An all-digital associated particle imaging system for the 3D determination of isotopic distributions
Mauricio Ayllon Unzueta, Bernhard Ludewigt, Brian Mak, Tanay Tak, Arun Persaud
AAchieving high resolution with an all-digital associated particle imagingsystem for the 3D determination of isotopic distributions
Mauricio Ayllon Unzueta, a) Bernhard Ludewigt, Tanay Tak, and Arun Persaud b) Acceleration Technology & Applied PhysicsLawrence Berkeley National Laboratory1 Cyclotron Road, CA 94720, USA (Dated: 16 September 2020)
Associated particle imaging (API) is a non-destructive nuclear technique for the 3D determination of isotopic distri-butions. By detecting the alpha particle associated with the emitted neutron in the deuterium-tritium fusion reactionwith a position and time resolving detector, the direction of the 14 . C, O, Si, Al, and Fe. We present a descriptionof the system with simulations and experimental results indicating a lateral (X-Y) resolution of 2 to 4 cm and a depth(Z) resolution of 6 . I. INTRODUCTION
Non-destructive carbon-in-soil measurement methods areimportant for understanding and quantifying soil-based car-bon sequestration techniques on a large scale since soil is thelargest storage pool of terrestrial carbon . Monitoring car-bon in soil also supports improvements in soil health and cropyield . The standard procedure to measure carbon concen-tration in soils today consists of taking core (point) samplesand analyzing them in a chemistry lab using loss on ignition(LOI) techniques . This destructive procedure takes from afew days to weeks before results are obtained, and results froma few sampling points are then often used to extrapolate thecarbon distribution for an entire field or larger areas. As partof an ARPA-e funded effort to develop better sensors for soiland imaging of roots, we are developing an API instrumentfor quantifying carbon distributions in soil. This instrument,when fully developed into a commercial system, is expectedto be able to non-destructively analyze soil volumes (50 × ×
30 cm ) in-situ within minutes depending on carbon con-centration, allowing better estimates on a field scale. Addi-tionally, its capabilities allow for centimeter resolution in allthree dimensions in order to account for carbon heterogeneity.Non-API neutron based methods for soil characterization havebeen reported before , including instruments that are usingtime-tagged neutron signals and pulsed neutron generators .The API system consists of a sealed-type neutron generator,an alpha particle detector, and two gamma-ray detectors, i.e. alanthanum bromide (LaBr ) and a sodium iodide (NaI) scintil-lation detectors. These components are arranged as schemati-cally shown in Figure 1. a) Electronic mail: [email protected]; Also at Nuclear Engineering De-partment, University of California, Berkeley.; Now at Solar system explo-ration division, NASA Goddard Space Flight Center, Greenbelt, Maryland. b) http://ibt.lbl.gov; Electronic mail: [email protected] Soil 50 cm60 cm ShieldingLaBr/NaI 𝜸 𝑪(𝒏, 𝒏 ′ 𝜸 ) 𝑪 Alpha detector ECR plasma ion source (D+T) Solid state drive αn Waveguide ~ 90 cmAPI cone
FIG. 1. Schematic illustration of the API technique. 14 . C) are generated in the sample (soil) and detectedwith a LaBr or NaI detector. The neutron generator works by accelerating a charged par-ticle beam consisting of deuterium (D) and tritium (T) ionsonto a titanium target where they accumulate and undergo DTfusion reactions within a small surface area of approximately2 mm in diameter. The nuclear reaction shown in Equation 1results in a two-particle decay, and hence the neutron and thealpha particle are emitted back-to-back in the center-of-massreference frame with fixed energies. D + T → α ( . ) + n ( . ) .
96% (1) a r X i v : . [ phy s i c s . i n s - d e t ] S e p The detection of the alpha particle in a position-sensitivedetector provides information about the direction and time theneutron was emitted. The high-energy neutron can exit thevacuum chamber and excite a nucleus in the assayed sam-ple by inelastic scattering. The de-excitation, which for thenuclei of interest in the soil application occurs on a picosec-ond timescale, is accompanied by the emission of one or moregamma rays with energies characteristic of the isotope. Thesegamma rays can be detected with a fast scintillator and theirtimes and energies recorded. Based on the time difference be-tween the alpha and gamma detection together with the calcu-lated associated neutron direction, the position of the inelasticscattering reaction can be calculated. By measuring many ofthese events, 3D elemental density profiles of the object ofinterest can be reconstructed. This process is exemplified inFigure 1, which shows a particular case where the inelasticscattering in a C nucleus leads to the production of a promptgamma ray.The origins of API can be traced back to the ’50s and ’60swhen the associated particle method (APM) was introducedwith the main objective of reducing the induced gamma back-ground (e.g. Okhuysen et al. and Csikai ) by recordinggamma rays in coincidence with the associated particle in aDD or DT fusion reaction, i.e. He or He, respectively. Inan early proof-of-principle paper Beyerle et al. obtained2D projections for different materials (water and table salt),hence showing some of the most important capabilities of thistechnique. Since then, API has found many uses in differ-ent areas of research and industry including detection of illicitdrugs , explosives , special nuclear material (SNM) , dia-mond search , and space exploration , among many otherapplications. Fast scintillators, fast electronics, and high-resolution position-sensitive photomultiplier tubes have re-cently enabled both sub-nanosecond time resolution and sub-millimeter position resolution. This combination allows forthe possibility of imaging objects with centimeter scale reso-lution. II. SYSTEM OVERVIEW
The high-resolution system that we developed is intendedfor proof-of-principle demonstration. A commercial systemfor carbon in soil measurements would require more gammadetectors, the operation of the neutron generator at signifi-cantly higher output rates, and an alpha detector readout ca-pable of handling rates on the order of 10 α / s . The ar-rangement of the neutron generator, gamma-ray detectors, andshielding for the measurements reported in this paper is shownin Figure 10a).The neutron generator is a compact, sealed-type APItube (DT108API, Adelphi Technology ) with a microwaveion source driven by a solid-state power supply (SairemGMS200WSM56) which couples to the plasma chamber viaa square waveguide with a three-stub tuner. The titanium tar-get, where neutrons are produced, is located inside the vac-uum chamber (the generator head) centered underneath theYttrium Aluminum Perovskite (YAP) scintillator (manufac- tured by Crytur ) and a 6-inch sapphire window. This ar-rangement allows for the scintillation photons produced bythe alpha particles striking the YAP crystal to be transported tothe outside of the vacuum chamber where a position-sensitivephotomultiplier tube (PSPMT, Hamamatsu H13700-03 ) isused to detect the light signals. The gamma detectors, a LaBr crystal (Saint-Gobain, 3-inch, B390S), and a NaI crystal (Al-pha Spectra, 5-inch, 20I20/5(9823)BN), are positioned out-side the tagged-neutron cone at the same height as the inter-rogated samples. Both detectors are shielded from the directneutron flux by 12 inches of high-density polyethylene placedbetween the generator and the detectors. The detectors them-selves are surrounded by lead bricks on four sides. The sur-face of the detectors facing the interrogated samples are onlycovered with a thin lead shield (2 mm). The surface facingaway from the samples is not shielded and allows for signaland high voltage cable connections. Finally, the data acquisi-tion is performed with a 16-channel fully digital system (XIA,PIXIE-16 Rev. F, 500 MHz ADC with 100 MHz FPGAs ).Seven signals from the detectors are preamplified and fed intothe PIXIE-16 for digitization and processing. Signals fromthe gamma detectors and that of the penultimate dynode ofthe alpha detector photomultiplier tube are time-stamped us-ing a digital Constant Fraction Discrimination (CFD) algo-rithm. Additionally, signal amplitudes are determined for thegamma signals (energies) and the four corner signals of thealpha detector. If an alpha and a gamma signal fall within aset coincidence time window the event times and pulse heightvalues are recorded. III. POSITION-SENSITIVE ALPHA DETECTOR
The alpha detector allows to tag neutrons emitted into acone, known as the API cone, and to determine the directionof the neutron and its time of flight. The design goal of a fi-nal position resolution of 5 cm at a distance of 60 cm from thesource led to the following requirements for the alpha detector.The alpha-gamma time resolution needs to be better than 1 ns,because a 14 . − .For the lateral dimensions, a 1 mm position resolution on thealpha detector is required due to geometry considerations re-garding the size of the neutron producing beam spot and adistance of at least 60 cm between the neutron production siteand the target nucleus. Since the YAP scintillator is located6 cm from the neutron production site, it also experiences ahigh alpha rate. For our geometry, the expected alpha rate is10 α / s for a generator output of 2 × n / s . The designdetails of the alpha detector and its performance characteriza-tion are presented in Unzueta et al. and only summarizedhere. The scintillator signal needs to have a short rise time foroptimal time resolution, a fast decay time for reduced pileupat the expected high count rate, and a sufficient light outputfor accurate position determination. The cerium-doped YAPinorganic scintillator was chosen due to the following reasons:it can withstand vacuum bakeout temperatures, it has a fast re-sponse (rise time of approximately 3 ns), a short decay time of27 ns, a high light yield of approximately 5000 photons / MeVfor alpha particles (17 000 to 20 000 photons / MeV for gammarays), and sufficient energy resolution (20% for 5 MeV al-phas). It is also non-hygroscopic and hence easy to handle.The YAP scintillator is coupled to the PSPMT via a sapphirewindow vacuum interface. The finite-element software pack-age COMSOL Multyphysics was used to optimize the ge-ometry, understand the light spread onto the photocathode,estimate the total light transmission, and simulate the positionreconstruction based on a 4-corner readout scheme. The mainparameters chosen for the simulations are shown in Table I.The surface of the YAP facing the incoming flux of alphaparticles is coated with a reflective aluminum layer with athickness of 400 nm to increase the number of photons thatreach the photocathode per alpha interaction. This allows forimproved photon statistics, and hence an improved positionresolution. Figure 2 shows the COMSOL simulation resultsof one alpha interaction and its resulting light spread onto thephotocathode with and without the reflective surface. FIG. 2. COMSOL simulation of scintillation photon transportthrough one-sixteenth of the alpha detector system showing a) thetransmitted light with no mirror surface, and b) the transmitted lightwith the mirror surface. The transmission increases by a factor of 2to approximately 6.6% with no significant change in the diameter ofthe light projection onto the photocathode. The light spread directlyinfluences the position reconstruction and readout. The white linesindicate the detector pixels.
The spread of the scintillation light over several pixelsmakes it possible to determine the center-of-gravity positionwith a sub-pixel resolution based on the following reconstruc-tion algorithm x = A + BA + B + C + Dy = A + CA + B + C + D , (2)where A, B, C, and D are the energy values read at each cor-ner of the 4-corner readout scheme. However simple, this al-gorithm also introduces positional errors particularly near theedges of the detector, which collect only a fraction of thesephotons. This effect was studied using the simulation soft-ware LTspice and the results are shown in Figure 3. Thisedge effect can be corrected with more advanced reconstruc-tion techniques aided by simulations, and the details will befurther discussed in a future paper.In order to experimentally quantify the position resolu-tion and uniformity of the alpha detector, aluminum masks y [ a . u . ] FIG. 3. LTspice output showing the resulting calculated position(blue dots) from a distributed DC current source. The source distri-bution derived from the COMSOL light collection simulations wasapplied every 0 . with different hole patterns were placed in between an Am(3 . Am decays primarily by theemission of an alpha particle with an average energy of ap-proximately 5 . . Am source. This system was placed inside a vacuumchamber evacuated to a few mTorr, and coincident data wastaken for 200 s. The 6 inch flange with the sapphire window,YAP holder, and one of the masks are shown in Figure 5.The position reconstruction was performed using Equa-tion 2. The resulting image corresponding to the 256-holemask is shown in Figure 6. Note the high spatial uniformityexcept near the edges where light spread is not uniform aspredicted in the LTspice simulations above. Additionally, weobserve a small non-linear effect (see curvature at the top andbottom) of each reconstructed image that we believe is due tostray capacitance on the readout board.Additionally, notice how even though a 16 ×
16 mask wasused, only a 14 ×
14 array is observed in Figure 6, as pre-
Name Material Thickness (mm) Refractive Index (at
370 nm ) Photocathode Bialkali – –PMT window UV glass 1.5 1.5354Optical grease PhenylSiO CH .FIG. 4. Different aluminum mask designs used for the alpha detectorperformance tests. The flood-field mask on the left has 256 apertureswith a 3 mm center-to-center separation, the same separation as forthe PSPMT pixels. The mask on the right was designed to determinethe position resolution of the alpha detector.FIG. 5. Setup used to test the response of the YAP crystals, the uni-formity of the reconstruction algorithm, and the achievable resolu-tion. The sapphire window, YAP, and aluminum holder shown arethe same as the ones mounted on the neutron generator. dicted by COMSOL and LTspice simulations shown in Fig-ure 3, which shows this non-linear edge effect.Figure 7 shows the experimental results of using the maskon the right of Figure 4 with a hole pattern with decreasing FIG. 6. Position reconstruction of the mask configuration shown onthe left of Figure 4 using Equation 2. center-to-center distance specially designed to measure theposition resolution of the system. Notice that even aperturesthat are 0 . et al. . This position resolution is five times betterthan the requirement of 1 mm stated in the introduction. IV. PIXIE-16 DATA ACQUISITION SYSTEM
The PIXIE-16 is an all-digital waveform analyzer that op-erates at 500 MHz. Some of its capabilities regarding energyand time determination in the context of our application aredescribed below.
FIG. 7. Position resolution test of our detector system showing a se-ries of holes separated by varying distances. Note that the minimumseparation between the holes (edge-to-edge) is 0 . A. Energy determination
The PIXIE-16 implements a filter design that allows forsome degree of pileup correction in the sense that it can cor-rectly measure the energy of a pulse that is on top of anotherone having a single decay constant. The details of the algo-rithm can be found in Tan et al. . However, pileup correc-tion was not used in the measurements reported here. We planto implement the pileup correction for future experiments in-volving higher neutron rates. For the set o measurements pre-sented in this article, the PIXIE-16 was set to integrate the fullenergy peak with the proper baseline subtraction. This ap-proach works well for low event rates (alphas and gammas).For reference, using a standard Na radioactive source weobtained an energy resolution of 3% at 511 keV for the LaBr detector, which agrees well with the data provided by the man-ufacturer. B. Time determination
The arrival times of the alpha particle and the gamma ray,which are used to calculate the neutron time of flight, needto be measured with excellent resolution for calculating thedepth of interaction. As noted previously, achieving the goalof a depth resolution of 5 cm requires a time resolution of ap-proximately 1 ns. The time resolution depends on the intrinsicproperties of the detector and the signal processing electron-ics. For a more in-depth discussion regarding state-of-the-arttiming techniques and differences between analog and digi-tal systems, refer to publications such as Jokhovets et al. .A digital constant fraction discrimination algorithm (CFD) isimplemented in the PIXIE-16 for determining the pulse arrivaltime. The advantage of the CFD method is a much smallersignal time walk obtained by determining the arrival time ata constant fraction of the pulse amplitude. The CFD algo-rithm implemented in this version of the PIXIE-16 is shown in Equation 3. CFD ( k ) = w (cid:18) k + L ∑ i = k a ( i ) − k − B + L ∑ i = k − B a ( i ) (cid:19) − (cid:18) k − D + L ∑ i = k − D a ( i ) − k − D − B + L ∑ i = k − D − B a ( i ) (cid:19) , (3)This equation has four free parameters, w , B , D , and L . Theconstant fraction w varies between 0 and 1, and the other threeare integer values indicating a number of points in the digi-tized trace. Finally, the ADC trace data is denoted by a ( i ) .Due to the implementation details of the CFD algorithm inthe FPGA, the parameters cannot be arbitrarily chosen. Forexample, the integration times are constrained to multiples offive because the clock frequency of the FPGAs (100 MHz) isfive times lower than the digitizer frequency (500 MHz). Theparameters were optimized offline for the three different de-tectors of the API system. We analyzed coincident signaltraces collected with a Na source that emits two 511 keVgamma rays simultaneously. The results indicated that theparameter that makes the most significant change is w , themultiplicative factor by which the trace amplitude is reducedto a certain fraction. The time resolution of the system im-proves as w decreases. However, at the same time the peak ofthe CFD trace that is used for triggering becomes smaller inamplitude, and hence the CFD threshold has to be set closerto the noise level, which sets a lower limit on w . The opti-mal value of w that could be implemented in custom firmwarewas 0.3125. As can be seen in Figure 8, a time resolutionof 1 .
73 ns was achieved, which is an improvement of 300 pscompared to the standard firmware with a w value of 1. The F r e q u e n c y [ a . u ] Default PIXIE-16, FWHM = 2.05 nsNew Firmware, FWHM = 1.73 ns
FIG. 8. CFD calculation for default PIXIE-16 parameters comparedto the case where only w is changed from 1 to 0.3125 for the YAP-LaBr combination. Note the time resolution improvement of ap-proximately 300 ps. Note: the time resolution of the actual API sys-tem is significantly better due to the higher signal amplitudes gener-ated by the alpha particles and higher energy gamma rays. actual system has an even better time resolution with an upperlimit of 1 .
25 ns (equivalent time calculated from the Z reso-lution discussed below also includes effects of scattering andreconstruction errors therefore the quoted time resolution isan upper limit) because INS gamma rays from carbon havehigher energy compared to Na and therefore better photonstatistics resulting in less noisy rise times.The appropriate time windows to be implemented in thedata acquisition (DAQ) logic depend on the arrival times ofthe coincident alpha particle and gamma rays. The main com-ponents are the flight times of the neutron and alpha particles(geometry dependent), and the electron transit times of the re-spective photomultiplier tubes. Experimental data indicate atotal time delay between the alpha (YAP) and gamma (LaBr )signals of approximately 80 ns. Events are being recordedin coincidence logic when two out of three detectors triggerwithin a time window of 30 ns. Therefore, in addition toalpha-gamma events, we also record gamma-gamma events.However, the latter do not appear at a significant rate due tothe several order of magnitude lower gamma count rates andare then discarded during the offline data analysis. The result-ing pre-processed data is recorded and used for further analy-sis. V. API SYSTEM PERFORMANCE
The overall performance of API systems can be quantifiedin terms of its position resolution in 3D and its ability to ob-tain a prompt gamma-ray spectrum from a specific volume ina given time. The measurement time will vary depending onthe nature and size of the interrogated sample, the number ofgamma detectors employed for the measurement, the capabil-ity of the alpha detector, and the neutron rate. The measure-ment time will ultimately be limited by a maximum neutronrate of about 2 × n / s where accidental coincidences be-tween gamma and alphas will start dominating the signal .In the following discussion, we focus on the resolution of theAPI system and the gamma response to specific samples rele-vant to soil composition. A. API reconstruction algorithm
The pre-processed data from the DAQ are used to recon-struct the 3D location of a neutron-induced inelastic scatter-ing event followed by the emission of a prompt gamma ray.The ( x , y ) position on the YAP crystal of the alpha detectoris calculated from the 4-corner energies as explained in Sec-tion III. Figure 9 illustrates how the scattering location ( x , y , z )in the sample is then calculated based on simple vector alge-bra. If we assume a neutron point source located at a knowndistance from the YAP crystal, we can calculate the directionof the velocity vector of the alpha particle, (cid:126) a . Assuming thatthe neutron travels in the opposite direction of that alpha par-ticle and together with the measured time between the alphaand gamma arrival, we can calculate the position of the scat-tering location by solving a quadratic equation that takes thetime of flight of the gamma and neutron into account. Themathematical details of the algorithm can be found in Ref. 28.The main assumptions in the reconstruction are that theneutrons are monoenergetic (14 . ◦ from each other in the lab system, and the positionof the gamma detector is a point in space. Additionally, the al- (0,0, 𝑧 )(0,0,0) (𝑥 , 𝑦 , 0)(𝑥, 𝑦, 𝑧)(𝑥 , 𝑦 , 𝑧 ) 𝒏 𝒖𝒈 Gamma detector Neutron sourceSca ering loca on-
L/2 + L/2 𝒅 +z θ 𝒂 YAP
FIG. 9. Schematic representation (not to scale) of the API recon-struction technique based on vector algebra. pha, gamma, and neutron are taken to have fixed velocities forsubsequent calculations. All of these assumptions are approx-imations of the actual system and each of them contributes tothe overall error in the position reconstruction. In our designthe main contribution to the angular uncertainty of the emittedneutrons is due to the size of the ion beam spot on the neutrongenerating target of approximately 2 mm and the position res-olution of the alpha detector of < . ◦ for an X-Y resolution at 60 cm distance of about2 cm. The depth resolution is dominated by the timing uncer-tainty given that a 14 . B. Position resolution
In order to test the system resolution in three dimen-sions, we performed a series of experiments using graphitebricks (99% C) and detecting the single INS gamma ray of4 .
439 MeV. The experimental results presented below wereobtained with the LaBr gamma-ray detector, which has bettertime and energy resolution than the NaI detector. The graphitesamples were arranged in two different configurations: 1) twothin (1 cm) slabs stacked in Z with varying distances betweenthem in order to measure the depth resolution, as shown inFigure 10b) and 2) two thick (6 cm) graphite bricks placednext to each other (X-Y plane) and their distance varied alongthe X dimension, as shown in Figure 10c). The neutron gen-erator was operated at 50 kV producing a neutron output of ≈ × neutrons / s.Figure 11 shows the experimental results for three different Neutron generator12" Polyethylene 12" PolyethyleneLead shielded3" LaBr detector Lead shielded5" NaIAPI coneTarget area a) b) c)
FIG. 10. Experimental setup used to characterize the system: a) schematic of the setup showing the position of the neutron source, the shieldingand the detectors b) depth resolution measurement using thin (1 cm) graphite slabs, and c) X-Y resolution using thick (6 cm) graphite bricks.
50 60 70 80 90 100Z [cm]010203040506070 C o un t s [ a . u . ]
16 cm
50 60 70 80 90 100Z [cm]010203040506070
50 60 70 80 90 100Z [cm]010203040506070 Z [ c m ] FIG. 11. LaBr experimental results for the depth resolution measurements with two thin graphite slabs with varying distances among them.The bottom plots show X-Z intensity maps of the 3D locations of the reconstructed events and the top plots show the integrated counts vs. Zwith Gaussian curves used to fit the two peaks. Note that at 16 cm separation, the two slabs are clearly separated. The intensity maps also showthe top slab being exposed to a higher neutron flux as expected. cases where the top graphite slab was brought closer to thebottom one starting at 16 cm separation between them. Theirradiation time for each case scenario was one hour. The datawas processed by selecting events of 4 .
439 MeV gamma en-ergy together with its single escape peak and by selecting onlythe graphite area in the X-Y plane. The intrinsic depth res-olution of the system is shown in Figure 11 where the two slabs are resolved down to a distance of about 6 cm. The mea-sured Z-resolution, defined by the full width half maximum(FWHM) of the Gaussian fit, for the LaBr -YAP combinationis 6 . ± .
20 10 0 10 20X [cm]01020304050 C o un t s [ a . u . ]
20 10 0 10 20X [cm]01020304050
20 10 0 10 20X [cm]01020304050
20 10 0 10 20X [cm]01020304050
20 10 0 10 20X [cm]1050510152025 Y [ c m ]
20 10 0 10 20X [cm]1050510152025 20 10 0 10 20X [cm]1050510152025 20 10 0 10 20X [cm]1050510152025
FIG. 12. LaBr experimental results for the system X-Y resolution measured with graphite bricks. The bottom plots show X-Y intensity mapsof the 3D locations of the reconstructed events and the top plots show the integrated counts vs. X with the sum of 200 Gaussian curves used tofit the two peaks. The blocks were then brought together in one-centimetersteps. The irradiation time for each case scenario was 3000 s.1D-Histograms of the measured data were globally fitted withthe sum of 200 Gaussians equally spaced across a certainwidth. However, outwards scattering of neutrons near theedge of a graphite brick adds an additional fall off for theedges in the histogram and therefore the measured FWHMcan only be used as an upper limit for the resolution of theinstrument. Figure 12 shows the results of a representative setof these measurements where a FWHM of 4 . ± . C. Single-element gamma response
As mentioned previously, one of the most important char-acteristics of the API technique is the ability to obtain prompt gamma spectra from a specific volume, so that backgroundgammas from surrounding materials or delayed emission(such as from neutron capture) are greatly reduced. Therefore,we measured single-element spectra of the main elements insoil in order to generate energy spectrum templates for futuresoil analysis and to validate MCNP6 simulations. Figure 13
Iron sample (SS1018) Time histogram
Iron peak
XY counts filtered in me Iron energy spectrum
Time [ns] Energy [MeV]
FIG. 13. Example of the analysis procedure for obtaining elementalgamma spectra for specific elements. The photograph of the sampleis a top view from the perspective of the neutron generator. TheLaBr detector is located to the left of it. shows an iron sample (SS1018) of 3 .
16 kg that was irradiatedfor 100 min using a neutron generator voltage of 50 kV. Thesample was placed approximately 60 cm underneath the neu-tron generator. From the measured data X, Y, and Z coordi-nates are calculated and the events are restricted to the volumeof the sample under test. An energy histogram of all the eventsinside this volume is then generated. The inelastic gammaspectrum of natural iron as measured is shown on the right ofFigure 13.The same procedure was used to obtain element-specificgamma spectra for various elements identified as the mostabundant in forest and agricultural soils: carbon, aluminum,oxygen, iron, and silicon.The measured spectra were generally linear up to the car-bon peak but showed some non-linearity at higher gamma-rayenergies. Therefore, we used a linear + quadratic calibrationfunction. The measured elemental energy spectra served tobenchmark our MCNP6 simulations. Simulations are gen-erally needed in order to design the instrument, plan futureexperiments, and understand the sensitivity of the system todifferent elemental concentrations. They can be used to opti-mize specific design parameters and can support the analysisof experimental data. We simulated the experiment in twosteps: 1) Neutron-induced gamma-ray production in the sam-ple and 2) gamma-ray transport to the detector with its spe-cific response function. Figure 14 shows the measured spectra C MCNPExperiment10 Al C t s [ a . u ] Fe O Si FIG. 14. Comparison between measured gamma-ray spectra andMCNP6 simulations for elements relevant to soil composition. Notethe overall agreement. However, there are significant discrepanciesfor Al, in particular. The spectra were normalized by the highestpeak. with their corresponding simulation. While there is generallygood agreement, there are some significant discrepancies inrelative intensities such as for the 1 .
72 MeV gamma-ray linefrom Al(n,n’ γ ) originating from the transition 2 .
73 MeV → .
01 MeV. The ENDF /B-VI library was used because of itsbetter agreement with experiments compared to most currentreleases of ENDF . The reason seems to be the attempt to transition from natural compounds to individual isotopes inlater versions, which created gaps and overall poorer agree-ment with experimental data . The results presented in Fig-ure 14 show the capability of the system to analyze sampleswithin a small volume and obtain their gamma signature. Itis possible to create a library of response functions for spe-cific elements, and by matching samples with a more complexcomposition determine their relative abundance (basic com-ponent analysis). This approach is sometimes used in the oilexploration industry . However, for large soil samples, sim-ple template matching will not be enough since the energydistribution of neutrons at depth will not be monoenergeticanymore due to scattering in the top layers of the soil, andtherefore the elemental response will be different from that ofthe measured spectra shown in Figure 14. VI. RESULTS AND CONCLUSIONS
A prototype of an all-digital high-resolution associated par-ticle imaging system for the determination of isotopic 3D dis-tributions in soils has been built. We found that our approachof coupling a monolithic YAP crystal to a sapphire vacuumwindow gave superior resolution and higher light yields thanpreviously developed approaches using fiber-optic faceplates,such as in Cates, Hayward, and Zhang . Experimental testsshowed that the position of the alpha particle can be mea-sured with a resolution of 0 . . ± . could lead to even betterdepth resolution.We obtained gamma-ray spectra from different elementalmaterials including C, O, Si, Al, and Fe and usedthese data to benchmark Monte Carlo simulations. We foundgenerally good agreement confirming that the radiation trans-port code MCNP6 can be used to optimize the system andsupport the data analysis.Currently, the maximum neutron rate the system can op-erate at is limited by pileup on the alpha detector due tothe long RC delays introduced by the four-corner resistivenetwork used to read out the position of the alpha particle.Data presented in this paper was taken at a neutron rate of5 × neutrons / s. However, the system also works withminimal position degradation at rates up to 1 × neutrons / s(not shown). Utilizing the built-in pileup correction of thePIXIE-16 will increase the rate capability further. However,in order to achieve the full rate capability of an API system of2 × neutrons / s, faster readout designs, such as reading outrows and columns instead of just the four corners, are under0development.In conclusion, the results presented indicate that this APIsystem will meet the design goals for measuring the carbondistribution in soil once higher rate capabilities are imple-mented. We also demonstrated that the system can be usedto measure energy spectra for 5 × × voxels overa 50 × ×
30 cm sample volume. Measured responsesfrom single elements agree with MCNP6 simulations. Workin progress includes switching to an improved setup allow-ing operation at higher neutron rates. Additionally, we need tocharacterize neutron scattering effects and attenuation in soil.Finally, we also need to implement models to reconstruct soilelemental densities. AUTHOR’S CONTRIBUTION
All authors contributed to writing and editing the paperand to the experimental work. Mauricio Ayllon Unzueta didmost of the measurements discussed in this paper and ranall MCNP6 simulations. Tanay Tak worked mostly on theSPICE simulations and the X-Y reconstruction in the alphadetector. Mauricio Ayllon Unzueta, Bernhard Ludewigt, andArun Persaud worked on the instrument design, experimentalsetup, data acquisition system, and data analysis. Arun Per-saud worked on the hardware control and is also the principalinvestigator of the project.
DATA AVAILABILITY
The data, analysis scripts, and simulation scripts areopenly available on Zenodo at https://doi.org/10.5281/zenodo.4008740 , reference number 34.
ACKNOWLEDGMENTS
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