thus to a diferent variation of their velocities, according to the diferent stopping range of the various species for the used material. Ten, if a timeresolved detector is placed at a proper distance, it would be possible to recognize the contribution of the various populations, as schematically shown in Figures 5(a) and 5(b). Te method would be applied by punching one hole in the imaging system used for the parabolic traces detection, allowing for ions to pass through it and reach the timeresolved detector. Tis would allow to simultaneously obtain information on the alphas from the Tomson spectrometer (for higher energies) and the ToF methodology (for lower energies).
As discussed, in each position of the A/Z � 2 trace, only particles with a certain energy per nucleon will be detected. For a generic position in this trace, we now consider a simplifed model of a δ-like Dirac distribution of the energies. In the basic scheme shown in Figure 5(b), particles with energy and velocity E in and v in , respectively, will pass through a foil flter and those with enough energy will emerge on the other side with E out and v out . In particular, it will be E out � k i (E in i , f) E in [43] with k i (E in i , f) the attenuation coefcient depending on the type of the incoming particle, its energy, and the flter characteristics (material and thickness, here labelled as f). Tis attenuation can be determined by SRIM [41] simulations. Te time of detection t i of each ion can be determined by knowing at which distance from the flter the time-resolved detector is placed (d TOF ), the type of flter used, and the energy of the incoming particle (E in i ), as follows: where v i out is the velocity of the ion after crossing the flter and m i is the ion mass. Te temporal interval between the detection of an alpha particle and a carbon ion can be written as follows: where m p and m n are the proton and neutron mass, respectively, and the relation E C 6+ � 3E α was exploited. For a fxed energy, determined by the positioning of the ToF detector behind a certain (x, y) point of the imaging plane, and a given d TOF , the delay would depend only on the material and thickness of the flter, represented by the attenuation coefcient k i (E ini , f) and can thus be used to discriminate the ion species by comparing the arrival times. Equation (7) was applied to compute the delays, supposing to use a 2 μm aluminium foil as flter along the particle path. Te attenuation coefcients for alphas and carbon ions, depicted in Figure 6(a), were computed by means of SRIM simulations [41] in the energy range of interest (0.6 MeV < E alpha < 3 MeV). In Figure 6(b), the delays for diferent TOF line lengths are reported.
It is possible to see that two diferent regimes exist. For alphas energies lower than ≃0.7 MeV, the computed delays result to be lower than zero. Since, from equation (6), the temporal distance is defned as ∆t � t c − t α , this means that t c < t α , hence carbon ions would reach the detector before alphas. For higher energies, on the other hand, alphas arrive frst on the detector and, for a TOF line length of 50 cm, delays up to several tens of nanoseconds are obtained, which are well in the range of efcient ToF detection by fast diamond detectors [44].
Nevertheless, some remarks are necessary. Even in case of an ideal δ-like distribution, the alignment of a diagnostic based on this scheme is not trivial since a displacement of a few millimetres of the ToF line can lead to the blinding of the diagnostic. Moreover, for many of the energies shown in Figure 6, the obtained delays are of a few nanoseconds. Terefore, a detector with high temporal resolution is needed. In the case of chemical-vapor-deposition diamond detectors, often used in time-of-fight measurements [43,45], this is usually achieved by single crystal structures, having temporal resolution better than ∼0.8 ns and high charge collection efciency. On the other hand, this kind of structures can be grown up to a surface of a few square millimetres resulting in a small solid angle covered worsening the alignment issue.
Moreover, in a realistic scenario, the energy distribution for each detected ion species is not a δ-like distribution but will have a certain width. Hence, each point of the parabolic trace will correspond to an energy span and not to a single energy value. Te amplitude of the energy span to consider in each point can be related to the size of the pinhole image on the detector plane [19,40]. Te latter defnes the energy resolution of the spectrometers along the parabola trace, and this will correspond to the FWHM of the Gaussian distribution of the energies to be considered in our computations. As a result, instead of a single time of arrival for each species, there will be a temporal window where α particles will be detected and a temporal window where carbon and other ions will arrive (see Figure 5(b)). To be still able to use the ToF technique to discriminate the various contributions, it is thus necessary for the fastest carbon ion to be slower than the slowest alpha particle. Alternatively, if this condition is not satisfed, it is possible to compute the time interval where the two populations overlap and defne the portion of the alpha time window free from other ions, here in after labelled ∆t * .
Taking into account the energy distribution due to the fnite pinhole extension, the requirements for the energy resolution become even more strict. Indeed, by applying equation (4) with the parameters of the considered Tomson spectrometer and assuming a pinhole image size ranging from 0.5 mm to 1.5 mm, the obtained ∆E for alphas and carbon ions is reported in Figures 7(a)   Laser and Particle Beams bunches has been also computed and is reported in Figure 7(c).
Taking these values as the width of the energy distribution to consider for each particle energy, it is possible to compute the temporal interval ∆t where the signal generated by the alphas is free from the carbon ions contribution (see examined energy falls into one of the other cases. Tis also clarifes Figure 8(f ), where only negative delays are present, indeed the situation depicted in Figure 8(d) never occurs for the parameters examined here and, for each energy, the behaviour of the two bunches is described by one of the cases a-c. It is possible to see that, even considering a broad energy distribution, an appreciable ∆t can still be defned. In this case, it is useful to consider not only the whole separation of the traces but also their partial overlapping, defning ∆t * the temporal interval where only alphas are detected. By doing so, the methodology can still be applied. Nevertheless, for bigger pinhole sizes, the width of the energy distribution increases causing a decrement in ∆t, issue that can be partially solved by extending the TOF line length.
In this scheme, it is also necessary to assess the efect of the flter on the particle motion. It is indeed well known that particles traversing a material undergo a modifcation of their trajectory. Tis efect is more severe for particles energies in a range comparable with the thickness of the material used as flter. In these conditions a broadening of the energy distribution is also experienced. Te latter will, in turn, cause a broadening of the temporal interval interested by a certain energy during TOF measurements. Namely, alpha particles having energies ≃600 keV can be detected at a certain time t TOF ± ∆t broad . SRIM simulations were performed to quantitatively estimate this efect for the scheme considered here i.e., alphas with energies ≥ 600 keV up to 3 MeV impinging on 2 μm thick aluminium. Te range covered by the energy distribution of the alphas entering in the flter with 600 keV is ≃25 keV, within the ∆E already considered due to the spectrometer energy resolution (see Figure 7(a)). Te trajectories of the particles, though, are strongly afected by the presence of the flter and the beam outcoming from it is strongly divergent. Nevertheless, this efect rapidly decreases for increasing particle energies.
Another efect to consider is the one given by the electrostatic-magnetostatic defector which also produces a clear increase on the tangential (both horizontal and vertical) components of the particle velocity, due to the efect of both magnetic and electric felds. Tis increases the beam radius and makes it dependent on the distance from the defector. Terefore, the beam section on the detector plane will be much larger than that on the flter plane, according to the flter-detector distance. So, on one side, larger distances ease the separation of the particle bunches. On the other side, the requirement for large-area detectors increases, and on the other hand, large area detectors mean low temporal resolution. Terefore, for a specifc alpha energy, an optimum value for the ToF line length has to be found.
A way to deal with this issue may be the employment of suitable electric-magnetic lenses, capable to correct the beam divergence given by the spectrometer, and to keep the detector diameter small also at large fight distances. However, this is of course at the expenses of the detector complexity.

Conclusions
Te diferential flter method seems to be a viable solution for the univocal detection of α-particles in low-rate fusion reactions. An optimal implementation of this methodology, able to give characterization of a wide portion of the broad alpha spectrum, requires the spectrometer to be designed trying to obtain a large spatial dispersion of incoming particles, so large felds, and large drift distances are needed. Tis would ease the optimal flter placement along the whole parabola trace, but gives problems in case compact spectrometers are needed, as required for high sensitivity devices useful for diagnostics of proton-11B fusion reactions [19]. Te prototype presented in this article is planned to be used soon in tailored p-11B experimental campaigns.
Te discussed methodology of diferential fltering can be applied not only in the context of the proton-boron fusion reactions but also to monitor the alphas produced during the deuterium-deuterium fusion reaction and the deuteriumtritium one. In this case, the parabolic trace of the fully stripped alpha particles is not useful since the deuterium will also contribute to the signal on the very same A/Z � 2 trace and, being more penetrant with respect to alpha particles, the diferential fltering method is not capable of excluding its contribution. Nevertheless, if we consider the parabolic trace having A/Z � 4, the deuterium will not contribute to the signal whereas the 4 He + may be detected instead. On this trace, an approach similar to what discussed earlier can thus be applied for their characterization.
Te methodology that foresees the integration of a timeresolved detector in the Tomson spectrometer could, in principle, provide very interesting results for the univocal discrimination of low energy alpha particles. Nevertheless, the technique presents some signifcant technical issues concerning the TP-TOF assembly alignment, and the need for high temporal resolution, high sensitivity, and large area detectors. All this points need to be faced and assessed for the technique to be successfully applied in a real-case scenario. Te use of an electric-magnetic lens to correct the beam divergence can be very useful to highly improve the detector requirements, but at the expenses of the whole device complexity.
Te methodologies here shown are of primary interest for the univocal identifcation of alpha products in experiments of laser-generated fusion reactions. Especially in cases of low yields, the simultaneous presence of a large number of laser-accelerated ions diferent from fusion products very often makes their actual characterization technically impossible by common diagnostic methodologies [19].

Data Availability
Te data used in this study are available from the author upon reasonable request.

Disclosure
Views and opinions expressed are however those of the authors only and do not necessarily refect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. Te involved teams have operated within the framework of the Enabling Research Project: ENR-IFE.01.CEA "Advancing shock ignition for directdrive inertial fusion."

Conflicts of Interest
Te authors declare that they have no conficts of interest.