Simultaneous measurements for fast neutron flux and tritium production rate using pulse shape discrimination and single crystal CVD diamond detector

This paper presents the development of a simultaneous measurement method for fast neutron energy spectra and tritium production rates within mixed radiation fields using a single crystal chemical vapour deposition diamond detector combined with a lithium fluoride (LiF) foil. The method involves the separation of pulses with rectangular shapes and the determination of the depth position within the single crystal diamond (SCD) struck by fast neutrons or nuclear reaction products including recoil tritons from the LiF foil based on pulse width, extracting pulse events occurred at the specific bulk region and the surface region of the SCD. Subsequently, unfolding techniques were employed to analyse the energy deposition spectrum of pulses at the specific bulk region which are induced only by fast neutrons, allowing the deduction of the fast neutron energy spectrum. To evaluate the tritium production rate, the energy deposition spectrum of pulses from events occurring at the SCD surface facing the LiF foil was analysed. By estimating the energy deposition spectrum solely induced by fast neutrons striking the SCD surface and subtracting it from the energy deposition spectrum of events at the SCD surface, the contribution of energetic ions, such as recoil tritons generated by the 6Li(n,α)3H reaction in the LiF foil, was determined. The fast neutron flux and tritium production rate obtained through this study were consistent with particle transport calculations, demonstrating the successful development of a method suitable for performance testing of fusion reactor blankets.

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Introduction
The breeding blanket (BB) of the deuterium-tritium (D-T) fusion reactor has multiple roles: generating fuel tritium and converting neutron energy to heat.Many different concepts of BB have so far been proposed for fusion reactors which are based on water-cooled ceramic breeder, helium-cooled ceramic breeder, helium-cooled lithium lead, and watercooled lithium lead method, self-cooled liquid metal concept, and so on [1][2][3][4][5][6][7][8].All the proposed BB are designed using the most advanced and updated calculation tools and nuclear data libraries [9][10][11][12][13].However, uncertainties in these calculations, particularly regarding the tritium breeding ratio, can affect BB performance, impacting reactor operational scenarios, plant costs, and nuclear waste production.It is thus essential to compare the calculation predictions to measured quantities such as fast neutron flux and tritium production rate using a blanket mock-up.
The detector required for these measurements must possess, among others, high radiation dose tolerance, high-temperature tolerance, and fast response capabilities.Additionally, it should be as compact as possible to minimise its impact on neutron transport.A recent comprehensive study on the lifespan of a single crystal diamond (SCD)-based detector for 14 MeV neutrons reported a detection efficiency degradation to about 70% when irradiated at approximately ∼0.55 × 10 14 n cm −2 [14].Another report indicated that the detector showed no degradation in signal or count rate accuracy by 14 MeV neutron irradiation under 573 K [15].These performance evaluations were conducted for the detector with the 500 µm thick SCD, and improvements are expected as the thickness of the SCD decreases.Additionally, SCD-based detectors are significantly more compact compared to other neutron detectors [16].Considering these superior functions, an SCD-based detector shows promise for testing a blanket mock-up.
Recent advancements in fabricating artificial SCDs through chemical vapour deposition (CVD) processes have made detector-grade SCDs commercially available [17].A single crystal CVD diamond detector (SDD) can detect fast neutrons through elastic collisions and (n,α) reactions [18].Moreover, by placing a foil of lithium compounds on the surface of the SCD, it can react with neutrons via the 6 Li(n,α) 3 H reaction.In the 6 Li(n,α) 3 H reaction the nuclear reaction products, which include recoil tritons and alpha particles, are energetic ions that implant into the SCD, depositing detectable energy [19].This enables the evaluation of tritium production reactions.
The SDD is indeed sensitive to fast neutrons and energetic ions, as mentioned earlier.Additionally, it exhibits sensitivity to gamma-rays.Gamma-rays are typically produced as prompt gamma-rays following neutron capture reactions.Consequently, the SDD must operate effectively to independently quantify both the fast neutron flux and the tritium production rate in the blanket, even within a mixed radiation field.
In our previous study, we successfully demonstrated the measurement of energetic ions generated by the 6 Li(n,α) 3 H reaction while effectively rejecting gamma-rays using the pulse shape discrimination (PSD) technique [20,21].Furthermore, we showcased an advanced PSD method for extracting pulses induced by fast neutrons [22,23].In this paper, we present a comprehensive analysis for evaluating, simultaneously, the fast neutron flux and the tritium production rate using a single detector.

PSD method
The pulse in the SDD is induced by the drift of free charge, which consists of electron-hole (e-h) pairs generated by radiation within the SCD [24,25].Consequently, the initial depth distribution of these e-h pairs in the SCD, depending on where the SCD is struck by radiation, significantly influences the shape of the pulse [19].Due to the SCD's sensitivity to various particles such as energetic ions, gamma-rays, and neutrons, several different pulse shapes can be observed in the SDD within a mixed radiation field.For instance, energetic ions tend to deposit their energy into the shallow depth region of the SCD.When a negative voltage is applied to the incident surface of the SCD, holes quickly drift toward this surface and do not contribute significantly to the pulse.Conversely, electrons at the incident surface drift toward the rear surface of the SCD, producing a constant current during the electron's drift.The current then abruptly decreases when electrons reach the rear surface, resulting in a wide rectangular-shaped pulse [26].In contrast, gamma-rays scatter electrons throughout the entire bulk of the SCD, creating a uniform distribution of electronhole pairs.This leads to the formation of a triangular-shaped pulse [26].
The shape of the pulse during fast neutron irradiation becomes more complex because fast neutrons can strike at various depth positions within the SCD.Electron-hole pairs can be formed as point-like entities within the SCD through processes like elastic collisions and nuclear reactions, such as the 12 C(n,α) 9 Be reactions.The shape of the pulse is directly influenced by the depth position within the SCD where the reaction occurs.For instance, fast neutron irradiation often results in two-step-like pulses.These pulses can be produced when fast neutron hits various depth positions of the SCD where the drift durations of electrons and holes toward the respective surface electrodes on the SCD are not equivalent.For example, when a fast neutron hits the bulk of the SCD near the surface with negative voltage applied, holes and electrons drift toward opposite directions, producing a pulse.However, because holes can reach the surface applied with negative voltage sooner to be absorbed into the electrode there, the pulse corresponding to the hole drift disappears.Nevertheless, electrons continue to drift, contributing to the pulse, and ultimately reach the opposite surface.The resulting pulse shape consists of overlapping rectangular-shaped pulses with different widths (a narrow one caused by holes and a wider one by electrons), forming a two-step-like pulse.
On the other hand, there are several depth positions within the SCD where the pulse shape becomes rectangular.The first depth position corresponds to the incident surface of the SCD, similar to the case of energetic ions.The second depth position is at the rear surface of the SCD.In this case, when a negative voltage is applied to the incident surface of the SCD, the drift of holes induced at the rear surface towards the incident surface contributes to the pulse, resulting in a rectangularshaped pulse.However, due to the faster drift velocity of holes in the SCD compared to electrons [27,28], the width of this rectangular-shaped pulse becomes narrower.The third depth position is the ballistic centre region (BCR), where the drift durations of electrons and holes towards their respective surfaces of the SCD are roughly equivalent [26].In this case, the event results in a narrow rectangular-shaped pulse.
The PSD method employed in this study needed the capability to distinguish between pulses induced by fast neutrons and energetic ions generated by the 6 Li(n,α) 3 H reaction.The PSD method used in this work was specifically designed to extract two types of pulses: narrow rectangular-shaped pulses, which are induced by fast neutrons hitting at the BCR, and wide rectangular-shaped pulses, which can be induced by both energetic ions and fast neutrons at the surface of the SCD facing to the foil of lithium compound.To achieve this discrimination, the parameters of rectangularity R and the FW1/4PH (full width of one-fourth of the peak height) of each pulse were utilised in the PSD analysis.The rectangularity is defined as R = 4Q/3AW, where A, W, and Q represent the peak height, FW1/4PH, and the charge integral of each pulse exceeding A/4, respectively.Therefore, R should be closed to unity when the pulse shape is rectangular.To determine these parameters precisely, each pulse data with the sampling rate of 1 GHz (see section 2.2) was interpolated by a spline function.The program to analyse these parameters is written with python and is explained elsewhere [22].Based on our previous study, pulses with R > 0.63 and W in the range of 5 ns to 6.5 ns were extracted as events occurring at the BCR, while pulses with R > 0.63 and W in the range of 10 ns to 12 ns were associated with events occurring at the incident surface [23].
Other pulses within different ranges in R and W were eliminated in this process.It should be noted that pulses induced by gamma-ray are rejected in the above PSD processes, because the pulse shape by gamma-ray can be triangular.Including pulses by gamma-rays, two-step-like pulses induced by fast neutrons were also excluded (about 80% of pulses in RUN 1 below as the example), which should degrade the statistical accuracy of fast neutron measurement.

Single crystal CVD-SDD
The SDD (B12 Knof diamond detector) manufactured by Cividec instrumentation GmbH was used in this study [29].The active volume was 4.0 × 4.0 × 0.5 mm 3 .A 100 nm thick titanium electrode was deposited on both surfaces of the SCD.The lithium fluoride (LiF) foil with the thickness of 1.9 µm and with 95% 6 Li enrichment ( 6 LiF) deposited on the polyether ether ketone substrate was positioned to face one surface of the SCD, which is called the incident surface in this study.The distance between the incident surface of the SCD and the 6 LiF foil was approximately 1.8 mm.It is important to note that the detector was operated under ambient air conditions.Therefore, energetic ions produced in the 6 LiF foil travel through the ambient air region before injecting into the SCD.This removable foil was absent in RUN 1 (see below).For operation, the voltage of +250 V was applied to the electrode on the rear surface of the SCD by a high voltage power supply (ORTEC 428) through a pre-amplifier (CIVIDEC C2-HV broadband amplifier), which was powered with +12 V DC power supply (Matsusada Precision PLD-18-2).The amplified signal was recorded by the data acquisition (DAQ) system (Techno AP APV8102-14MWPSAGb) consisting of a fastprocessing analog-to-digital converter and a field programmable gate array system.The DAQ system had the sampling rate of 1 GHz and the resolution of 14 bit [30].

14 MeV neutron irradiation experiments
The 14 MeV mono-energetic neutron irradiation was carried out at OKTAVIAN facility of Osaka Univ [31].The neutron source consists of a tritium target, which comprises tritium atoms stored in a thin titanium layer deposited on a copper substrate.This target was irradiated with a 300 keV deuteron beam to produce fast neutrons through the 3 H(d,n) 4 He reaction.The SDD was positioned at two locations with different detector compositions which are listed in table 1.In RUN 1, the SDD was located at the 90 • angle to the deuteron beam direction.The distance between the SDD and the centre of the tritium target was set at 13 cm. 6LiF foil was not used in this case.In RUN 2, the SDD was located at a 95 degree angle to the deuteron beam direction within a cylinder-shaped moderator made of polyethylene (PE).This moderator was assembled by two cylinders with different thicknesses, with a smaller cylinder inserted into the larger one.The gap between these cylinders was less than 1 mm.The detector was inserted from the top of the moderator to a depth of 35 mm, aligning the height positions of the detector with that of the tritium target.The  top and bottom of the moderator assembly were left unfilled with PE.The distance between the SDD and the centre of the tritium target was set at 160 cm.In this case, 6 LiF foil was employed.The moderator served for slowing down a fraction of 14 MeV neutrons, converting them into thermal neutrons, thereby increasing the rate of the 6 Li(n,α) 3 H reaction in the 6 LiF foil.For these two cases, RUN 2 was conducted for the demonstration of a comprehensive evaluation of the fast neutron flux and the tritium production rate simultaneously, and RUN 1 was for a comparison.For a visual representation of the experimental setup, please refer to the schematic drawing for RUN 2 provided in figure 1.

Evaluation of neutron energy spectrum
The neutron energy spectra were evaluated by the unfolding technique for the energy deposition spectrum of pulses by events occurred at the BCR measured in RUN 1 and RUN 2. The energy deposition spectrum is a histogram of the number of energy deposition events in each energy bin, and can be defined as follows, The symbols Ψ, ω, θ, P, ϕ represent the number of energy deposition event per second [s −1 ], the noise-cut function [−], the overall PSD efficiency [−], the response matrix of the SCD for fast neutrons [−], and the number of neutrons injected into the SCD per second [s −1 ], respectively.The subscripts i and j denote the index number of energy bins with the range of 0.3-15.0MeV and with an interval of 0.3 MeV, consequently the total number of energy bins was 50.The response matrix of the SCD for fast neutrons was calculated at various neutron energies using the Geant4 Monte Carlo code [32,33].The overall PSD efficiency was defined as the ratio of the BCR pulse count to the overall pulse count.To account for the influence of the current threshold set for noise cutting in the DAQ system, a noise-cut function was applied to reshape the response matrix in low energy regions below 0.9 MeV.The specific parameters for these calculations were thoroughly evaluated in our prior study [34].To deduce the numbers of neutrons injected into the SCD in each energy bin (corresponding to the neutron energy spectrum), the iterative calculation for equation (1) was performed using the Newton-Raphson scheme.
To validate the deduced neutron energy spectrum obtained through the unfolding technique, we conducted a neutron transport calculation using the Monte Carlo N-Particle code (MCNP6) [35].We employed the ENDF/B-VII.1 Evaluated Nuclear Data Library [36] for this simulation.Our model included the various components of the experiment, such as the neutron source, moderator, the SDD, and the irradiation room.We ensured that the angular distributions of neutron energy and flux at the target matched those previously validated at the Fusion Neutron Source (FNS) of the Japan Atomic Energy Agency [37][38][39][40], because the OKTAVIAN employed the same target system as that in FNS.Subsequently, we compared the neutron energy spectrum at the position of the SDD to the deduced neutron energy spectrum.

Evaluation of tritium production rate
The tritium production rate should be evaluated using the energy deposition spectra of pulses by events occurring at the incident surface, because the incident energetic ions from 6 LiF foils lose most of their energy in the incident surface area.However, the energy deposition spectrum of pulses by events occurring at the incident surface was induced by not only energetic ions but also fast neutrons.To isolate the energy deposition spectrum induced solely by fast neutrons at the incident surface, we employed the energy deposition spectrum of pulses by events at the BCR.This approach was based on the assumption that the likelihood of fast neutrons hitting at any depth position within the SCD is independent of neutron energy [23].Consequently, we were able to deduce the energy deposition spectrum induced solely by energetic ions as follows, Here, ψ EI , Φ, Γ indicate the event number of the energy deposition solely by energetic ions in each energy bin, the event number in each energy bin in the energy deposition spectrum, and the neutron yield in the measurement, respectively.The subscript in Φ identifies the energy deposition spectrum of the BCR or the incident surface.The superscript indicates the usage of 6 LiF foil.The second term within the parentheses accounts for the contribution of fast neutrons in the energy deposition spectrum at the incident surface.This term relies on the ratio of the deposition spectrum at the BCR to the incident surface of the SDD without the 6 LiF foil, which we previously evaluated in our prior study [23].By subtracting the energy deposition spectrum at the incident surface from the estimated spectrum induced only by fast neutrons, we obtain the energy deposition spectrum induced solely by energetic ions, ψ EI .
Energetic ions were discriminated based on their deposited energy in the next step.The Q-value of the 6 Li(n,α) 3 H reaction is approximately 4.9 MeV, and this energy is distributed between the recoil energies of a triton (∼2.7 MeV) and an alpha particle (∼2.0 MeV).In our previous study, energetic ions of tritons and alpha particles by 6 Li(n,α) 3 H reaction were measured using SDD under thermal neutron irradiation [21].There were two distinct peaks corresponding to the recoil energies of tritons and alpha particles in the energy deposition spectrum.However, the results showed that the count rate of alpha particles can easily influenced by noises in the measurement systems and not useful for quantitative evaluation of tritium production rate.Therefore, in this study, we integrated the energy deposition spectrum around 2.7 MeV to count only the number of recoil tritons deposited in the SCD.Then, we evaluated the efficiency of recoil tritons generated in the 6 LiF foil to be deposited into the SCD to deduce the tritium production rate.For this purpose, we used the Particle and Heavy Ion Transport code System (PHITS) [41].In this computational simulation, we modelled both the 6 LiF foil and the SCD to simulate the transport of tritons with 2.7 MeV generated in the 6 LiF foil.Recoil tritons were generated uniformly within 6 LiF foil, and the attenuations of the recoil tritons in the foil and in the ambient air between the foil and the SCD were taken into account.The energy deposition tally in PHITS allowed us to deduce the deposition efficiency of recoil tritons into the SCD.Subsequently, the reciprocal number of this efficiency was multiplied by the number of recoil tritons deposited in the SCD obtained in the measurement to calculate the tritium production rate in the 6 LiF foil.Note that the model in PHITS applied here was already validated in our previous study [20,21].
To validate the deduced tritium production rate in the above method, the neutron transport calculation using MCNP6 was used as in the case of section 3.1.The reaction rate of 6 Li(n,α) 3 H reaction in 6 LiF was evaluated by the track-length tally.Then, this was compared to the actual measurement.The energy deposition spectra for all pulse-events and the results for pulse-events occurred at the BCR and the incident surface obtained by PSD processing in (a) RUN 1 and (b) RUN 2. (c) and (d) Focus on the results obtained by PSD processing for each experiment.Note that the event numbers in y-axis are normalised by neutron yields in each RUN.The deposited energy in x-axis was deduced by the calibration factor evaluated in alpha particle measurements from 241 Am.

Results and discussion
Figures 2(a) and (b) display the energy deposition spectra for all pulse events (without any PSD processing), events at the BCR and events at the incident surface obtained through PSD processing for RUN 1 and RUN 2, respectively.Note that all spectra in these figures are normalised by the neutron yield in each measurement.In figure 2(a) for RUN 1, the spectrum is dominantly composed of several peaks.According to some literature, peaks around 8.4 MeV and 6.0 MeV were assigned to the energy deposition events of energetic ions produced by 12 C(n,α) 9 Be (Q ∼ −5.702 MeV) and 12 C(n,n'2α)α (Q ∼ −7.275 MeV) reactions inside the SCD, respectively [42].Events in the lower energy deposition region are likely due to elastic collisions of fast neutrons.The results for events at the BCR in figure 2(c) for RUN 1 showed a similar profile to that for all pulse events.The profile of the energy deposition spectrum for events at the incident surface resembles that of the BCR except for the lower deposition energy region below 1 MeV.The inconsistency below 1 MeV resulted from the current threshold in the DAQ system, which was set for noise reduction [23].Even with the same deposited energy, the pulses at the BCR tend to exceed this threshold more frequently than those at the incident surface due to the narrower pulse width of BCR pulses, resulting in higher pulse height.
The results shown in figure 2(b) for RUN 2 were significantly different from those for RUN 1.In particular, a dominant peak around 1 MeV and an additional peak at 2.7 MeV were found.The peak at 2.7 MeV was assigned to the recoil tritons from the 6 LiF foil, which deposited energy into the incident surface region of the SCD.It was also considered that scattered neutrons by the PE cylinder and the walls of the irradiation room might make the peak around 1 MeV dominating the energy deposition spectrum.The results with PSD processing is shown in figure 2(d).The additional peak at 2.7 MeV was only observed in the events at the incident surface.On the other hand, the peak disappeared in the events at the BCR.This result strongly supports that the extracted pulses for the BCR is independent on the energetic ions and only induced by fast neutrons.Besides, even a significant peak at 2.7 MeV in the spectrum for events at the incident surface, there still are several peaks induced by the hits of fast neutrons as found in figure 2(c), indicating additional analyses are necessary to deduce the tritium production rate precisely as conducted below.
The energy deposition spectrum for pulses generated by events at the BCR for RUN 2 was subjected to analysis using the unfolding technique, as explained in section 3.1.The differential energy deposition spectrum reproduced by the unfolding processes is presented in figure 3(a).The fast neutron energy spectrum contributing to the deduced  Actual measurement (source −1 ) (2.6 ± 0.4) × 10 −7 C/E 1.12 ± 0.14 energy deposition spectrum is found in figure 3(b) alongside the estimated fast neutron energy spectrum obtained through MCNP6 calculation.Remarkably, the neutron flux near 14 MeV, as estimated by the unfolding technique, showed consistency with that calculated by MCNP6.Some peaks with relatively large uncertainty were observed in the deduced neutron energy spectrum within the energy range of 2-13 MeV.In particular, a notable and understandable discrepancy emerged between the deduced neutron energy spectrum obtained through unfolding and that estimated by MCNP6 in the lower energy region, specifically below 1 MeV.This divergence is attributable to the current threshold set in the DAQ system, which resulted in the rejection of events triggered by low-energy neutrons.A summary of the results obtained through unfolding to estimate the fast neutron flux is shown in table 2.
The energy deposition spectrum of energetic ions for RUN 2 was estimated by analysing the results of events at the incident surface using equation (2). Figure 4 illustrates the deduced energy deposition spectrum of energetic ions.A prominent peak at 2.7 MeV is evident, primarily due to recoil tritons.Additionally, a smaller peak is observed at around 1 MeV, attributed to recoil alpha particles.The presence of this minor count of alpha particles is likely due to the contribution of the current threshold set in the DAQ system.To focus on the counts associated with recoil tritons, we integrated the counts in the 2-3 MeV energy range and compared them to the count rate of recoil tritons estimated through the combination of MCNP6 and PHITS calculations in which each calculation model has been validated so far.The summarised results are  presented in table 3.These results demonstrate that the count rate for recoil tritons measured through this method aligns well with the transport calculations of neutrons and recoil tritons.Consequently, it is reasonable to conclude that the present method is suitable for measuring the tritium production rate.

Conclusion
In this study, we successfully demonstrated a simultaneous evaluation method for the fast neutron flux and the tritium production rate using a single small detector.The results obtained were consistent with transport calculations, validating the effectiveness of this approach.By utilising only one single crystal CVD diamond detector with a compact size, this method minimises the space required to insert the detector into the blanket.As such, it represents a powerful tool for conducting performance tests of fusion reactor blankets.

Figure 1 .
Figure 1.(a) Set-up for 14 MeV mono-energetic neutron irradiation at OKTAVIAN facility in RUN 2. (b) Cylinder-shape PE moderator composed of two PE cylinders.(c) Block diagram for this measurement.

Figure 2 .
Figure 2.The energy deposition spectra for all pulse-events and the results for pulse-events occurred at the BCR and the incident surface obtained by PSD processing in (a) RUN 1 and (b) RUN 2. (c) and (d) Focus on the results obtained by PSD processing for each experiment.Note that the event numbers in y-axis are normalised by neutron yields in each RUN.The deposited energy in x-axis was deduced by the calibration factor evaluated in alpha particle measurements from 241 Am.

Figure 3 .
Figure 3. (a)The deduced differential energy deposition spectrum compared to the actual measured differential energy deposition spectrum for BCR events in RUN 2 (Note that the unit in y-axis was different from that in figure2(d)).(b) The evaluated fast neutron energy spectrum by unfolding processes comparing to the estimated fast neutron energy spectrum using MCNP6.Both figures are normalised by the neutron yield in RUN 2.

Figure 4 .
Figure 4.The deduced energy deposition spectrum by energetic ions for RUN 2.

Table 1 .
Experimental conditions in 14 MeV neutron irradiation tests.The neutron yields in each RUN were measured by a fission chamber placed near the tritium target.

Table 2 .
The 14 MeV neutron flux evaluated in the present method in RUN 2compared to that estimated by MCNP6.C/E here indicates the ratio of the latter to the former.