REVIEW OF SCIENTIFIC INSTRUMENTS 85, 043503 (2014)
Second generation fusion neutron time-of-flight spectrometer at optimized rate for fully digital data acquisition X. Zhang,1,a) J. Källne,2,3 G. Gorini,3,4 M. Nocente,3,4 T. Fan,1 X. Yuan,1 X. Xie,1 and Z. Chen1 1
School of Physics, State Key Lab of Nuclear Physics and Technology, Peking University, Beijing 100871, China Department of Engineering Sciences, Uppsala University, Uppsala, Sweden 3 Dipartimento di Fisica “G. Occhialini,” Università di Milano-Bicocca, Piazza della Scienza 3, 20126 Milan, Italy 4 Istituto di Fisica del Plasma “Piero Caldirola,” Via R. Cozzi 53, 20125 Milan, Italy 2
(Received 28 November 2013; accepted 17 March 2014; published online 7 April 2014) The progress on high-rate event recording of data is taken as starting point to revisit the design of fusion neutron spectrometers based on the TOF (time-of-flight) technique. The study performed was aimed at how such instruments for optimized rate (TOFOR) can be further developed to enhance the plasma diagnostic capabilities based on measurement of the 2.5 MeV dd neutron emission from D plasmas, especially the weak spectral components that depend on discrimination of extraneous events. This paper describes a design (TOFOR II) adapted for use with digital wave form recording of all detector pulses providing information on both amplitude (pulse height) and timing. The results of simulations are presented and the performance enhancement is assessed in comparison to the present. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4869804] I. INTRODUCTION
Neutron emission spectroscopy (NES) is a diagnostic of fusion plasmas that requires dedicated instrumentation for measurement of the 2.5 and 14 MeV neutron emissions from d + d and d + t reactions, respectively.1 The dd rate is two orders of magnitude lower than that of dt under similar thermal conditions of D and DT plasmas. This means that 2.5 MeV neutron spectrometers need to have correspondingly higher detection efficiency in order to be on par with the performance of those for 14 MeV. However, the demand on energy resolution can be lowered, typically, from 2.5% to 6.5% (FWHM) for 4-keV plasmas. The leaders at present are neutron time-offlight (TOF) and magnetic proton recoil (MPR) spectrometers for dd and dt neutron emission, respectively.2 The TOF-technique for NES studies of tokamak plasmas has evolved since the 1980s3 up to the latest model TOFOR (TOF at optimized rate4 ) installed at JET in 2005.5 At the time proposed (1992), the conventional TOF measurements were based on using time-to-digital converter (TDC) which received start and stop signals for neutrons that scattered from one scintillator into a second. Such pairs of single scattering events were identified with pulse height discriminators providing the timing points and also suppression of unwanted event pairs.4 When installed at JET, TOFOR was equipped with a data acquisition system for digital time recording5, 6 in which the stored event histories of all detectors could be analyzed post-mortem and, subsequently, used to construct neutron TOF spectra. This offered significantly enhanced performance over the TDC technique in terms of count rate, besides benefitting time calibration and the handling of unwanted accidental event pairs.7 Recent advancements in signal processa) Authors to whom correspondence should be addressed. Electronic
ing electronics make it now possible to have data acquisition for neutron TOF spectrometers where the digital waveforms (DWF) of all detector pulses are recorded at high rates, data volumes, and precision. Such DWF data can be analyzed for extraction of the pulse information relating to both amplitude (pulse height) and timing. Recent tests of DWF electronics with TOFOR at JET have given encouraging results,8 which motivates considering a next generation design of TOFOR instruments whose scintillator geometry is adapted to the new DWF based data acquisition systems. In principle, a DWF based data acquisition system leads to improved resolution of the measured TOF spectrum and better identification of the desired neutron scattering events, and, hence, also discrimination of (undesired) extraneous ones. These latter events involve multiple neutron scatterings which do not have the constrained relationship between pulse height generated in the first scintillation detector and the TOF of “directly” scattered neutrons; these are referred to as multiple and single scattering events, MS and SS (equaling direct scattering), respectively. In this paper, we shall be concerned with the potential for enhanced discrimination of MS events through suitable choice of the geometry of TOFOR spectrometers. This is illustrated by a reference design dubbed TOFOR II which represents the next step in enhancing the instrumental capabilities for NES plasma diagnostics. II. PRINCIPLES OF THE TOF TECHNIQUE
The TOF technique is based on elastic neutron proton scattering in plastic scintillation detectors (S). Incoming neutrons (n) are scattered in the target scintillator S1 (Fig. 1), i.e., n + H → n + pr where recoiling protons, pr , deposit the energy ES1 specified by the scattering angle θ through
addresses: [email protected], [email protected], and Giuseppe.Gorini@ unimib.it 0034-6748/2014/85(4)/043503/9/$30.00
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ES1 = En (1 − cos2 θ ).
(1)
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tering in it; these are referred to as direct single scattering (SS) events in contrast to indirect ones involving (multiple) scatterings (MS). Multiple scattering is unavoidable in scintillators of finite thickness, but their admixture in the data used to determine S(tf ) should be reduced as it dulls the resolution relative to the optimal one furnished by the tf spectrum of direct events. Characteristic of indirect MS events is that they, for given En , can appear with longer and shorter flight times than those of direct events. This means that the correlation that exists between ES1 and θ for direct events, ES1 = En (1 − cos2 θ ) = 2mR2 tf−2 (1 − cos2 θ ) (4) FIG. 1. Schematics of fusion neutron spectrometer based on time of flight measurement with plastic scintillator detectors S1 and S2, and the underlying 2-body kinematics of elastic n + H → precoil + n .
A fraction of the scattered neutrons can undergo subsequent scattering in S2 depositing ES2 in the range ES2 < En ; it is typically registered as an event if ES2 exceeds a certain threshold. An incoming neutron is recorded through the event pair of signals produced in the two scintillation detectors. The time difference of the signal pairs, tf = t2 -t1 , is measured which is the basis for determining the energy of the scattered neutron (En ) and, subsequently, that of the incoming neutron from En = En /cos2 θ. (2) With the S1 and S2 detectors on the constant TOF sphere (of radius R, Fig. 2),9 the flight path of n is geometrically determined by g = 2R · cosθ and, kinematically, by k = vn · TOF where TOF = tf . (2) can now be rewritten as , (3) En = 2mR 2 t−2 f where m is the neutron mass. This one-to-one correspondence between the TOF of n , determined by tf = t2 -t1 , and the energy of n allows one to deduce the incoming neutron energy spectrum S(En ) from the measured tf spectrum. The relationship S(En ) ↔ S(tf ) is unique as long as the neutron reaches S2 by a single n + H scattering in S1 and is detected in S2 by the first n + H scat-
FIG. 2. Principles of the TOFOR neutron spectrometer with flat S1 and S2 scintillators placed tangentially on a sphere of radius R on which the flight path is = 2R · cosθ . The scattering angle θ is half the azimuthal one (θ = α/2). The S2 scintillators of which five are shown, cover the full spherical zone.
can be broken by MS events. In other words, beyond the kinematic confines of direct events of Eq. (4), there can only be MS events (and possibly background of other sorts), which can be used as a criteria for deselecting (discriminating) them in the collected data. The efficiency of the MS discrimination is based on the correlation between the parameters ES1 and tf −2 , where both would be measured quantities in TOFOR II with DWF system. The scattering angle, on the other hand, is known only to its range θ min < θ < θ max as determined by the spectrometer geometry where that of S2 is of special interest here (Fig. 1). This efficiency can be studied in simulation for given incident neutron energy which reduces Eq. (4) to ES1 (θ ) ∝ (1-cos2 θ ) = sin2 θ . Direct events are limited to occur in the range ES1< - ES1> set by θ min -θ max . For discrimination of real data of varying incoming energy, the 1/tf 2 factor of Eq. (4) is included defining the functions ES1< (tf ) and ES1> (tf ). These define the upper and lower boundaries of the direct event domain of experimental data when presented in the parameter plane ES1 vs. tf . The outlying events can be deselected as undesirables. There are no similar constraints on the energy deposition in S2 as it can be produced at any scattering angle (θ 2 ) being ES2 = En (1-cos2 θ 2 ) but for an upper boundary for direct events of ES2 ≤ En cos2 θ = 2m(R/tf )2 cos2 θ (where θ refers to scattering in S1). The (outlying) regions, beyond the boundaries on ES1 for direct scattering, besides the weak ones for ES2 , can be reached only by multiple scattering. The practical implementation of the TOFOR spectrometer4 used a ring of individual flat scintillators for the S2 detector (Fig. 2). The scintillators lie on the TOF sphere surface in the tangent points but deviate elsewhere due to the finite thickness and the lateral extension. The spherical zone, over which scattered neutrons are intercepted, is defined by the height of the scintillators and the azimuthal angle for the middle point (α o = 2θ o ). This means that the scattering angle range θ min to θ max is defined by the height of the S2 scintillator with a small (typically, at the scale of one tenth) modification due to the finite diameter of S1. Neutrons that scatter (on H) directly from S1 into S2, give rise to time signals t1 and t2 determining the scattered neutron flight time, tf = t2 -t1 . The actual flight paths λ between these signal points at scattering angle θ can vary from that of the TOF sphere, (θ ), so that neutrons of given En will give rise to a tf distribution of events of a certain width centered around the tf value defined by Eq. (3). The width represents a fundamental (geometrical) indetermination in the tf quantity for given En which we can call time resolution (tf /tf ).
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This can, through Eq. (3), be related to the resolution of the derived neutron energy spectrum, i.e., 2tf /tf ↔ En /En . Another factor affecting the tf , and En , resolution comes from the intrinsic (timing) error in the measurements of t1 and t2 . It will here only be qualitatively discussed in Sec. VI so resolution will refer to the geometry if not otherwise stated. The MS events are undesirable in the data used to determine the measured tf spectra as they degrade resolution and, hence, dulls the “one-to-one” correspondence between S(tf ) and S(En ). Therefore, MS event deselection (discrimination) in the data is key to optimizing the determination of the energy spectrum of the fusion neutron emission for given statistics (number of counts per second). The present study is about how the efficiency of the MS discrimination is affected by the choice of the scintillator geometry of the TOFOR type of spectrometers. Here, we put forward the archetype principles for such a design that we refer to as TOFOR II.
III. TOFOR II MODEL DESIGN
The TOFOR II design is studied with the aim to exhibit the performance gain which can be achieved relative to TOFOR (Fig. 3). The reference geometry used for scintillators is that of TOFOR but for the change of S2. In TOFOR II, the single ring of 32 trapezoidal S2 scintillators (of height h) was split into two rings referred to as S2a and S2b of heights ha and hb with ha + hb ≈ h. The S2 solid angle was the same in the two cases and also the thickness (15 mm). The dimensions of S2 scintillators of TOFOR II and TOFOR are shown in Table I besides the subtended scattering angle ranges. The S1 detector consists of 5 scintillator disks of 40 mm diameter and 5 mm thickness. The S1 and S2 scintillator elements are aligned so that their mid planes are tangential to the constant TOF sphere (radius R = 70.5 cm) with respect to their middle points. The flight path is, for instance, = 1221 mm for θ o = 30◦ (the angular middle point for S2 in Fig. 2) implying flight times of 65.1 ns for neutrons of En = 2.45 MeV scattered through n + H, and 27.1 ns for En = 14.1 MeV. The S2 scintillators are placed azimuthally so that α = 60◦ (θ = 30◦ ) is in the center of the split (S2a + S2b ) and the single (S2) ring systems (Fig. 3).
FIG. 3. Principles of TOFOR II (b) where the scattered neutrons are intercepted by two rings of S2 detectors of heights ha = hb compared to TOFOR (a) of height h ≈ ha + hb . The scattering angles refer to the center position in mid-planes of the S1 and S2 scintillators.
Rev. Sci. Instrum. 85, 043503 (2014) TABLE I. Summary of dimensions (mm) of the trapezoidal S2 scintillators of TOFOR II and TOFOR given as widths (w1 and w2 ), height (h), and thickness (t). Also shown are the scattering angle into the center (θ o degrees) and tips (θ min /θ max ) of S2a and S2b , and S2. Instrument
S2
w1
w2
h
t
θo
θ min /θ max
TOFOR-II TOFOR-II TOFOR
S2a S2b S2
94 115 95
114 128 134.7
176.2 166.6 350
15 15 15
26.5 33.5 30.0
23.0/30.0 30.0/37.0 23.0/37.0
IV. CALCULATIONS
The code Geant410 was used to simulate the transport of neutrons through the S1 and S2 scintillators and the recoiling protons deposited in the scintillators from the n + H elastic scatterings. The effect of elastic n + C scattering was considered as part of multiple scattering in the two scintillators. The response of the scintillators to the proton recoils was calculated as energy depositions of the recoil energies ES1 and ES2 within the scintillator volumes of S1 and S2, i.e., considering edge effects. The deposited energies were expressed in units of the equivalent electron deposition (keVee ) which would be proportional to the energy pulses produced; as energy and amplitude (pulse height) are related, they are used here interchangeably. The conversion from kinetic (keV) to deposited (keVee ) energy was done in GEANT4 code and the elastic cross sections used were those of the code library. The plastic scintillator material was the same as used in TOFOR, i.e., a density of 1.032 g/cm3 with a H/C atomic ratio of 1.1:1. In the model calculations, S1 was, for reasons of simplicity, represented as one scintillator 25 mm thick. This is acceptable in the present comparative study, while production data would consist of individual batches, one for each of the 5 mm scintillator elements. The S2 detector was made up of two rings (a and b) of 32 scintillators where those in each ring were identical. The simulations dealt only with reactions in the scintillator material so no tilting of scintillators was needed to compensate for light transport times to the PM tubes.5 Finally, it was assumed that a mono-energetic neutron beam, parallel to the spectrometer axis, was impinging uniformly over the area on the S1 target scintillator. The aim of the calculations was to determine the distribution of n + H single scattering points (x1 and x2 ) over the S1 and S2 scintillator volumes and the corresponding energy pulses generated at these positions, ES1 (x1 ) and ES2 (x2 ). The flight path length is defined by λ(x) where x = x1 -x2 . Each pair of start and end points for the flight path defines the scattering angle (θ between x and the spectrometer axis) which, for given beam energy, uniquely determines the recoil energy ES1 (in keV). The flight path distributions λ(x) over the S1 and S2 volumes, and the corresponding time-of-flight distributions tf (x), were simulated by Monte Carlo. Moreover, we have simulated the distribution of energy pulses ES1 (x), which have also the functional dependence ES1 (x1 ,θ ), that reduces to ES1 (θ ) for fully stopped recoils. In the case of a MS event, the recoil producing scattering in S1 can, for instance, be preceded or followed by a second scattering in S1. This would cause the neutron to be deflected by an angle θ MS thus changing the scattering angle from θ to θ ± θ MS thus
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FIG. 4. Results on simulated time-of-flight (tf ) spectra for the TOFOR II spectrometer in response to mono-energetic neutron beams of En = Eref = 2.45 and En = Eref ± 50% (corresponding to tf = 65, 53, and 92 ns). The spectra shown are based on the raw data (broken line) compared with those of selected events due to (direct) single scattering (solid line).
widening the kinematics domain of MS events in the ES1 -tf plane relative to that of single events given by Eqs. (2)–(4). Higher order MS events also occur and were part of the simulation including MS in S2, while 1st order MS in S1 would be dominant. The MS event contribution from S2 is essentially a scintillator volume effect so it would be smaller for TOFOR II compared to TOFOR. It can also be noted that the timing of MS events was taken as t1 and t2 for the first proton recoil, while ES1 and ES2 pulse energy sums (in keVee ) were used. The present study is concerned with the scintillator response to mono-energetic incoming neutrons with En = 2.5 MeV being the reference case. The focus is on the simulated time-of-flight spectra S(tf ) and the effect of applying MS discrimination to the event density distribution in the ES1 -tf plane. V. RESULTS
The response of the TOFOR II to mono-energetic neutrons was calculated in terms of the quantities tf and ES1 in
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comparison to that of TOFOR. Distinction was also made between SS and MS events, i.e., single (direct) scattering in S1 producing ES1 and single hit on one of the S2 scintillators, and those that involved additional scatterings (MS events). Examples of simulated tf distributions for TOFOR II are shown in Fig. 4 for incoming neutrons of En = 2.5 MeV (reference energy), or En = 1.2 and 3.7 MeV. The spectra are based on the raw data as recorded compared to those in the selected component of direct events. The full distributions are centered at the expected tf values for corresponding En values of the direct spectrum. The MS events manifest themselves in the full distribution as tails on both sides of the peaks of short and long flight times (tf< and tf> ). For instance, the 2–5 MeV spectrum is centered at tf = 65 ns with asymmetric tf< and tf> tails whose amplitudes become similar to that of the direct events at tf< ≈ 63.2 and tf> ≈ 68.6 ns. This happens at the amplitude level of about 1/50 relative to the peak but this will vary depending on the peak width. The results show that relative peak-tail amplitude features are similar over an extended neutron energy range. They can be taken as illustration of the SS-MS conditions under which the neutron emission from common tokamak plasmas would be observed, such as at JET. The determination of tf spectra should be based on data with reduced MS contribution. Such reduced data were obtained by deselecting events falling outside the kinematics region of direct n + H scattering in the ES1 -tf plane. The event density distribution that would be recorded by TOFOR II was simulated for 2.5 MeV incoming neutrons and compared with that for TOFOR (Fig. 5). Here, the direct events appear as a band of enhanced density centered around tf = 65.1 sitting on top of two streaks of MS events of much lower ( (tf ) for each batch.
(crescent shaped) distribution of direct events for TOFOR in Fig. 5. It can be quantified as causing a shift of tf = +0.5 and +2.0 ns from θ min to θ max passing to a minimum of tf = 0 in between. The curvature is much smaller for TOFOR II and, for instance, insignificant relative to the tf width of the band at about 3 ns. The data for TOFOR II exist in two batches as collected by the S2a and S2b scintillators which can be analyzed separately and, of course, presented individually (Figs. 6(c) and 6(b). The collected data can also be considered as a single batch for the (full) S2a+b scintillator of TOFOR II (Fig. 6(a)) which was used for comparison above with the S2 data of TOFOR (Fig. 5). The detailed TOFOR II results in Fig. 6 show that there is a bend in the direct event distribution also here but it is small as it is limited to within the batches with reduced angular acceptance range. The direct event distributions appear in a limited region of the parameter space of ES1 , tf , and θ as defined by 2-body kinematics (cf. Eq. (4)). The spreads ES1 max -ES1 min for incoming neutrons of 2.5 MeV (tfo = 65 ns) are ±61%, ±40%, and ±34% for S2a+b , S2a , and S2b as determined by the θ max /θ min angles in the table; the results for S2a+b are equivalent to those for S2 of TOFOR. The functions used as discrimination boundaries, shown in Figure 6, were normalized so that ES1> (tf ) = 1.1 · ES1 max and ES1< (tf ) = 0.9 · ES1 min for tf = tfo . Simulated tf spectra for TOFOR II are shown in Fig. 7 where those based on raw data are compared with those from reduced data. Data reduction was furnished by applying a single (gate) pair of ES1> (tf ) and ES1< (tf ) functions to the full S2a+b batch and a dual gate to the data divided into S2a and S2b batches. As can be seen, the discrimination leads to significant reductions of the tf< and tf> tails, while the peak itself is practically unaffected. For instance, the MS contribution on the tf< side is suppressed in amplitude to below the 10−2 level of the peak and its shape is substantially narrowed to having a very small deviation from the slope of the direct event peak. There is also a dramatic suppression of the MS contributions on the tf> side. As can be seen, TOFOR II furnishes enhanced discrimination in both regions, while the effect on tf< side would be most significant for extraction of information on the
FIG. 7. Simulated tf spectra for 2.5 MeV neutrons for the TOFOR II spectrometer without and with cuts on the pulse height of the ES1 signal. Shown are results where discrimination was applied to the combined batch (S2a+b ) of data (referred to as single cut) and individually to S2a and S2b batches (dual cut).
incoming neutron spectrum. The single gate results, on the other hand, are similar to those for TOFOR. What concerns MS involving S2, the contribution is a small ( = 68.6 ns (Fig. 7). These were taken as integration limits to determine the relative number of MS events in the tf< and tf> regions of the tf spectra based on raw data as well as those reduced by single and dual gate discrimination. The results in Table II show the following features. On the tf< (high En side) of the peak, the single gate discrimination suppresses the MS admixture by a factor 3, which increases to a factor of 17 with double discrimination. On the high tf> side, the single and double discrimination reduce the integrated MS levels by factors of about 5 from a high level of 27% compared to 3% for the tf< region. The numbers for TOFOR are similar to the single gate results quoted. The dual gate results thus illustrate the gain offered by a DWF data acquisition system on TOFOR II. TABLE II. Results on the relative contribution (%) of multiple scattering events on the low (tf< ) and high (tf> ) sides of the peak in the simulated tf spectrum of TOFOR II for 2.45 MeV neutrons before and after single/double discrimination. Discrimination
tf
None Single gate Dual gate
3.0 1.1 0.18
27.4 5.0 3.1
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FIG. 8. Results on simulated event density distributions of discriminated TOFOR II data D(tf ,Es1 ) for the data batches S2a+b , S2b , S2a , and the difference distribution Ddif = Dab -(Da + Db ). Also shown is the projection on the tf axis, Diff (tf )/Da+b (tf ). The constant tf lines are those from Fig. 7.
To further illustrate how the dual gate improves discrimination, we consider the event distributions D(tf ,ES1 ) for the S2a+b , S2a , and S2b batches of the discriminated TOFOR data (Fig. 8). Here we can note two general features of the results. One is that the dual gating leads to a marked decrease in the discriminated event density around 75 ns, which shows up as a kink in the tf spectra around tf = 78 ns (Fig. 7). Another is that enhanced MS event elimination is not limited to certain regions of the Es1 -tf plane but the density level is reduced over most of the single gated area. This is further displayed by the results on the difference distribution Ddif = Dab -(Da + Db ) and the projection of the ratio distribution Ddif (tf )/Da+b (tf ) on to the tf axis (bottom panels of Figure 8). The latter results confirm the general enhanced dual gate discrimination with the qualification for the wedge shaped region Ddif = 0. It arises because of the separation between the ES1> (tf ) and ES1< (tf ) functions for the S2a and S2b data batches. This gap between the lower/upper functions of S2a and S2b could be reduced by tightening the discrimination gates around the direct event region but must be done as a trade off between eliminating MS events and losing detection efficiency. The Diff (tf )/Da+b (tf ) graph shows that the dual cut discrimination is more than twice as efficient as that of single cut but for the region nearest to the range of direct events (63 < tf < 70 ns). The relative efficiency of dual cuts is directly related to the gap between the high/low discrimination functions used for the S2a and S2b batches. The simulated tf spectrum for 14 MeV neutrons is shown in Fig. 9 as based on the raw and doubly discriminated data for TOFOR II. In comparison to the 2.5 MeV spectrum (Fig. 7), the direct peak is narrower (by a factor of 2.5 as measured in ns) and its height is correspondingly increased relative to the surrounding MS dominated regions. This is in part the explanation for the observation that the relative MS contribution in the raw spectrum is lower by an order of magnitude than at En = 2.5 MeV. The dual gate discrimination has about the same beneficial effect on the tf spectrum as for 2.5 MeV in the region near the direct event peak. However, further out
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FIG. 9. Simulated TOFOR II results on the time of flight spectrum for 14MeV neutrons based on raw data and those subjected to single and dual discrimination cuts.
on the tf> side the discrimination efficiency is higher at En = 14 MeV so that the MS level in the region tf ≥ 50 ns is similar to that of 2.5 MeV for the equivalent range of tf ≥ 78 ns. These dual gate spectra end up having similar relative MS admixtures. It is interesting to note that inelastic scattering channels open up for En = 14 MeV, e.g., n + C–>C*(4.4 MeV) + n , which could give rise to the slope change that appears below 40 ns in the tf spectrum of Fig. 9. VI. DISCUSSION
The ES1 quantity is essential for discriminating undesired MS events over as large regions as possible in the parameter plane ES1 vs. En outside the “island” occupied by direct events, i.e., outside ES1 ∝ En · (1-cos2 θ ) for θ min ≤ θ ≤ θ max . The variation in ES1 is that of En whose spread, in turn, is that of the incoming flux (typically, at least, ±25% for 2.5 MeV dd neutrons from JET plasmas). The variation in the angular dependent factor is set by the S2 height (θ min -θ max ) which is about ±40% in the case of TOFOR resulting in a total variation of approximately −60% to +75% around an average of ES1 avg = 0.63 MeV for dd neutron emission. With fixed gate ES1 discrimination, one could deselect the events of pulse heights up to ES1 = 0.4 · ES1 avg on the low tf< side, which is the most important for plasma diagnostic applications,11–17 and above ES1 = 0.75 · ES1 avg that would (mostly) affect events on the tf > side. With DWF data, the deselection is applied to the 2D distribution of events in the ES1 -tf plane with the gate functions ES1< (tf ) and ES1> (tf ) (in Fig. 8) which reduces the discrimination limits to their θ dependence, i.e., ES1 < 0.6 · ES1 avg and ES1 > 0.6 · ES1 avg . With split S2, the gate limits are narrowed along with the θ min /θ max apertures leading to an increased discrimination efficiency for TOFOR II of about a factor of two. The MS events one wants to eliminate appear over an extended region in the ES1 -tf plane (Figs. 5 and 6). The region is bounded by tf ≥ tf min that can be ascribed mostly as due to double scattering taking place in S1 with
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tf min varying with ES1 . By re-writing Eq. (4), one obtains tf min = (λmin /cosθ )(1/2mEn )1/2 , where λ is the flight path with the embedded ES1 dependence (from Eq. (1)) 1/cosθ = (1-ES1 /En 2 )−1/2 ≈ 1 + 0.5ES1 /En , i.e., tf min (ES1 ) = λmin (1/2mEn )1/2 (1 + 0.5ES1 /En ). The tf min limit corresponds to neutrons that have been energy down-scattered but not further than what is needed to produce recoils of energy ES1 , i.e., En ≥ En -ES1 . The lowest tf min is λmin /(2mEn )1/2 . It is asymptotically approached for ES1 → 0, i.e., tf min (0). The values are given by the θ min limits for Sa and S2b (being the same as for S2), tf min = 52 and 56 ns for S2a with neutrons of En = 2.5 MeV (Figs. 5 and 6). These events are due MS in S1 predominantly from n + C scattering. From these points, tf min boundaries for the MS events increases along with ES1 up to and beyond tf ≈ 70 ns. For flight time of direct events (tf = 65 ns), the MS event boundary coincide with the upper ES1 limit of direct events. This reflects the situation that the minimum flight path in this case is occurring for the case that the λmin occurs for θ ≈ θ max , i.e., it is the same as the maximum λ. Here we note that the MS regions on the tf< side of the direct event bands vary with respect to their extension depending on their tf min (0) values, while they share the same functional ES1 dependence (Fig. 8). This is one cause of the increased discrimination efficiency of dual over single gating. The other is that the dual decreases the event density in the undiscriminated regions except for the wedged shape part because of the gap between the upper and lower bounds (ES1> and ES1< ) of the S2a and S2b batches. The overlap between these energy ranges should be minimized to increase the kinematics region to which dual gate discrimination can be applied. However, this is a matter of trade off with not cutting into the direct event region leading to a loss in spectrometer efficiency. What can be done is to increase the heights of the S2a and S2b scintillators which decrease the relative wedge area without too much sacrifice of resolution as noted below. We shall make some comments on the scintillator geometry in this context. The first is that the trapezoidal shape gives a sharp definition of the scattering angle aperture and, hence, also the ES1 gate definitions. Second, splitting the S2 detectors into three instead of two rings as for TOFOR II, would give a relatively small gain in performance as the additional scintillator gap would lessen the relative discrimination efficiency. Third, other geometries (cf. Ref. 3) could be used such as using hexagonal scintillators to cover the same S2 area as for the TOFOR type of spectrometers. Such a geometry would not be suitable for use together with DWF data acquisition system because of the great number of scintillators needed (about 5 times as many) and the shape. The MS events of the tf> side of the direct event distribution can involve extra n + H or n + C scattering in either S1 or S2. MS events form streaks of enhanced densities that can be seen in the ES1 -tf plane in Fig. 5, going diagonally and horizontally, respectively. The diagonal MS streak, involving n + H or n + C scattering, has a lower tf limit (tf min ), which varies as (1/ES1 )1/2 starting in the kinematic region of the direct events. The tf width of this streak is attributable to the variation θ allowed by the heights of S2a+b , S2a , and S2b (cf. Fig. 8). The tf> region, within the limits of the discrimination functions, ES1< (tf ) and ES1> (tf ), in Fig. 8, is populated by MS
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events due to n + C scatterings at a small energy loss to the scattered neutron but potentially large angular changes (θ MS ). For instance, the average θ MS is about 60◦ to send a neutron into S2 whose energy is decreased by a factor of two and having an average flight time of tf ≈ 130 ns, with a variation from +10 for θ max to −10% for θ min (and correspondingly narrower for the split S2). The efficiency of the discrimination will depend on the quality of the ES1 signal as embedded in the pulse height resolution of the light as recorded by the PM tubes. To this end, it has been realized that the S1 of TOFOR with the three light guides attached to each scintillator gave rather poor light transmission. This could potentially be improved using only two short light guides with possible added boost by increasing the thickness, together with the scintillator element, from 5 to 6 mm. The accompanying increase in multiple scattering would, in the case of TOFOR II, be balanced by the enhanced discrimination efficiency connected with improved pulse height resolution. It would also mean that one can set tighter discrimination gates, especially, allowing the gap between ES1
Second generation fusion neutron time-of-flight spectrometer at optimized rate for fully digital data acquisition X. Zhang,1,a) J. Källne,2,3 G. Gorini,3,4 M. Nocente,3,4 T. Fan,1 X. Yuan,1 X. Xie,1 and Z. Chen1 1
School of Physics, State Key Lab of Nuclear Physics and Technology, Peking University, Beijing 100871, China Department of Engineering Sciences, Uppsala University, Uppsala, Sweden 3 Dipartimento di Fisica “G. Occhialini,” Università di Milano-Bicocca, Piazza della Scienza 3, 20126 Milan, Italy 4 Istituto di Fisica del Plasma “Piero Caldirola,” Via R. Cozzi 53, 20125 Milan, Italy 2
(Received 28 November 2013; accepted 17 March 2014; published online 7 April 2014) The progress on high-rate event recording of data is taken as starting point to revisit the design of fusion neutron spectrometers based on the TOF (time-of-flight) technique. The study performed was aimed at how such instruments for optimized rate (TOFOR) can be further developed to enhance the plasma diagnostic capabilities based on measurement of the 2.5 MeV dd neutron emission from D plasmas, especially the weak spectral components that depend on discrimination of extraneous events. This paper describes a design (TOFOR II) adapted for use with digital wave form recording of all detector pulses providing information on both amplitude (pulse height) and timing. The results of simulations are presented and the performance enhancement is assessed in comparison to the present. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4869804] I. INTRODUCTION
Neutron emission spectroscopy (NES) is a diagnostic of fusion plasmas that requires dedicated instrumentation for measurement of the 2.5 and 14 MeV neutron emissions from d + d and d + t reactions, respectively.1 The dd rate is two orders of magnitude lower than that of dt under similar thermal conditions of D and DT plasmas. This means that 2.5 MeV neutron spectrometers need to have correspondingly higher detection efficiency in order to be on par with the performance of those for 14 MeV. However, the demand on energy resolution can be lowered, typically, from 2.5% to 6.5% (FWHM) for 4-keV plasmas. The leaders at present are neutron time-offlight (TOF) and magnetic proton recoil (MPR) spectrometers for dd and dt neutron emission, respectively.2 The TOF-technique for NES studies of tokamak plasmas has evolved since the 1980s3 up to the latest model TOFOR (TOF at optimized rate4 ) installed at JET in 2005.5 At the time proposed (1992), the conventional TOF measurements were based on using time-to-digital converter (TDC) which received start and stop signals for neutrons that scattered from one scintillator into a second. Such pairs of single scattering events were identified with pulse height discriminators providing the timing points and also suppression of unwanted event pairs.4 When installed at JET, TOFOR was equipped with a data acquisition system for digital time recording5, 6 in which the stored event histories of all detectors could be analyzed post-mortem and, subsequently, used to construct neutron TOF spectra. This offered significantly enhanced performance over the TDC technique in terms of count rate, besides benefitting time calibration and the handling of unwanted accidental event pairs.7 Recent advancements in signal processa) Authors to whom correspondence should be addressed. Electronic
ing electronics make it now possible to have data acquisition for neutron TOF spectrometers where the digital waveforms (DWF) of all detector pulses are recorded at high rates, data volumes, and precision. Such DWF data can be analyzed for extraction of the pulse information relating to both amplitude (pulse height) and timing. Recent tests of DWF electronics with TOFOR at JET have given encouraging results,8 which motivates considering a next generation design of TOFOR instruments whose scintillator geometry is adapted to the new DWF based data acquisition systems. In principle, a DWF based data acquisition system leads to improved resolution of the measured TOF spectrum and better identification of the desired neutron scattering events, and, hence, also discrimination of (undesired) extraneous ones. These latter events involve multiple neutron scatterings which do not have the constrained relationship between pulse height generated in the first scintillation detector and the TOF of “directly” scattered neutrons; these are referred to as multiple and single scattering events, MS and SS (equaling direct scattering), respectively. In this paper, we shall be concerned with the potential for enhanced discrimination of MS events through suitable choice of the geometry of TOFOR spectrometers. This is illustrated by a reference design dubbed TOFOR II which represents the next step in enhancing the instrumental capabilities for NES plasma diagnostics. II. PRINCIPLES OF THE TOF TECHNIQUE
The TOF technique is based on elastic neutron proton scattering in plastic scintillation detectors (S). Incoming neutrons (n) are scattered in the target scintillator S1 (Fig. 1), i.e., n + H → n + pr where recoiling protons, pr , deposit the energy ES1 specified by the scattering angle θ through
addresses: [email protected], [email protected], and Giuseppe.Gorini@ unimib.it 0034-6748/2014/85(4)/043503/9/$30.00
85, 043503-1
ES1 = En (1 − cos2 θ ).
(1)
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tering in it; these are referred to as direct single scattering (SS) events in contrast to indirect ones involving (multiple) scatterings (MS). Multiple scattering is unavoidable in scintillators of finite thickness, but their admixture in the data used to determine S(tf ) should be reduced as it dulls the resolution relative to the optimal one furnished by the tf spectrum of direct events. Characteristic of indirect MS events is that they, for given En , can appear with longer and shorter flight times than those of direct events. This means that the correlation that exists between ES1 and θ for direct events, ES1 = En (1 − cos2 θ ) = 2mR2 tf−2 (1 − cos2 θ ) (4) FIG. 1. Schematics of fusion neutron spectrometer based on time of flight measurement with plastic scintillator detectors S1 and S2, and the underlying 2-body kinematics of elastic n + H → precoil + n .
A fraction of the scattered neutrons can undergo subsequent scattering in S2 depositing ES2 in the range ES2 < En ; it is typically registered as an event if ES2 exceeds a certain threshold. An incoming neutron is recorded through the event pair of signals produced in the two scintillation detectors. The time difference of the signal pairs, tf = t2 -t1 , is measured which is the basis for determining the energy of the scattered neutron (En ) and, subsequently, that of the incoming neutron from En = En /cos2 θ. (2) With the S1 and S2 detectors on the constant TOF sphere (of radius R, Fig. 2),9 the flight path of n is geometrically determined by g = 2R · cosθ and, kinematically, by k = vn · TOF where TOF = tf . (2) can now be rewritten as , (3) En = 2mR 2 t−2 f where m is the neutron mass. This one-to-one correspondence between the TOF of n , determined by tf = t2 -t1 , and the energy of n allows one to deduce the incoming neutron energy spectrum S(En ) from the measured tf spectrum. The relationship S(En ) ↔ S(tf ) is unique as long as the neutron reaches S2 by a single n + H scattering in S1 and is detected in S2 by the first n + H scat-
FIG. 2. Principles of the TOFOR neutron spectrometer with flat S1 and S2 scintillators placed tangentially on a sphere of radius R on which the flight path is = 2R · cosθ . The scattering angle θ is half the azimuthal one (θ = α/2). The S2 scintillators of which five are shown, cover the full spherical zone.
can be broken by MS events. In other words, beyond the kinematic confines of direct events of Eq. (4), there can only be MS events (and possibly background of other sorts), which can be used as a criteria for deselecting (discriminating) them in the collected data. The efficiency of the MS discrimination is based on the correlation between the parameters ES1 and tf −2 , where both would be measured quantities in TOFOR II with DWF system. The scattering angle, on the other hand, is known only to its range θ min < θ < θ max as determined by the spectrometer geometry where that of S2 is of special interest here (Fig. 1). This efficiency can be studied in simulation for given incident neutron energy which reduces Eq. (4) to ES1 (θ ) ∝ (1-cos2 θ ) = sin2 θ . Direct events are limited to occur in the range ES1< - ES1> set by θ min -θ max . For discrimination of real data of varying incoming energy, the 1/tf 2 factor of Eq. (4) is included defining the functions ES1< (tf ) and ES1> (tf ). These define the upper and lower boundaries of the direct event domain of experimental data when presented in the parameter plane ES1 vs. tf . The outlying events can be deselected as undesirables. There are no similar constraints on the energy deposition in S2 as it can be produced at any scattering angle (θ 2 ) being ES2 = En (1-cos2 θ 2 ) but for an upper boundary for direct events of ES2 ≤ En cos2 θ = 2m(R/tf )2 cos2 θ (where θ refers to scattering in S1). The (outlying) regions, beyond the boundaries on ES1 for direct scattering, besides the weak ones for ES2 , can be reached only by multiple scattering. The practical implementation of the TOFOR spectrometer4 used a ring of individual flat scintillators for the S2 detector (Fig. 2). The scintillators lie on the TOF sphere surface in the tangent points but deviate elsewhere due to the finite thickness and the lateral extension. The spherical zone, over which scattered neutrons are intercepted, is defined by the height of the scintillators and the azimuthal angle for the middle point (α o = 2θ o ). This means that the scattering angle range θ min to θ max is defined by the height of the S2 scintillator with a small (typically, at the scale of one tenth) modification due to the finite diameter of S1. Neutrons that scatter (on H) directly from S1 into S2, give rise to time signals t1 and t2 determining the scattered neutron flight time, tf = t2 -t1 . The actual flight paths λ between these signal points at scattering angle θ can vary from that of the TOF sphere, (θ ), so that neutrons of given En will give rise to a tf distribution of events of a certain width centered around the tf value defined by Eq. (3). The width represents a fundamental (geometrical) indetermination in the tf quantity for given En which we can call time resolution (tf /tf ).
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This can, through Eq. (3), be related to the resolution of the derived neutron energy spectrum, i.e., 2tf /tf ↔ En /En . Another factor affecting the tf , and En , resolution comes from the intrinsic (timing) error in the measurements of t1 and t2 . It will here only be qualitatively discussed in Sec. VI so resolution will refer to the geometry if not otherwise stated. The MS events are undesirable in the data used to determine the measured tf spectra as they degrade resolution and, hence, dulls the “one-to-one” correspondence between S(tf ) and S(En ). Therefore, MS event deselection (discrimination) in the data is key to optimizing the determination of the energy spectrum of the fusion neutron emission for given statistics (number of counts per second). The present study is about how the efficiency of the MS discrimination is affected by the choice of the scintillator geometry of the TOFOR type of spectrometers. Here, we put forward the archetype principles for such a design that we refer to as TOFOR II.
III. TOFOR II MODEL DESIGN
The TOFOR II design is studied with the aim to exhibit the performance gain which can be achieved relative to TOFOR (Fig. 3). The reference geometry used for scintillators is that of TOFOR but for the change of S2. In TOFOR II, the single ring of 32 trapezoidal S2 scintillators (of height h) was split into two rings referred to as S2a and S2b of heights ha and hb with ha + hb ≈ h. The S2 solid angle was the same in the two cases and also the thickness (15 mm). The dimensions of S2 scintillators of TOFOR II and TOFOR are shown in Table I besides the subtended scattering angle ranges. The S1 detector consists of 5 scintillator disks of 40 mm diameter and 5 mm thickness. The S1 and S2 scintillator elements are aligned so that their mid planes are tangential to the constant TOF sphere (radius R = 70.5 cm) with respect to their middle points. The flight path is, for instance, = 1221 mm for θ o = 30◦ (the angular middle point for S2 in Fig. 2) implying flight times of 65.1 ns for neutrons of En = 2.45 MeV scattered through n + H, and 27.1 ns for En = 14.1 MeV. The S2 scintillators are placed azimuthally so that α = 60◦ (θ = 30◦ ) is in the center of the split (S2a + S2b ) and the single (S2) ring systems (Fig. 3).
FIG. 3. Principles of TOFOR II (b) where the scattered neutrons are intercepted by two rings of S2 detectors of heights ha = hb compared to TOFOR (a) of height h ≈ ha + hb . The scattering angles refer to the center position in mid-planes of the S1 and S2 scintillators.
Rev. Sci. Instrum. 85, 043503 (2014) TABLE I. Summary of dimensions (mm) of the trapezoidal S2 scintillators of TOFOR II and TOFOR given as widths (w1 and w2 ), height (h), and thickness (t). Also shown are the scattering angle into the center (θ o degrees) and tips (θ min /θ max ) of S2a and S2b , and S2. Instrument
S2
w1
w2
h
t
θo
θ min /θ max
TOFOR-II TOFOR-II TOFOR
S2a S2b S2
94 115 95
114 128 134.7
176.2 166.6 350
15 15 15
26.5 33.5 30.0
23.0/30.0 30.0/37.0 23.0/37.0
IV. CALCULATIONS
The code Geant410 was used to simulate the transport of neutrons through the S1 and S2 scintillators and the recoiling protons deposited in the scintillators from the n + H elastic scatterings. The effect of elastic n + C scattering was considered as part of multiple scattering in the two scintillators. The response of the scintillators to the proton recoils was calculated as energy depositions of the recoil energies ES1 and ES2 within the scintillator volumes of S1 and S2, i.e., considering edge effects. The deposited energies were expressed in units of the equivalent electron deposition (keVee ) which would be proportional to the energy pulses produced; as energy and amplitude (pulse height) are related, they are used here interchangeably. The conversion from kinetic (keV) to deposited (keVee ) energy was done in GEANT4 code and the elastic cross sections used were those of the code library. The plastic scintillator material was the same as used in TOFOR, i.e., a density of 1.032 g/cm3 with a H/C atomic ratio of 1.1:1. In the model calculations, S1 was, for reasons of simplicity, represented as one scintillator 25 mm thick. This is acceptable in the present comparative study, while production data would consist of individual batches, one for each of the 5 mm scintillator elements. The S2 detector was made up of two rings (a and b) of 32 scintillators where those in each ring were identical. The simulations dealt only with reactions in the scintillator material so no tilting of scintillators was needed to compensate for light transport times to the PM tubes.5 Finally, it was assumed that a mono-energetic neutron beam, parallel to the spectrometer axis, was impinging uniformly over the area on the S1 target scintillator. The aim of the calculations was to determine the distribution of n + H single scattering points (x1 and x2 ) over the S1 and S2 scintillator volumes and the corresponding energy pulses generated at these positions, ES1 (x1 ) and ES2 (x2 ). The flight path length is defined by λ(x) where x = x1 -x2 . Each pair of start and end points for the flight path defines the scattering angle (θ between x and the spectrometer axis) which, for given beam energy, uniquely determines the recoil energy ES1 (in keV). The flight path distributions λ(x) over the S1 and S2 volumes, and the corresponding time-of-flight distributions tf (x), were simulated by Monte Carlo. Moreover, we have simulated the distribution of energy pulses ES1 (x), which have also the functional dependence ES1 (x1 ,θ ), that reduces to ES1 (θ ) for fully stopped recoils. In the case of a MS event, the recoil producing scattering in S1 can, for instance, be preceded or followed by a second scattering in S1. This would cause the neutron to be deflected by an angle θ MS thus changing the scattering angle from θ to θ ± θ MS thus
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FIG. 4. Results on simulated time-of-flight (tf ) spectra for the TOFOR II spectrometer in response to mono-energetic neutron beams of En = Eref = 2.45 and En = Eref ± 50% (corresponding to tf = 65, 53, and 92 ns). The spectra shown are based on the raw data (broken line) compared with those of selected events due to (direct) single scattering (solid line).
widening the kinematics domain of MS events in the ES1 -tf plane relative to that of single events given by Eqs. (2)–(4). Higher order MS events also occur and were part of the simulation including MS in S2, while 1st order MS in S1 would be dominant. The MS event contribution from S2 is essentially a scintillator volume effect so it would be smaller for TOFOR II compared to TOFOR. It can also be noted that the timing of MS events was taken as t1 and t2 for the first proton recoil, while ES1 and ES2 pulse energy sums (in keVee ) were used. The present study is concerned with the scintillator response to mono-energetic incoming neutrons with En = 2.5 MeV being the reference case. The focus is on the simulated time-of-flight spectra S(tf ) and the effect of applying MS discrimination to the event density distribution in the ES1 -tf plane. V. RESULTS
The response of the TOFOR II to mono-energetic neutrons was calculated in terms of the quantities tf and ES1 in
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comparison to that of TOFOR. Distinction was also made between SS and MS events, i.e., single (direct) scattering in S1 producing ES1 and single hit on one of the S2 scintillators, and those that involved additional scatterings (MS events). Examples of simulated tf distributions for TOFOR II are shown in Fig. 4 for incoming neutrons of En = 2.5 MeV (reference energy), or En = 1.2 and 3.7 MeV. The spectra are based on the raw data as recorded compared to those in the selected component of direct events. The full distributions are centered at the expected tf values for corresponding En values of the direct spectrum. The MS events manifest themselves in the full distribution as tails on both sides of the peaks of short and long flight times (tf< and tf> ). For instance, the 2–5 MeV spectrum is centered at tf = 65 ns with asymmetric tf< and tf> tails whose amplitudes become similar to that of the direct events at tf< ≈ 63.2 and tf> ≈ 68.6 ns. This happens at the amplitude level of about 1/50 relative to the peak but this will vary depending on the peak width. The results show that relative peak-tail amplitude features are similar over an extended neutron energy range. They can be taken as illustration of the SS-MS conditions under which the neutron emission from common tokamak plasmas would be observed, such as at JET. The determination of tf spectra should be based on data with reduced MS contribution. Such reduced data were obtained by deselecting events falling outside the kinematics region of direct n + H scattering in the ES1 -tf plane. The event density distribution that would be recorded by TOFOR II was simulated for 2.5 MeV incoming neutrons and compared with that for TOFOR (Fig. 5). Here, the direct events appear as a band of enhanced density centered around tf = 65.1 sitting on top of two streaks of MS events of much lower ( (tf ) for each batch.
(crescent shaped) distribution of direct events for TOFOR in Fig. 5. It can be quantified as causing a shift of tf = +0.5 and +2.0 ns from θ min to θ max passing to a minimum of tf = 0 in between. The curvature is much smaller for TOFOR II and, for instance, insignificant relative to the tf width of the band at about 3 ns. The data for TOFOR II exist in two batches as collected by the S2a and S2b scintillators which can be analyzed separately and, of course, presented individually (Figs. 6(c) and 6(b). The collected data can also be considered as a single batch for the (full) S2a+b scintillator of TOFOR II (Fig. 6(a)) which was used for comparison above with the S2 data of TOFOR (Fig. 5). The detailed TOFOR II results in Fig. 6 show that there is a bend in the direct event distribution also here but it is small as it is limited to within the batches with reduced angular acceptance range. The direct event distributions appear in a limited region of the parameter space of ES1 , tf , and θ as defined by 2-body kinematics (cf. Eq. (4)). The spreads ES1 max -ES1 min for incoming neutrons of 2.5 MeV (tfo = 65 ns) are ±61%, ±40%, and ±34% for S2a+b , S2a , and S2b as determined by the θ max /θ min angles in the table; the results for S2a+b are equivalent to those for S2 of TOFOR. The functions used as discrimination boundaries, shown in Figure 6, were normalized so that ES1> (tf ) = 1.1 · ES1 max and ES1< (tf ) = 0.9 · ES1 min for tf = tfo . Simulated tf spectra for TOFOR II are shown in Fig. 7 where those based on raw data are compared with those from reduced data. Data reduction was furnished by applying a single (gate) pair of ES1> (tf ) and ES1< (tf ) functions to the full S2a+b batch and a dual gate to the data divided into S2a and S2b batches. As can be seen, the discrimination leads to significant reductions of the tf< and tf> tails, while the peak itself is practically unaffected. For instance, the MS contribution on the tf< side is suppressed in amplitude to below the 10−2 level of the peak and its shape is substantially narrowed to having a very small deviation from the slope of the direct event peak. There is also a dramatic suppression of the MS contributions on the tf> side. As can be seen, TOFOR II furnishes enhanced discrimination in both regions, while the effect on tf< side would be most significant for extraction of information on the
FIG. 7. Simulated tf spectra for 2.5 MeV neutrons for the TOFOR II spectrometer without and with cuts on the pulse height of the ES1 signal. Shown are results where discrimination was applied to the combined batch (S2a+b ) of data (referred to as single cut) and individually to S2a and S2b batches (dual cut).
incoming neutron spectrum. The single gate results, on the other hand, are similar to those for TOFOR. What concerns MS involving S2, the contribution is a small ( = 68.6 ns (Fig. 7). These were taken as integration limits to determine the relative number of MS events in the tf< and tf> regions of the tf spectra based on raw data as well as those reduced by single and dual gate discrimination. The results in Table II show the following features. On the tf< (high En side) of the peak, the single gate discrimination suppresses the MS admixture by a factor 3, which increases to a factor of 17 with double discrimination. On the high tf> side, the single and double discrimination reduce the integrated MS levels by factors of about 5 from a high level of 27% compared to 3% for the tf< region. The numbers for TOFOR are similar to the single gate results quoted. The dual gate results thus illustrate the gain offered by a DWF data acquisition system on TOFOR II. TABLE II. Results on the relative contribution (%) of multiple scattering events on the low (tf< ) and high (tf> ) sides of the peak in the simulated tf spectrum of TOFOR II for 2.45 MeV neutrons before and after single/double discrimination. Discrimination
tf
None Single gate Dual gate
3.0 1.1 0.18
27.4 5.0 3.1
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FIG. 8. Results on simulated event density distributions of discriminated TOFOR II data D(tf ,Es1 ) for the data batches S2a+b , S2b , S2a , and the difference distribution Ddif = Dab -(Da + Db ). Also shown is the projection on the tf axis, Diff (tf )/Da+b (tf ). The constant tf lines are those from Fig. 7.
To further illustrate how the dual gate improves discrimination, we consider the event distributions D(tf ,ES1 ) for the S2a+b , S2a , and S2b batches of the discriminated TOFOR data (Fig. 8). Here we can note two general features of the results. One is that the dual gating leads to a marked decrease in the discriminated event density around 75 ns, which shows up as a kink in the tf spectra around tf = 78 ns (Fig. 7). Another is that enhanced MS event elimination is not limited to certain regions of the Es1 -tf plane but the density level is reduced over most of the single gated area. This is further displayed by the results on the difference distribution Ddif = Dab -(Da + Db ) and the projection of the ratio distribution Ddif (tf )/Da+b (tf ) on to the tf axis (bottom panels of Figure 8). The latter results confirm the general enhanced dual gate discrimination with the qualification for the wedge shaped region Ddif = 0. It arises because of the separation between the ES1> (tf ) and ES1< (tf ) functions for the S2a and S2b data batches. This gap between the lower/upper functions of S2a and S2b could be reduced by tightening the discrimination gates around the direct event region but must be done as a trade off between eliminating MS events and losing detection efficiency. The Diff (tf )/Da+b (tf ) graph shows that the dual cut discrimination is more than twice as efficient as that of single cut but for the region nearest to the range of direct events (63 < tf < 70 ns). The relative efficiency of dual cuts is directly related to the gap between the high/low discrimination functions used for the S2a and S2b batches. The simulated tf spectrum for 14 MeV neutrons is shown in Fig. 9 as based on the raw and doubly discriminated data for TOFOR II. In comparison to the 2.5 MeV spectrum (Fig. 7), the direct peak is narrower (by a factor of 2.5 as measured in ns) and its height is correspondingly increased relative to the surrounding MS dominated regions. This is in part the explanation for the observation that the relative MS contribution in the raw spectrum is lower by an order of magnitude than at En = 2.5 MeV. The dual gate discrimination has about the same beneficial effect on the tf spectrum as for 2.5 MeV in the region near the direct event peak. However, further out
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FIG. 9. Simulated TOFOR II results on the time of flight spectrum for 14MeV neutrons based on raw data and those subjected to single and dual discrimination cuts.
on the tf> side the discrimination efficiency is higher at En = 14 MeV so that the MS level in the region tf ≥ 50 ns is similar to that of 2.5 MeV for the equivalent range of tf ≥ 78 ns. These dual gate spectra end up having similar relative MS admixtures. It is interesting to note that inelastic scattering channels open up for En = 14 MeV, e.g., n + C–>C*(4.4 MeV) + n , which could give rise to the slope change that appears below 40 ns in the tf spectrum of Fig. 9. VI. DISCUSSION
The ES1 quantity is essential for discriminating undesired MS events over as large regions as possible in the parameter plane ES1 vs. En outside the “island” occupied by direct events, i.e., outside ES1 ∝ En · (1-cos2 θ ) for θ min ≤ θ ≤ θ max . The variation in ES1 is that of En whose spread, in turn, is that of the incoming flux (typically, at least, ±25% for 2.5 MeV dd neutrons from JET plasmas). The variation in the angular dependent factor is set by the S2 height (θ min -θ max ) which is about ±40% in the case of TOFOR resulting in a total variation of approximately −60% to +75% around an average of ES1 avg = 0.63 MeV for dd neutron emission. With fixed gate ES1 discrimination, one could deselect the events of pulse heights up to ES1 = 0.4 · ES1 avg on the low tf< side, which is the most important for plasma diagnostic applications,11–17 and above ES1 = 0.75 · ES1 avg that would (mostly) affect events on the tf > side. With DWF data, the deselection is applied to the 2D distribution of events in the ES1 -tf plane with the gate functions ES1< (tf ) and ES1> (tf ) (in Fig. 8) which reduces the discrimination limits to their θ dependence, i.e., ES1 < 0.6 · ES1 avg and ES1 > 0.6 · ES1 avg . With split S2, the gate limits are narrowed along with the θ min /θ max apertures leading to an increased discrimination efficiency for TOFOR II of about a factor of two. The MS events one wants to eliminate appear over an extended region in the ES1 -tf plane (Figs. 5 and 6). The region is bounded by tf ≥ tf min that can be ascribed mostly as due to double scattering taking place in S1 with
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tf min varying with ES1 . By re-writing Eq. (4), one obtains tf min = (λmin /cosθ )(1/2mEn )1/2 , where λ is the flight path with the embedded ES1 dependence (from Eq. (1)) 1/cosθ = (1-ES1 /En 2 )−1/2 ≈ 1 + 0.5ES1 /En , i.e., tf min (ES1 ) = λmin (1/2mEn )1/2 (1 + 0.5ES1 /En ). The tf min limit corresponds to neutrons that have been energy down-scattered but not further than what is needed to produce recoils of energy ES1 , i.e., En ≥ En -ES1 . The lowest tf min is λmin /(2mEn )1/2 . It is asymptotically approached for ES1 → 0, i.e., tf min (0). The values are given by the θ min limits for Sa and S2b (being the same as for S2), tf min = 52 and 56 ns for S2a with neutrons of En = 2.5 MeV (Figs. 5 and 6). These events are due MS in S1 predominantly from n + C scattering. From these points, tf min boundaries for the MS events increases along with ES1 up to and beyond tf ≈ 70 ns. For flight time of direct events (tf = 65 ns), the MS event boundary coincide with the upper ES1 limit of direct events. This reflects the situation that the minimum flight path in this case is occurring for the case that the λmin occurs for θ ≈ θ max , i.e., it is the same as the maximum λ. Here we note that the MS regions on the tf< side of the direct event bands vary with respect to their extension depending on their tf min (0) values, while they share the same functional ES1 dependence (Fig. 8). This is one cause of the increased discrimination efficiency of dual over single gating. The other is that the dual decreases the event density in the undiscriminated regions except for the wedged shape part because of the gap between the upper and lower bounds (ES1> and ES1< ) of the S2a and S2b batches. The overlap between these energy ranges should be minimized to increase the kinematics region to which dual gate discrimination can be applied. However, this is a matter of trade off with not cutting into the direct event region leading to a loss in spectrometer efficiency. What can be done is to increase the heights of the S2a and S2b scintillators which decrease the relative wedge area without too much sacrifice of resolution as noted below. We shall make some comments on the scintillator geometry in this context. The first is that the trapezoidal shape gives a sharp definition of the scattering angle aperture and, hence, also the ES1 gate definitions. Second, splitting the S2 detectors into three instead of two rings as for TOFOR II, would give a relatively small gain in performance as the additional scintillator gap would lessen the relative discrimination efficiency. Third, other geometries (cf. Ref. 3) could be used such as using hexagonal scintillators to cover the same S2 area as for the TOFOR type of spectrometers. Such a geometry would not be suitable for use together with DWF data acquisition system because of the great number of scintillators needed (about 5 times as many) and the shape. The MS events of the tf> side of the direct event distribution can involve extra n + H or n + C scattering in either S1 or S2. MS events form streaks of enhanced densities that can be seen in the ES1 -tf plane in Fig. 5, going diagonally and horizontally, respectively. The diagonal MS streak, involving n + H or n + C scattering, has a lower tf limit (tf min ), which varies as (1/ES1 )1/2 starting in the kinematic region of the direct events. The tf width of this streak is attributable to the variation θ allowed by the heights of S2a+b , S2a , and S2b (cf. Fig. 8). The tf> region, within the limits of the discrimination functions, ES1< (tf ) and ES1> (tf ), in Fig. 8, is populated by MS
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events due to n + C scatterings at a small energy loss to the scattered neutron but potentially large angular changes (θ MS ). For instance, the average θ MS is about 60◦ to send a neutron into S2 whose energy is decreased by a factor of two and having an average flight time of tf ≈ 130 ns, with a variation from +10 for θ max to −10% for θ min (and correspondingly narrower for the split S2). The efficiency of the discrimination will depend on the quality of the ES1 signal as embedded in the pulse height resolution of the light as recorded by the PM tubes. To this end, it has been realized that the S1 of TOFOR with the three light guides attached to each scintillator gave rather poor light transmission. This could potentially be improved using only two short light guides with possible added boost by increasing the thickness, together with the scintillator element, from 5 to 6 mm. The accompanying increase in multiple scattering would, in the case of TOFOR II, be balanced by the enhanced discrimination efficiency connected with improved pulse height resolution. It would also mean that one can set tighter discrimination gates, especially, allowing the gap between ES1
