Study on a compact and adaptable Thomson Spectrometer for laser-initiated 11B(p,α)8Be reactions and low-medium energy particle detection

Thomson Spectrometers are of primary importance in the discrimination of particles produced by laser-plasma interaction, according to their energy and charge-mass ratio. We describe here a detailed study on a set of Thomson Spectrometers, adaptable to different experimental situations, with the aim of being placed directly within the experimental chamber, rather than in additional extensions, in order to increase the solid angle of observation. These instruments are suitable for detection of low-medium energy particles and can be effectively employed in laser-plasma experiments of 11B(p,α)8Be fusion. They are provided with permanent magnets, have small dimensions and compact design. In these small configurations electric and magnetic fringing fields play a primary role for particle deflection, and their accurate characterization is required. It was accomplished by means of COMSOL electromagnetic solver coupled to an effective analytical model, very suitable for practical use of the spectrometers. Data from experimental measurements of the magnetic fields have been also used. We describe the application of the spectrometers to an experiment of laser-plasma interaction, coupled to Imaging Plate detectors. Data analysis for spectrum and yield of the detected radiation is discussed in detail.


Introduction
Laser-plasma interaction generates charged and neutral particles, together with electromagnetic waves ranging from RF-microwaves to γ rays [1]. Particle discrimination is of extreme importance to understand phenomena related to the interaction, but is one of the most difficult type of diagnostics [1,2]. It can be performed by time-of-flight (TOF) detectors, track detectors (CR-39, PM355. . . ), electrostatic and/or magnetostatic spectrometers [1][2][3][4]. TOF-detectors give particle velocity, but supply no information on specie or charge. Track-detectors can count the number of particles and, when used with suitable filters, supply also information on energy and specie [5]. Electrostatic or magnetostatic spectrometers link deflection to particle properties and are very useful when species are known, i.e. to characterize electron beams. When multiple species are present, as common in laser-target experiments, Thomson Spectrometers (TSs) are much more advantageous, since combine both electrostatic and magnetostatic deflection [6,7]. Incoming particles, selected by a pinhole, draw 2D pictures on the detector plane, from which information on particle energy and charge/mass ratio can be achieved. Many recent papers deal with definition, characterization and use of TSs for investigating laserplasmas [7][8][9][10][11][12]. In general, electrostatic and magnetostatic deflections occur on different stages of the device. The resulting long spectrometers are difficult to adapt to an experimental vacuum chamber normally filled with many objects, and are usually placed in some extensions of it, far from target. This is a main limits for the sensitivity, and for the adaptability of the device to different experimental conditions.

JINST 11 C05010
decay [14], either through the 8 Be ground state ( 11 B+p → α 0 + 8 Be, with Q value = 8.59 MeV) or through the 8 Be * excited state ( 11 B+p → α 1 + 8 Be * , Q = 5.65 MeV) and its related decay ( 8 Be * → 2α 12 , Q = 3.028 MeV). The main channel is the second (α 1 ) and only 1% of reaction products come from the first contribution (α 0 ). The total fusion cross-section of 11 B(p, α) 8 Be has a high maximum (σ ∼ 1.2 b) associated with a wide resonance at centre-of-mass energy E cm = 660 keV, and a lower resonance (σ ∼ 0.25 b) at E cm = 148.5 keV [18,20]. Some experiments effectively demonstrated the production of α particles by 11 B(p, α) 8 Be in laser-plasma context [13][14][15][16][17][18][19], with a low yield generally expected in these conditions. It is of fundamental importance for the comprehension of these experiments to characterize in details not only possible fusion products, but also proton and boron ions together with all the other species generated in the experiment. This was the main reason to start working on such ion spectrometers.
Peculiar features of the proposed devices are: simultaneous electric and magnetic deflection (here achieved by permanent magnets), small and compact structure, tailored shielding against electromagnetic pulses (EMPs). These are fields in the radiofrequency-microwave frequencies, generated by laser-plasma interaction for broad ranges of laser intensity and duration (10 11 -10 21 W/cm 2 , 10 −15 -10 −8 s) [21][22][23][24]. They can have frequency spectra up to several gigahertz, duration up to hundreds of nanosecond and very high intensity (up to some MV/m), which is thought to be scaling with the target distance. For these reasons they can heavily affect the electronic equipment present inside and also nearby the experimental chamber. Typically, time-of-flight detectors become blind for a long time interval, and in many cases some devices can be even damaged.
The TSs features allow them to be placed inside the vacuum chamber and to be suitable to many different experimental conditions. On the other hand, this compactness implies short electrode length; thus primary role on particle deflection comes from electric and magnetic field immediately external to the electrode area (fringing fields) [10,25]. Thus, simple equations commonly used for the spectrometer modelling [8,10,11,25] are here not accurate. For this reason we developed an effective analytical model of the structure, coupled to tailored electromagnetic numerical modelling by a commercial solver and to experimental measurements of the magnetic field. In this work we show the successful use of these spectrometers in characterization of 11 B(p, α) 8 Be experiments by laser-target interaction, when coupled to Imaging Plate (IP) detectors [10,11]. In particular, accurate data analysis for spectrum and yield of the detected particles is discussed in detail.

Structure description
Several prototypes of these small and compact spectrometers were designed and realized [26,27] on the purpose to be suitable to many different experimental conditions. They have scalable Neodymium permanent magnets and simultaneous electrostatic-magnetostatic deflection. The scheme of one of the proposed structures is shown in figure 1 together with two of its realizations, whose parameters are indicated in table 1. Electrodes and magnets have same length and width. A robust iron frame allows the magnets to be fixed in place, despite the mutual repulsive force. Kapton foils are important to isolate electrodes and avoid electrical discharges. The BIG version has been thought for energetic ions up to some tens of MeV, whereas the SMALL one is more suitable for -2 -  [26,27], together with two of its realizations: the 'SMALL' and the 'BIG' one. lower energies and its magnetic field is easily scalable. In table 1 measurements of the maximum orthogonal magnetic field, performed by Hall probe, are indicated for some realizations of the two prototypes. One version of the SMALL spectrometer, with magnetic field scaled to be low, was used also as magnetic spectrometer for electrons [27]. In figure 2 it is shown the internal structure of a mounting example of the SMALL spectrometer when used in real experiments. Similar configuration is applied to the usual BIG case. These setups were employed in recent experiments performed at École Polytechnique with LULI2000 and ELFIE laser systems [18,19], and mounted inside the vacuum chamber, ∼ 30 cm far from target. In these conditions protection against X-rays and electromagnetic pulses (EMPs) is a very delicate issue, because both limit the spectrometer sensitivity. X-rays affect the background on the detector (in this case Imaging Plate), and are mainly generated by direct laser-plasma interaction, with important contributions coming also from X-rays emissions by particle bremsstrahlung on chamber surface and on objects spread within it. Suitable Al and lead shields were thus used to limit this effect.
Spectrometer proximity to target makes mitigation of EMP effects important and very delicate, because of the high intensity of expected fields [23,24]. An ideal protection from EMPs would require a completely-closed conductive shield with thickness enough larger than the skin-depth at the lowest signal harmonics. In common cases the shield may be not enough thick and anyway some holes are always present (e.g. pinholes and electrode connections). Thus EMP fields can enter the spectrometer, and this is known to be one of the main factors producing parabola tracks on the detector plane modulated by some sinusoids [12,28,29]. It is particularly detrimental when -3 - superimposition of different parabolas is produced. The effect mainly occurs when EMP electric field couples with the conductive poles of the active regions, acting as parallel-plate waveguides. The short length of the single stage of deflection in spectrometers here studied greatly attenuate this coupling, compared to common devices with long dual-stages. The choice of permanent magnets reduces external connections. The use of dual power supply for the electrodes, related suitable connections for the ground contacts and general high care on shielding leads to overall high rejection to EMP effects.

Detector
The high level of EMP intensity at small distance from target makes hard and often impossible the use of active detectors as microchannel-plates. The choice of Imaging Plates or CR39 plastic track detectors is thus mandatory. In this work we will present measurement results achieved with BAS-TR and BAS-MS Imaging Plate models, whose properties are in table 2 [30,31]. The main difference is that BAS-TR has not protective layer, and the sensitive layer has much lower thickness. So it is suitable for low-energy particles. To reduce background due to X-rays, we added to BAS-TR a 3 µm Al filter, directly on the detector plane. The presence of protective layers imposes low-energy thresholds on particles, depending on the species. We calculated them by SRIM simulations (see table 3) [32].

Modeling
In figure 3, a scheme of the Thomson Spectrometer principle is shown. Usually, modeling of electrostatic and magnetostatic fields in these devices considers them constant within the active regions (here, having b length in figure 1 and 3), neglecting fringing fields [7,8,10,11]. This is not accurate for these compact realizations [9,25] since these fields play an important role on particle deflection. Thus, suitable modeling of them by COMSOL T M , a commercial electromagnetic numerical solver based on Finite Element Method [33], was here used together with measurements of magnetostatic fields by Hall probe. In figure 4 results of simulated vertical components of fields along the y−symmetry-axis (see figure 3) are shown for both SMALL and BIG configurations. Applied voltage is 5 kV and 9 kV respectively. The maximum magnetic field is 2.1 kG and 4.3 kG -4 -   respectively, as from measurements in specific realized prototypes (table 1). Simulations also showed that transversal changes of these profiles can be considered negligible, as far as we use pinholes enough symmetrically centered in the xz plane with respect to electrodes and magnets, and with diameter much lower than t (see figure 1 and table 1). Particles emitted from target pass through pinholes, are subject to electrostatic-magnetostatic deflection and then continue their motion up to the detector. For each particle, the point of -5 - interception in the detector plane is indicated with the (x, z) coordinates. From Newton's Second Law, we developed a classical set of equations relating these coordinates to particle properties, but here taking into account the nonuniform fields: where q i , m i , v i and E i are particle charge, mass, velocity and energy, respectively and are the integral coefficients including the nonuniform fields, where L 12 , b and L D are shown in figure 3. For the SMALL spectrometer L 12 = 280 mm and L D = 287 mm, and for the BIG one L 12 = 345 mm and L D = 322 mm. L 12 distance defines, together with pinhole diameter, the solid angle covered by the spectrometer and so to its sensitivity, whereas L D is associated with the optical track enlargement on the detector plane, once L 12 is fixed. Simulated electric fields, simulated and measured magnetic fields are used to evaluate A E and A B . As classical in previous modeling with uniform fields [7,8,10,11], in this way eqs.
x 2 , passing from origin and with coefficient dependent on m i /q i ratio, and link parabolic coordinates to particle energy. With these equations, information on particles are supplied from parabolas stored on the detector, but it is necessary to know the orientation with respect to the x and z spectrometer axis. This is usually a very delicate issue and requires stable and calibrated configurations. Moreover, when passive detectors are used (Imaging Plates, CR-39) their orientation may vary because of not exact replacement after each experiment. Nevertheless, from eqs. (2.1-2.2) it is possible to determine a very useful formula giving particle energy with respect to ρ 2 = x 2 + z 2 , i.e. the distance from axes origin: where k = q i A B / (2m i ρ). In this case no information on orientation is needed, but it is necessary to make hypothesis on the specific type of particle (i.e. m i and q i ).

Experimental measurements 3.1 Experiment description
We describe here the first use of the SMALL and BIG spectrometers in an experiment on the initiation of 11 B(p, α) 8 Be reactions, performed at LULI2000 facility of École Polytechnique [16,18,19]. The scheme of the experiment is in figure 5. A laser beam having λ = 527 nm, 1 ps duration and 23 J energy (indicated in figure 5 as the yellow 'Pico beam') was focused with normal incidence on 20 µm Al plain target (with focal position on Al surface) at intensity ∼ 6 · 10 18 W/cm 2 . The Al target was closely followed by a parallel 10 µm Al foil needed as target protection, because in other shots of the same experimental campaign -here not reported -another laser beam from opposite direction was used [16,18,19]. The two Al foils are indicated as a whole in figure 5. We expect that under these conditions TNSA mechanism on first Al foil accelerates fast particles coming from impurities deposited on the rear side of the target [34]. So we should mainly achieve H, C, N, O, Al, . . . particles. Those with higher energies are mainly directed along target normal, whereas for smaller energies the emission cone around this normal has increasing angles. Ions then meet the second Al foil, and those with enough energy may reach the natural boron target (consisting of 20% 10 B and 80% 11 B), interacting with it. As stated in the Introduction, cross-section of 11 B(p, α) 8 Be has high resonance at E cm = 660 keV centre-of-mass energy [18,20], so incoming protons with enough energy may start this reaction, whose products were effectively measured in ref. [16,18] by tracks on CR39, with low yield. A SMALL spectrometer was placed on the equatorial plane (see figure 5), equipped with 0.2 mm conical pinhole and BAS-TR detector with 3 µm Al protection. A BIG spectrometer was at +25 • with respect to equatorial plane, with 1 mm conical pinhole and BAS-MS plate. Fujifilm FLA7000 scanner was used to retrieve data from IPs and conversion formula from greyscale levels to PSL (PhotoStimulated Luminescence counts) was used [11]. The use of Thomson Spectrometers -7 - is here devoted to the characterization of all ions involved in this experiment, and potentially also to possible fusion products, in case of yield higher than in cases described in ref. [16,18].

Data analysis
We show in figure 6 the PSL image produced on BAS-TR by the SMALL spectrometer fed with 5 kV and having 2.1 kG maximum B field, as in figure 4. The circle at (0, 0) coordinates is the pinhole image on detector due to X-rays from target. Only one parabola track is detected. We superimposed to the experimental image parabolas computed using eqs. (2.1-2.4) for some possible species and a very good fitting was obtained for protons, as expected. The intensity changes along the experimental trace, and with this choice of PSL scale the parabola thickness is rather close to the pinhole-image diameter. Indeed, IP sensitivity and dynamics are very high, and in figure 6b we show the same figure 6a with a different PSL scale. Now the trace has intensity much more saturated and it is much enlarged versus the upper extreme, corresponding to lower proton energies. However, this is a second-order effect, visible when PSL scale approaches the minimum value, which should be expected since ion scattering on pinhole edges and space-charge effects produce more beam enlargement on the detector plane for particles with lower energies. It is apparent that there is good separation of proton track, having A/Z = 1 (A = mass number, Z = charge state) from the closest trace A/Z = 2, even in the enlarged case of figure 6b.
To determine the total number of particles, we defined a curved domain Ψ horizontally contained within two blue curves (see figure 7a), enough larger than the trace, to include some background. Black dots, grey traces and stains on IP image are the result of small holes on the Al cover and residual X-ray contribution, and a procedure of adaptive background subtraction took care of them. For each fixed z-coordinate the PSL-background was estimated in correspondence of each blue curve. The resulting two PSL values were averaged and this value was considered constant for any pixel within Ψ at that z-coordinate. Thus, we multiplied it for the total number of pixels at that coordinate, obtaining a Background(z) integrated function. For a particle of known charge (proton, in this case) z is related to energy by eq. (2.2). Thus, the final Background(E p ) function (where E p is the proton energy) is shown with the red curve in figure 7b.
To determine the spectrum quantitatively, we horizontally-added the PSLs values for those pixels in Ψ at fixed z, obtaining the blue curve Integral(E p ) in figure 7b as function of proton -8 - energy (by using eq. (2.2)). The black curve in the same picture is the function Integral BG (E p ) = Integral(E p )−Background(E p ), so the total number of PSLs versus energy after the background subtraction. The device resolution depends on pinhole, and in particular on the diameter D p of its image on the detector plane (circle at (0,0) coordinates). Since eq. (2.2) is nonlinear, the energy intervals [E p-min (i)E p-max (i)] (with i interval index) associated with D p have decreasing width along the proton trace. We define and as the sets of averaged proton-energies and PSL-integrals associated with each interval, respectively. IP calibrations supplying the number of PSL per single proton are available in a given energy range [30]. We determined the particle spectrum from the total number of PSLs by adapting those calibrations for protons to the case of their deceleration caused by 3 µm of Al. Unfortunately the calibrations did not cover enough our low energy range and we extended them conservatively as a constant. In figure 7c the extended calibration is shown, together with energy sampling (at E p-s (i) energies) due to pinhole resolution. The resulting proton spectrum, shown in figure 7d for E p-s (i) energies, is obtained by dividing Int p-s (i) for the sampled calibrations in figure 7c and for the 4.0 · 10 −7 sr solid angle covered by the pinhole. It is apparent that it has a sharp lower threshold around 300 keV which is in very good agreement with the expected energy cut-off of the 3 µm Al, indicated in table 3. This gives an indication of the good accuracy of results. High-energy cut-off is ∼ 1.5 MeV. The total number of particles and those per steradian are indicated in table 4.
-9 - Table 4. Total number of protons through the pinhole and per solid angle for the two spectrometers.   We show in figure 8a-b the PSL image produced on BAS-MS by BIG spectrometer fed with 9 kV and having 0.43 kG maximum B field (table 1 and figure 4). Again only one trace was detected, with good fitting to calculated red parabola for protons, and good separation to the others. Trace intensity was much lower than for the other spectrometer. For a better visualization, in figure 8b we had to improve the image contrast; for this reason the pinhole image at axes origin appears blurry. We applied the same procedure described before for the SMALL spectrometer, and we show in figure 9a the curves defining the Ψ domain. Final proton spectrum is shown in figure 9b and total proton numbers are given in table 4. The large pinhole gave associated solid angle of 6.6 · 10 −6 sr, leading to very good overall sensitivity -higher than for the SMALL spectrometer -and estimated lower-threshold density E LT−BIG−P ∼ 8 · 10 7 particles MeV −1 sr −1 for protons (figure 9b). Anyway, this decreased the resolution, inevitable drawback when high sensitivity is required [35]. Future trade-off conditions may be chosen depending on the case. High-energy cut-off is ∼ 1.5 MeV, in good agreement with data from SMALL spectrometer; but low-energy one is ∼ 800 keV, whereas the expected was ∼ 600 keV (table 3). We think that this difference could be easily explained considering both spectrometer low energy-resolution and low intensity of the trace with respect to background.

Number of protons SMALL Spectrometer BIG Spectrometer
-10 -No sinusoidal modulation of parabolas is observed in these first measurements, sign of EMP effective rejection. Particle yield is much higher for the SMALL spectrometer. This could be explained with its position closer to the Al foil normal, where more particles at high energies are generated. According to TNSA, particles are expected at lower energies when moving far from target normal, but in this case the energy filtering by the 10 µm Al foil and the 9 µm plastic cover of BAS-MS plate have reasonably stopped them. The high sensitivity of Imaging Plates allowed to both spectrometers a good dynamics, also for the case of very low number of particles (BIG case). We were not able to detect traces for A/Z 1 parabolas, corresponding to He, B, C, N, O, Al, . . . reasonable species. These possible particle flows had energies lower than thresholds required for the detectors and for passing through the 10 µm Al foil, or their number was lower than the E LT spectrometer sensitivity. In particular, in this experiment expected He +1 and He +2 number of particles per solid angle -taking into account their different (and less intense) PSL calibrations with respect to that for protons [36] -resulted at least two orders of magnitude lower [16,19] than the estimated BIG spectrometer sensitivity. For future experiments, this can be further improved by decreasing the background level. Moreover, the increasing of the solid angle of observation would certainly help in this sense but at expenses of energy resolution, how seen in figure 7b [35], and with possibility for trace superimposition. Nevertheless, in the present experiment the spectrometers were able to supply precise characterization, at two different angles of emission, of proton beam generated by TNSA and responsible of the 11 B(p, α) 8 Be reactions, important for the experiment comprehension and quantitative modelling. Remarkable resolution in the proton spectrum by the SMALL device was achieved thanks to the little pinhole.

Improved prototypes
To increase the spectrometer sensitivity, we improved the BIG configuration to reduce X-ray contaminations of the detector response. In figure 10 we show a structure mounted within a thick Al cylinder, lead-shielded on the side facing the target, and equipped with two concentric pinholes. General protection against X-rays was enhanced with respect to past prototypes. We believe that important X-ray contribution may come from electrons able to enter the spectrometer, easily deflected by static fields on the internal surface of the Al shield, with important bremsstrahlung illumination of the detector. The two-pinhole configuration, outlined in the scheme of figure 10b, deals with it. A weak magnet is placed just outside the first large pinhole (P1) and practically affects only low-medium energy electrons, deflected so to not enter the second smaller pinhole (P2) and interacting at most with the region between the two pinholes (P1 and P2). In figure 10c the picture of a realized prototype is shown. Effective shielding and grounding are visible.

Conclusions
We have described the main features of compact Thomson Spectrometers thought to be used for the study of processes with low-medium energy particles, and specifically for laser-initiated 11 B(p, α) 8 Be interactions. High sensitivity is required, and for this reason they are put as close as possible to target. Thus, tailored solutions against X-rays and EMPs were necessary. The use of passive Imaging Plates detectors improved EMP immunity and enhanced device sensitivity.
-11 - The total deflection of these compact structures is highly affected by electric-magnetic fringing fields, and this required numerical simulations, experimental measurements and effective analytical modelling of fields and particle deflection. We showed the first experimental results achieved with two prototypes of these spectrometers, when a proton beam generated by TNSA on thin Al foil interacted with B target. An adaptive process of background subtraction was conceived and applied to detector measurements. This is very important to exploit the high sensitivity and dynamics of Imaging Plates for low particle fluxes in laser-plasma context, locus of intense X-ray emissions. Quantitative spectroscopic description of the generated proton beam was achieved at different angles of emission, important for the experiment comprehension and quantitative modelling. High resolution was obtained with the SMALL spectrometer and high sensitivity with the BIG one. For both devices results were compatible with theoretical expectations. We were not able to detect parabola traces for He +1 and He +2 and in general for A/Z 1 because of energy thresholds and possible number of particles lower than spectrometer sensitivity. Apart from increasing the solid angle of observation, which decreases energy resolution and can produce trace superimposition, this can be further amplified by background lowering. Some spectrometer prototypes have been already improved in this sense and will be tested in future experiments.