Fissile mass estimation by pulsed neutron source interrogation

I. Israelashvili a,n, C. Dubi a, H. Ettedgui a, A. Ocherashvili a, B. Pedersen b, A. Beck a,E. Roesgen b, J.M. Crochmore b, T. Ridnik a, I. Yaar a

a Nuclear Research Center of the Negev, P.O.B 9001, Beer Sheva 84190, Israelb Nuclear Security Unit, Institute for Transuranium Elements, Joint Research Centre, Via E. Fermi, 2749, 21027 Ispra, Italy

a r t i c l e i n f o

Article history:Received 3 August 2014Received in revised form22 February 2015Accepted 23 February 2015Available online 4 March 2015

Keywords:Active interrogationFissile mass estimationSVM

a b s t r a c t

Passive methods for detecting correlated neutrons from spontaneous fissions (e.g. multiplicity and SVM)are widely used for fissile mass estimations. These methods can be used for fissile materials that emit asignificant amount of fission neutrons (like plutonium). Active interrogation, in which fissions areinduced in the tested material by an external continuous source or by a pulsed neutron source, has thepotential advantages of fast measurement, alongside independence of the spontaneous fissions of thetested fissile material, thus enabling uranium measurement.

Until recently, using the multiplicity method, for uranium mass estimation, was possible only foractive interrogation made with continues neutron source. Pulsed active neutron interrogation measure-ments were analyzed with techniques, e.g. differential die away analysis (DDA), which ignore orimplicitly include the multiplicity effect (self-induced fission chains).

Recently, both, the multiplicity and the SVM techniques, were theoretically extended for analyzingactive fissile mass measurements, made by a pulsed neutron source. In this study the SVM technique forpulsed neutron source is experimentally examined, for the first time. The measurements were conductedat the PUNITA facility of the Joint Research Centre in Ispra, Italy. First promising results, of massestimation by the SVM technique using a pulsed neutron source, are presented.

& 2015 Elsevier B.V. All rights reserved.

1. Introduction

Neutron counting is one of the most widely used and usefultechniques for non-destructive testing (NDT) and mass assay offissile materials. Neutron counting techniques for fissile massassay can be categorized into (1) passive methods, in which thespontaneous fission neutrons are measured, and (2) active meth-ods, in which fissions are induced in the sample and the emittedneutrons are measured.

In passive methods, fast neutrons from spontaneous fissionsare measured. Since the interaction cross sections of fast neutronsare relatively low for most materials these neutrons are notinteracting within the sample and the measurement is not verysensitive on the sample's size and shape. The effect of inducedfissions in passive measurements (i.e. self multiplication effect) iscorrected by methods, such as multiplicity [1] and SVM [2]. Thesemethods have a “closed” solution for passive fissile mass estima-tions, but they are feasible only for materials that emit a significantamount of fission neutrons per gram. Unlike the multiplicitymethod, the SVM does not count the number of single, double

and triple coincidences in the detection signal, but rather itmeasures the Skewness, Variance and Mean (SVM). The threequantities are, respectively, the third, second and first centralmoments of the signal time dependence.

Active interrogation techniques, by external continuous orpulsed neutron source, has the potential advantages of both, fastmeasurement as well as independency of the spontaneous fissionsrate of the tested material (enabling uranium measurement).However, the penetration of thermal-neutrons into the sample isdependent on the sample's geometry, density and isotopic com-position. Hence, additional information about source neutronspenetration into the sample is required. This effect is called “selfshielding effect” and it has been discussed in detail elsewhere[3,4,5] along with various methods that may be used to calculatethe effect.

In the past, the multiplicity method was extended and exam-ined for active mass estimations using continuous neutronsources [6,7,8]. Active interrogation with a pulsed neutron source,e.g. differential die away analysis (DDA) or coincidence DDA, hasthe capabilities of detecting and estimating mass of low levelspecial nuclear materials (SNM) in cargo, crates and barrels [9–14].However, this method lacks the ability of correction for self-multiplication effect, for unknown sample, and therefore cannotestimate precisely the fissile material mass of multiplying sample.

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http://dx.doi.org/10.1016/j.nima.2015.02.0480168-9002/& 2015 Elsevier B.V. All rights reserved.

n Corresponding author. Tel.: þ972 50 6239075.E-mail address: israelashvili@gmail.com (I. Israelashvili).

Nuclear Instruments and Methods in Physics Research A 785 (2015) 14–20

In the DDA method, a 14 MeV (d, T) neutron generator producesrepetitive pulses of neutrons that are directed into an inspectedcargo. As each pulse passes through the cargo, the neutrons arethermalized and absorbed. The thermal neutron population decayswith a time constant dependent on the inspected medium. If SNMis present in the cargo, the thermalized neutrons from the sourceinduce fissions that produce a new source of fast neutrons, whichdecays within a time that is very similar to that of the thermalneutron die away of the surrounding cargo.

Recently, both, the multiplicity and the SVM techniques weretheoretically extended for the analysis of active fissile massinterrogation made by a pulsed neutron source [15,16,17], takinginto account the self multiplication effect. In this type of activepulsed neutron interrogation, the fast DT neutrons slow-down in amoderator medium, surrounding a cavity where the SNM is placed(see Fig. 1). The built-up thermal neutron flux induces fissions inthe sample cavity and the resultant fission fast-neutrons aremeasured. In this type of interrogation, one may expect five typesof neutron sources (see [15]):

1. Fissions induced by the thermal flux neutrons: This “fissionsource” is expected to be the main neutron source. In case ofa small bare SNM sample inside a PUNITA type assembly, theintensity of this source should be directly proportional to themass of the detected sample and to the thermal flux at thatlocation.

2. Leakage through the thermal neutron shields: Some of theepithermal neutrons, generated by the DT tube and sloweddown in the moderator, will be detected, although the detec-tors are protected by a layer of thermal absorber and thedetection window is open only after the neutrons from thegenerator are mostly thermalized.

3. Spontaneous fissions: Neutrons emitted by spontaneous fissionsin the sample. This neutron source may be neglected whenmeasuring highly enriched uranium (HEU) samples.

4. Random neutron source: “Poissonian Source”, mainly due to (α,n) reactions and cosmic background. In the PUNITA activemeasurement facility, where our measurements were per-formed, the Poissonian source was substantially smaller thanthe main fission source, and thus was neglected.

5. Self-induced fission chains: Neutrons emitted in fissions causednot by the thermal neutron flux, but from neutrons generatedby the fissions induced in the sample by the thermal flux. Wewill refer to this source as the “fission chain” source.

The spontaneous fissions source and the leakage from thethermal flux can be measured separately, before the active inter-rogation. Since we assume that the first source—and the first

source alone—is proportional to the mass of the tested sample, wemust isolate the main fission source from the remaining sources.The model assumptions (1. point source diffusion theory model, 2.single energy group, 3. exponentially decay of thermal flux, 4.known proportion between number of induced fissions in thesample and its mass), in both the multiplicity and the SVMextended models, are the same. However, the effect of thevariations in the thermal flux, due to variations of the DT neutrongenerator's yield, was neglected in the multiplicity method but notneglected in the SVM method.

In this study, the SVM technique for a pulsed neutron source isexamined, for the first time. The main principle in the SVMmethod is to measure the first three central moments (Mean,Variance and Skewness) of the number of detections in eachgenerator pulse and compare it to a set of three analyticalequations, listed below (Eqs. (1)—(3), see [17]). Note that forconvenience we use here notations which are a bit different fromthe notations used in [17]. Also note that in this work, as a firststage, we use the equations assuming no variation occurs in theneutron pulses intensity. Solving these equations for the threesources (fission source, Poisson source and fission chains) asunknowns will result the fission source.

In the present measurements, all of the 235U masses used werefairly small, as listed in Table 1. Hence, the effect of self-multiplication (fission chains) may be neglected (for example,the multiplication factor for sample 4 (which is the largest) wasbounded by simulation to 0.048). In response, only two neutronsources (fission source and Poisson source) are presented, and onlythe first two equations of the SVM method, for the mean andvariance, are sufficient

Mean¼ ATPd D1U� 1�Uð Þð ÞId;1 ð1Þ

Variance¼ ATP2dUD2Id;2þMean ð2Þ

Skewness¼ ATP3dUD3Id;3þ3UVariance�2UMean ð3Þ

where Id,1, Id,2 and Id,3 are system constants, defined as:

Id;1 ¼e� λþλdð ÞT0 λdeλdT0 eλT �1

� ��λeλT0 eλdT �1� �� �

λd λd�λ� �

Id;2 ¼eλT�2 λþλdð ÞT0 2λd�λ

� �eλTþ2λdT0 eλT �1

� �2þλe2λT0 2λde2λd eλT �1� �þλeλT e2λdT �1

� �� �h i2λd λd�λ

� �2λd�λ� �

Id;3 ¼e�2λT�3λT0 �3λdT0

3λd 3λd�λ� �ð2λ2�5λλdþ3λ2dÞ

� 9λ3de2λTþ3λdT0 eλT �1

� �3þ2λ3e2λTþ3λT0 1�e3λdT

� ��

þ9λλ2d eλT �1� �2

e3λdTþ3λT0 �e2λTþ3λdT0 þe3λdT0 þ3λT� �

Fig. 1. Cross-section of PUNITA showing the permanently mounted neutron detectors and the neutron generator (a) and a schematic layout of the pulsing regime of theneutron generator (b).

I. Israelashvili et al. / Nuclear Instruments and Methods in Physics Research A 785 (2015) 14–20 15

þλ2λd eλT �1� �

ð9eλTþ3λdTþλT0 �3e3λd þ3λT0 þ2e2λTþ3λdT0

þ2e4λTþ3λdT0 �4e3λTþ3λdT0 Þo

AT is the total neutron source (first unknown), U is the ratiobetween the amplitudes of the fission source and the total source(second unknown).The fissile mass is equal to the multiplication ofAT �U. Dl¼2.414, D2¼4.638 and D3¼6.816 [18] are the Divenfactors of 235U. To is the time difference between two consecutivepulses and T is the length of the time interval, in which thedetector counts the number of neutron detections. 1/λ is the dieaway time of the fission counters, 1/λd represents the thermal fluxdie away time at the flux monitor location inside the cavity and Pdis the detection efficiency. All the above known parameters werepre-measured, prior to the samples measurements. Note, asmentioned above, that additional information is needed for theself-shielding effect.

Implementation of the SVM model requires a measurementsystem in which signals of both, generator neutrons and inducedfission neutrons, can be simultaneously recorded, for each pulse.This way, offline calculation of the mean, variance and skewness ofthe number of detections (of sample signals) in different pulses, ispossible. The PUNITA assembly, in which all of the experimentswere conducted, is a system capable of performing this type ofmeasurements.

2. Experimental setup and measurements

2.1. The PUNITA assembly

All measurements were performed in the JRC-Ispra PulsedNeutron Interrogation Test Assembly (PUNITA) [19,20]. This sys-tem is designed for experimental studies in non-destructive assay(NDA) methods for nuclear safeguards and security. The facility iscomposed of a large graphite liner surrounding the central samplecavity. The (D–T) pulsed neutron generator and the sample arelocated inside the sample cavity. Various permanently installedneutron detectors are located in and around the system. Thedimensions of the sample cavity are 500 mm by 500 mm by800 mm. This design yields a relatively high neutron flux insidethe cavity and provides flexibility with respect to detector config-urations. As such PUNITA is a versatile tool for studying detectionmethods although not an instrument intended for field installa-tion. A vertical cross section of PUNITA is shown in Fig. 1(a), withthe permanently installed neutron detectors visible.

The pulsing of the neutron generator (Model A-211 fromThermo Fisher Scientific Inc.), at 100 Hz and pulse width of20 ms, is tailored to the exponential decay of the thermal neutronflux in the sample cavity with a decay time of about 1.0 ms (seeFig. 1(b) and black graph in Fig. 2). The interrogating thermal fluxpeaks at about 280 ms after the 14 MeV neutron burst [21]. Due tothe pulsing of both the Penning ion source and the accelerationvoltage this generator model is able to produce a sharp burst of14 MeV neutrons with absolutely no neutron emission betweenbursts. This fact together with the very low duty cycle of 0.001 ofthe generator allows separation of the neutron interrogation into a“early period” (from zero to 100 ms) and a “thermal period” (from280 ms to 9 ms). In this study we concentrated on the inducedfissions of five CBNM—U3O8 references (Table 1) in the “thermalperiod”.

PUNITA has three neutron data recording sets (see Fig. 1(a)).Source monitors: 32 3He (4 bar) 1 m, 1'' diameter tubes,

embedded in the polyethylene shielding outside the graphite liner.These detectors monitor fast neutrons flux, created by the neutron

generator and escaping from the graphite. The source monitors areused to normalize the generator intensity.

Fission counters: 96 3He (4 bar) 1 m, 1'' diameter tubes, locatedwithin polyethylene and cadmium, behind the graphite moderator.The fission counters are detecting neutrons of energies aboveCadmium cut-off (approximately 0.4 eV). These detectors, are shutdown during each generator pulse (width of 20 μs). Therefore,they measure the fast neutrons emitted by the induced fissions inthe sample during the “epithermal and thermal period” only. Off-line analysis enables the user to select the desired time region orregions between 20 ms and 9000 ms, after each pulse. Notice that afew of the many thermal neutrons produced by the slowing downand thermalization of the (D–T) generator neutrons are detected inthe fission counters, probably because of imperfections in the Cdshield. This is manifested by the shape of the long term decaycurve (1/λd, see Fig. 2) which matches that of the unshieldedthermal neutron decay curve. This long term decay curve repre-sents approximately the “asymptotic” thermal neutron decay inthe PUNITA cavity, while the early faster decay (1/λ), following theend of the pulse, represents the die away time of the thermalneutrons in the polyethylene moderator surrounding the 3He.Thus it is property of the fission counters and is basically unrelatedto the overall system.

Flux monitor: One 3He (0.01 bar) 0.6 m, 1'' diameter tube, locatedwithin the sample cavity and monitors the thermal flux within thesample cavity.

As mentioned above, one of the SVM model requirement is torecord simultaneously both, generator neutrons and inducedfission neutrons. To fulfill this requirement, the three PUNITA datarecording sets were connected to different entries of a six channelsMulti-scaler (MSC) device (MCS6), which was synchronized by thePUNITA's reset pulses. The MSC device recorded time stamp ofeach detection, in a 27 ms time period, with an accuracy of 0.1 ns.

2.2. Pre-measurement parameters estimation

Neutron count distributions vs. time after generator pulse, asmeasured in different detectors, are shown in Fig. 2. The averageneutron's die away time in the system (1/λ) was estimated to be67.570.3 ms, by fitting a single exponential function to the fissioncounter MCS data over a time window of 400–700 ms (shown in Fig. 2,the blue line for the measurement of 4.46% enriched uranium sampleand the green line for background measurement). The thermalneutrons die-away time (1/λd) was estimated to be 743715 ms, byfitting a single exponential function to the flux monitor MCS data intime window of 100–2000 ms (black graph in Fig. 2).

The offline analysis encompassed calculating, for each genera-tor pulse, the sample signal intensity and the generator intensity.Then, calculating the mean, variance and skewness of the numberof detections (of sample signals) in different pulses.

The generator intensity was calculated according to the number ofneutron detections, in the source monitor, in time region between0.68–1.44ms. In this time region, the dead time effect is insignificantand the fast neutrons flux, created by the neutron generator, decayswith a constant decay time (see purple line in Fig. 2). The samplesignal intensity was calculated according to the number of neutrondetections, in the fission neutron counter, in time region between2–5ms. The upper limit of 5 ms was chosen since by this time thethermal flux has decayed significantly (see black line in Fig. 2).Detections above this limit are attributed to delayed neutrons andcosmic neutrons. The lower limit of 2 ms was chosen by measuringthe CBNM000 sample (see Table 1), which contains no fissile mass. Inthis measurement, the mean and variance should have the samevalue. The mean and variance values for different lower limits of thetime window are shown in Fig. 3(a), and the ratio variance to mean is

I. Israelashvili et al. / Nuclear Instruments and Methods in Physics Research A 785 (2015) 14–2016

shown in Fig. 3(b). When setting the lower limit to 2 ms, the ratiovariance to mean, is around 1.

2.3. Samples

The mass and the enrichment of the tested samples are listed inTable 1. As mentioned above, the penetration of thermal-neutronsinto the sample is dependent on the sample's geometry, densityand isotopic composition. Hence, all samples, with one exception,had the same geometry, density and total mass, differing only inthe enrichment level. The set comprises five sealed cans of CBNM—powder U3O8 reference [22] and one identical sample containingno fissile material. The cans are made from ASTM-6061-T6aluminum and contain 200.1 g of oxide. The outer can diameteris 80mm and the can height is 89 mm. The internal diameter of the

can is 70 mm. Fill height, defined by the degree of compressionapplied to the powder by the plunger, for all samples is20.870.5 mm, except for sample CBNM446 for which the heightis 15.870.5 mm. Note that in our measurements, the CBNMsamples are physically much smaller than the cavity, and are ofthe same size. Hence, the coupling of the source to the samples isessentially fixed and dependent on the self-shielding-factor (SSF)of each sample to an isotropic thermal flux. The self-shieldingeffect for these samples, taking into account also for the attenua-tion in the can, was estimated in [23]. The estimated SSF, as well asthe effective 235U mass (¼ 235U mass � SSF), are also listed inthe table.

2.4. Measurements and analysis

In each measurement, one uranium sample was located withinthe cavity and the pulsed neutrons generator was operated. Therecorded MCS6 data was analyzed offline. For example, Fig. 4shows the counts per DT pulse, in the relevant time windows,measured by the source monitors, the flux monitor and the fissioncounters, for sample CBNM446, as function of the neutron pulsenumber. The DT pulse frequency was 100 Hz for a duration of�900 s (�90,000 pulses). The bands of data represent the densepattern of pulses and only appear continuous on this scale. Thevariation is due to pulse-to-pulse differences in DT yield. Inaddition, all intensities are gradually decline during the generatoroperation; hence, one should not neglect the variations in theneutron pulse intensity during the experiment.

The SVM method, as stated before, aims to “separate” betweenthe main fission source and the additional sources, by solving a setof three equations. The procedure for mass estimation, using theSVM method, is the following:

(1) For each generator pulse, the number of neutron detections inthe fission neutron counter is calculated, in time regionbetween 2–5 ms after the pulse (in this time region onlyneutrons from pure thermal induced fissions are collected, asmentioned above).

(2) The mean and variance of the number of detections indifferent pulses is calculated, and the set of Eqs. (1) and (2)is solved for the two unknowns (AT and U). The knownparameters were measured to be To¼8000 ms, T¼7800 ms,1/λd¼743 ms, 1/λ¼67.51 ms and Pd¼0.135 (see section 2.2).

(3) The amplitude of the main fission source, Af, is defined asAf¼U �AT. This parameter should be proportional to the 235Ueffective mass in the detected sample.

(4) One of the samples is used as a “control sample”, in order tocalibrate the ratio between the amplitude of the fission sourceand the mass M.

(5) The 235U effective mass is estimated.

Fig. 3. (a) Mean and variance values for different lower ends of the time window, as calculated from a measurement without any fissile material. The upper end of the timewindow is 5000 ms. (b) Corresponds to Mean/Variance ratio.

Table 1Mass and enrichment of the tested samples [22]. The SSF are estimated from data in[23].

Sample Total U mass[g]

Enrichment[wt%]

235U mass[g]

SSF Effective 235Umass [g]

CBNM000 0 0 0 0.971 0CBNM031 169.089 0.317 0.524 0.947 0.507CBNM071 169.283 0.7119 1.205 0.906 1.092CBNM194 169.528 1.942 3.292 0.829 2.725CBNM295 169.624 2.949 5.002 0.768 3.834CBNM446 169.525 4.462 7.564 0.715 5.401

Fig. 2. Neutron count distributions vs. time after generator pulse, as measured indifferent detectors (summed for �90,000 pulses). (For interpretation of thereferences to color in this figure legend, the reader is referred to the web versionof this article.)

I. Israelashvili et al. / Nuclear Instruments and Methods in Physics Research A 785 (2015) 14–20 17

Alternatively, since in those particular measurements the effectof self-multiplication is neglected, due to the small fissile materialmass, one can use the DDA method to estimate the fissile masses,by following the procedure:

(1) The neutron counts distribution vs. time after generator pulseis measured, in the fission neutron counters (summed for allpulses (�90,000)) (See Fig. 5).

(2) The distribution is normalized to the total generator intensity,measured by the source monitor.

(3) The total count in the range 700–4700 μs is calculated (blackhatching lines in Fig. 5).

(4) The measured background is subtracted from the total count(4 counts per pulse, in our case). The result should be the totalnumber of counts coming from neutrons generated by themain fission source (recall that the continuous source andfission chains contributions are neglected).

(5) One of the samples is used as a “control sample”, i.e. knownmass that we use to calibrate the ratio between the number ofdetections and the mass.

(6) For each sample, the effective mass of fissile material isestimated, using the calibration and the total number ofcounts.

3. Results and discussion

Distributions of the number of neutron detections, measuredby the fission counters in time region between 2–5 ms after eachgenerator pulse, are shown in Fig. 6(a). Mean, variance andskewness of these distributions, as well as the DDA counts inrange of 700–4700 μs divided by the generator intensity, areshown in Fig. 6(b) and listed in Table 2 for every sample. Therightmost column in Table 2 shows the measured DDA decay time,based on a single exponential weighted fit in range of 1300–2600 μs. The statistical uncertainties for the DDA counts are listedin the table. The statistical uncertainties for the central momentsare not listed since the statistical uncertainties of the second andthird moments depend on the fourth and sixth moments, whichare difficult to sample. For estimating the uncertainty in estimat-ing the effective 235U masses by the SVM (in Table 3), we took thefollowing consideration as a first approximation: Since the mainfactor in the mass calculation is the mean (the rest are secondorder corrections), the relative error on the mass is proportional tothe mean relative error: that is, the statistical relative error is

Fig. 4. (a) MCS6 data integrals for source monitors in time window of 680–1440 ms. (b) Flux monitor integral in time window of 100–2500 ms. (c) integrals of fission neutroncounters in time window of 2000–5000 ms. The measured sample was CBNM446 with the highest 235U content. The bands of data represent the dense pattern of pulses andonly appear continuous on this scale.

Fig. 5. Neutron count distributions vs. time after generator pulse, as measured inthe fission neutron counters (summed for �90,000 DT generator pulses).

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ffiffiffiffiffiffiffiffiffiffiffiffiffiffiVariance

n

q� �=Mean, where n is the number of DT pulses. Since there

were �90,000 DT pulses, the statistical relative error is �0.3%.The systematic error is estimated as �3% due to uncertainty ofDiven values ect.

An interesting thing to see how do the Mean, the (variance–mean) and the (Skewness�3 �Varianceþ2 �Mean) respond to 235Ueffective mass (recall Eqs. (1)–(3)). This is shown in Fig. 6(c).

As seen in Fig. 6(a), the distribution for dummy sample(CBNM000) is Poissonian, while the greater the 235U mass is, themore different is the distribution from the Poisson one. For thedummy sample, the mean and variance values are the same whilethe skewness value is high (See Fig. 6(b)). While the 235U mass

Fig. 6. (a) Distributions of the number of neutron detections, measured by the fission counter in time region between 2–5 ms after each generator pulse. The different colorsrepresent the various samples. (b) Mean, variance and skewness, of distributions shown in (a) vs the 235U effective mass. Also presented, DDA counts in the range of 700–4700 μs (divided by the generator intensity). (c) Mean, (variance–mean) and (Skewness�3 �Varianceþ2 �Mean), of distributions shown in (a), vs. the 235U effective mass.

Table 2First, second and third measured central moments, of the number of detections.The two rightmost columns show the DDA counts in range of 700–4700 μs dividedby the generator intensity and the measured DDA decay time, based on a singleexponential weighted fit in range of 1300–2600 μs.

Sample Mean Variance Skewness DDA counts DDA decay time [ms]

CBNM000 0.25 0.25 2.08 0.2270.3% 760.472.3%CBNM031 0.55 0.61 1.56 0.3770.2% 769.971.6%CBNM071 0.77 0.88 1.35 0.5470.2% 769.771.4%CBNM194 1.45 1.72 1.02 1.0370.2% 761.371.0%CBNM295 1.93 2.28 0.92 1.3670.2% 758.870.8%CBNM446 2.43 2.90 0.80 1.7270.1% 759.970.7%

Table 3Estimated 235U masses, by the DDA and SVMmethods. The numbers in brackets arethe percentage deviation from the known mass.

Sample Estimated effective235U mass [g] by DDA

Estimated effective235U mass [g] by SVM

Known effective235U mass [g]

CBNM031 0.5570.7% 0.6973.0% 0.507CBNM071 1.1670.4% 1.2373.0% 1.092CBNM194 2.9370.3% 3.1473.0% 2.725CBNM295 4.1070.3% 4.0673.0% 3.834CBNM446 5.4070.2% 5.4073.0% 5.401

Fig. 7. Estimated 235U masses, by the SVM (red triangles) and the DDA (bluesquares) methods. The fifth sample was taken as the “control sample”. Dashed linerepresents the exact values of the mass. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)

I. Israelashvili et al. / Nuclear Instruments and Methods in Physics Research A 785 (2015) 14–20 19

increases, the difference between the mean and the varianceincreases and the skewness value decreases.

A linear relationships between the 235U effective mass and themean, the (variance–mean) and the (skewness�3 � varianceþ2 �mean), can be seen in Fig. 6(c), as expected from Eqs. (1)–(3).

The measured DDA decay times exhibit no dependence on the235U mass.

Mass estimation of the measured samples are listed in Table 3and shown in Fig. 7, for both, SVM and DDA methods. In bothmethods, sample CBNM446 was taken as the “control sample”.

Two effects may affect the results, self-multiplication and self-shielding. As mentioned before, in our measurements the effect ofself-multiplication is neglected since the 235U masses were fairlysmall (see Table 1) and contained low density powder with highsurface-to-volume ratio. Hence, even though the DDA techniquelacks the ability self-multiplication correction, both methodsresulted in, approximately, the same estimations for all samples.In future measurements, of samples with non-negligible self-multiplication effect, the ability of the SVM method to correctself-multiplication could be demonstrated.

The self-shielding effect influences the penetration of thethermal neutron flux into the sample and hence affects both,SVM and DDA estimations. The SVM and DDA estimations are ingood agreement with the known 235U effective masses, which arecorrected to the self-shielding effect.

These results indicate the practical feasibility of the SVMtechnique, for small mass estimations, using pulsed neutronsource. Still, measurements of a large number of samples, of biggermasses (in which self-multiplication cannot be negligible), areneeded in order to validate the technique and in order todemonstrate the advantage of the SVM method over existingactive interrogation methods.

4. Summary and conclusions

In this study we experimentally examined, for the first time,the SVM technique for pulsed neutron source. Pulsed neutroninterrogation, of five CBNM—U reference items, was performed inthe PUNITA facility. All samples, with one exception, had the samegeometry and total mass, differing only in the enrichment level.These first results, of mass estimations by the active-SVM method,are promising but still preliminary in the sense of implementationof the method. Nonetheless, measurements of samples, in whichthe effect of self-multiplication cannot be neglected, shouldbe implemented in order to demonstrate the advantage of theSVM method over existing relevant nuclear material safeguardmethods.

Appendix A. Supporting information

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.nima.2015.02.048.

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