Performance assessment of self-interrogation neutron resonance densitometry for spent nuclear fuel assay

Nuclear Instruments and Methods in Physics Research A 729 (2013) 247–253

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Performance assessment of self-interrogation neutron resonance densitometry for spent nuclear fuel assay Jianwei Hu a,n, Stephen J. Tobin b, Adrienne M. LaFleur b, Howard O. Menlove b, Martyn T. Swinhoe b a Reactor and Nuclear Systems Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, PO Box 2008, MS-6172, Oak Ridge, TN 37831-6172, United States b Nuclear Engineering and Nonproliferation Division, Los Alamos National Laboratory, United States

art ic l e i nf o

a b s t r a c t

Article history: Received 8 May 2013 Received in revised form 30 May 2013 Accepted 8 July 2013 Available online 20 July 2013

Self-Interrogation Neutron Resonance Densitometry (SINRD) is one of several nondestructive assay (NDA) techniques being integrated into systems to measure spent fuel as part of the Next Generation Safeguards Initiative (NGSI) Spent Fuel Project. The NGSI Spent Fuel Project is sponsored by the US Department of Energy's National Nuclear Security Administration to measure plutonium in, and detect diversion of fuel pins from, spent nuclear fuel assemblies. SINRD shows promising capability in determining the 239Pu and 235U content in spent fuel. SINRD is a relatively low-cost and lightweight instrument, and it is easy to implement in the field. The technique makes use of the passive neutron source existing in a spent fuel assembly, and it uses ratios between the count rates collected in fission chambers that are covered with different absorbing materials. These ratios are correlated to key attributes of the spent fuel assembly, such as the total mass of 239Pu and 235U. Using count rate ratios instead of absolute count rates makes SINRD less vulnerable to systematic uncertainties. Building upon the previous research, this work focuses on the underlying physics of the SINRD technique: quantifying the individual impacts on the count rate ratios of a few important nuclides using the perturbation method; examining new correlations between count rate ratio and mass quantities based on the results of the perturbation study; quantifying the impacts on the energy windows of the filtering materials that cover the fission chambers by tallying the neutron spectra before and after the neutrons go through the filters; and identifying the most important nuclides that cause cooling-time variations in the count rate ratios. The results of these studies show that 235U content has a major impact on the SINRD signal in addition to the 239Pu content. Plutonium-241 and 241Am are the two main nuclides responsible for the variation in the count rate ratio with cooling time. In short, this work provides insights into some of the main factors that affect the performance of SINRD, and it should help improve the hardware design and the algorithm used to interpret the signal for the SINRD technique. In addition, the modeling and simulation techniques used in this work can be easily adopted for analysis of other NDA systems, especially when complex systems like spent nuclear fuel are involved. These studies were conducted at Los Alamos National Laboratory. Published by Elsevier B.V.

Keywords: SINRD NDA Spent fuel Fissile content Safeguards Nonproliferation

1. Introduction Self-Interrogation Neutron Resonance Densitometry (SINRD) is one of several nondestructive assay (NDA) techniques being integrated into systems to measure spent fuel as part of the Next Generation Safeguards Initiative (NGSI) Spent Fuel Project [1]. SINRD has been extensively studied at Los Alamos National Laboratory (LANL) by LaFleur et al. [2–4]. SINRD is a relatively low-cost and lightweight instrument that does not require an

n

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active source. Instead, SINRD makes use of the neutrons emitted mainly by spontaneous fission from 244Cm and other nuclides inherent in the spent fuel to interrogate the spent fuel itself. The signals of SINRD detector are affected by a number of nuclides in the spent fuel. In order to measure plutonium isotopes (as one of the goals of the NGSI Spent Fuel Project), it is important to quantify the isotopic impact of these nuclides to be able to separate out contributions from other nuclides. Quantification of isotopic impact on SINRD signals also helps to understand what the instrument really measures. Continuing the work reported previously [5], this paper focuses on the isotopic impact on the SINRD signal. (The research was performed at LANL when the lead author was a post-doctoral research associate at LANL.)

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When the source neutrons (mainly by spontaneous fission as aforementioned) travel through the spent fuel assembly, fissions and absorptions take place when the neutrons react with the nuclides in the fuel. The nuclides with both large microscopic cross sections and significant quantities (e.g., 239Pu and 235U) in the fuel will leave “marks” on the neutron spectrum. By detecting these “marks”, one can correlate the detector response to nuclide content of the fuel. Filtering materials with certain thickness are used in SINRD to constrain the energy ranges that the neutron detectors can detect. The energy ranges can be further refined by combining count rates from several neutron detectors. The concept of SINRD is also illustrated graphically in Fig. 1, which shows a sketch of the SINRD instrument [4]. As shown, the instrument contacts one side of the fuel assembly. Four different filtering (or absorbing) materials are used: gadolinium (Gd), hafnium (Hf), cadmium (Cd), and boron carbide (B4C). Four fission chambers (FCs) are used in this detector, three of which are covered with filtering materials: the Gd+Hf FC (covered with 0.025-mm Gd and 0.5-mm Hf), also referred to as Gd FC if there is no Hf coverage; the Bare FC (no filtering material coverage); the Cd FC (covered with 3-mm Cd); and the Fast Flux Monitor (FFM) FC (embedded in a polyethylene box that is coated with 1-mm Cd liner, and the box is behind a 1.0-cm-thick wall of B4C). The count rate difference between Gd FC and Cd FC is referred to as “Gd Cd”; similarly, the count rate difference between Gd+Hf FC and Cd FC is referred to as “Gd+Hf Cd”; FFM/(Gd+Hf Cd) is the count rate of FFM FC divided by the count rate difference of Gd+Hf FC and Cd FC. Table 1 summarizes the abbreviations used here for clarity.

These filtering materials preferentially absorb neutrons within certain neutron energy ranges due to the variations of cross sections of these materials, and the remaining neutrons may be detected in the FCs. Subtracting count rates between two different FCs (covered with different filters) will capture a specific “window” in the neutron energy spectrum. For example, because Gd strongly absorbs neutrons below 0.05 eV and Cd strongly absorbs neutrons below 1.0 eV, the count rate difference between these two FCs (referred to as “Gd Cd”) is proportional to the number of neutrons entering the two FCs with energy in the window of [0.05, 1.0] eV. Any creation and absorption of neutrons in the fuel within this energy window will have an impact on the “Gd Cd” count rate, provided moderation in the neutron energy between the fuel and the FC is not significant. Because most neutrons are born in the fast energy range and moderated down to thermal energies, absorption plays a dominant role. Any nuclide that has a large absorption cross section in the energy window of interest and a significant abundance in the fuel, such as 239Pu (with large resonance absorption around 0.3 eV) and 235U, will have an important impact on this count rate. The SINRD technique is designed to detect the depression in neutron flux within the Gd Cd energy window and then correlate the depression (reduction in count rate) to the mass of key nuclides that are responsible for the neutron absorption. This unique feature of “detecting the absence” of neutrons (i.e., depression of neutron flux in particular energy range) also adds to the complexity of the SINRD technique. In order to measure plutonium in the fuel assembly, it is important to separate out the contribution of 235U, which requires quantification of the individual contribution of each key nuclide.

2. Quantification of individual impact of key nuclides using perturbation method 2.1. Perturbation study

Fig. 1. Configuration of the SINRD detector [4].

Given the complexity of the SINRD signal, there is no direct way to quantify the individual contribution of each nuclide. Perturbations of individual key nuclide concentrations and analysis of the impacts on detector count rates can provide potential correlations between SINRD count rates and concentrations of these nuclides. In the MCNPX models [6], the atom density (and thus mass) of each of the eight important nuclides (as listed in Table 2) in the fuel assembly was “perturbed” in each case, and the changes in the FC count rate ratios of “FFM/(Gd+Hf Cd)” and “(Gd Cd)/Bare” were tallied. These two ratios were determined to best demonstrate the detection capabilities of SINRD [2,5]. Because everything else in the assembly remained unchanged during the perturbation, the change in the count rate ratio could be solely attributed to the change in that particular nuclide. A weighting (or sensitivity) coefficient (referred to as “wt. coeff.” in

Table 1 List of abbreviations used to refer to the fission chambers and combinations of count rates of different fission chambers. Abbreviations

Description and/or explanation

Gd FC Cd FC Gd+Hf FC Bare FC

Fission chamber covered with gadolinium liner (0.025 mm thick) Fission chamber covered with cadmium liner (3 mm thick) Fission chamber covered with both gadolinium and hafmium liners (0.025 mm and 0.5 mm thick, respectively) Fission chamber not covered with any filtering materials Fast flux monitor, fission chamber embedded in a polyethylene box that is coated with 1-mm Cd liner, and the box is behind a 1.0-cm-thick wall of boron carbide (B4C) Count rate of the Gd FC subtracted by that of the Cd FC Count rate of the Gd+Hf FC subtracted by that of the Cd FC Count rate of the FFM FC divided by “Gd+Hf Cd” “Gd Cd” divided by count rate of the Bare FC

FFM FC Gd Cd Gd+Hf Cd FFM/(Gd+Hf Cd) (Gd Cd)/Bare

J. Hu et al. / Nuclear Instruments and Methods in Physics Research A 729 (2013) 247–253

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Table 2 Change in count rates and ratios due to the changes in mass of eight nuclides.a Nuclide

ΔMass, %

(Gd Δ(Gd

U238 U235 Pu239 Pu240 Nd143 Pu241 Np237 Am241

30 30 30 30 60 60 60 60

Cd)/Bare ratio Cd), %

FFM/(Gd+Hf

ΔBare, %

ΔRatio, %

Wt. coeff.

Total wt.

4.72 0.02 0.82 1.65 1.12 0.55 0.21 0.56

0.05 1.23 0.43 0.87 0.35 0.03 0.38 0.73

0.0007 1.96 1.00 4.12 0.73 0.14 3.49 11.88

0.12 2.84 1.00 2.01 0.14 0.03 0.43 0.84

4.7 1.2 1.3 2.5 1.5 0.5 0.6 1.3

Δ(Gd+Hf

Cd) ratio

Cd), %

5.4 1.2 4.4 2.3 2.1 0.2 1.2 1.0

ΔFFM, %

ΔRatio, %

2.70 3.03 4.25 0.75 0.57 2.46 0.23 0.45

2.57 4.16 8.24 1.49 1.46 2.27 0.92 0.51

Wt. coeff.

Total wt.

0.002 0.35 1.00 0.37 0.46 0.60 0.45 0.44

0.31 0.51 1.00 0.18 0.09 0.14 0.06 0.03

FFM / (Gd+Hf -Cd) 239Pu Fission Rate

a Abbreviations used: “Δ” stands for change of certain quantity (e.g., “ΔRatio” means the change in the count rate ratio against the non-perturbed case); “wt. coeff.” stands for the weighting coefficient of the particular nuclide in terms of its impact on the count rate ratio (on a per-gram basis) and was normalized against 239Pu; “total wt.” means the total impact of a particular nuclide on the count rate ratio given its total mass in this assembly (again normalized relative to 239Pu).

0.16

Gd-Cd / Bare

0.15 0.14 0.13 0.12 0.11 0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

U-235 Fraction (wt%HM)

16.5

15.5

14.5

13.5

12.5

11.5 0.36%

BU: 15-GWd

0.40%

0.44%

0.48%

0.52%

60-GWd

0.56%

0.60%

239

Pu Fraction (wt%)

Fig. 2. Correlations observed in previous work: (a) correlation between count rate ratio of Gd Cd/Bare and 235U mass fraction (“HM” stands for heavy metal) [7]; (b) correlation between count rate ratio of FFM/(Gd+Hf Cd) and 239Pu mass fraction (239Pu FCs used) with burnup increasing from left to right [2].

Table 2) of the perturbed nuclide was obtained by dividing the change in the count rate ratio by the amount of the mass perturbed for that nuclide. Furthermore, if the weighting coefficient is multiplied by the total mass of the nuclide in the assembly, the total impact (referred to as “total wt.” in Table 2) of the nuclide on the ratio could be quantified. The eight nuclides selected for this study were determined to be the most dominant ones for these two aforementioned ratios in an earlier study [5], which involved multiplying the mass and the absorption cross section of a particular nuclide in the energy window. During the perturbation the total density of the fuel was modified to reflect the changes of the nuclides. (For most cases, except for 238U, changes in the overall fuel density were relatively small because the perturbed nuclides account for small fractions of the fuel, even though the densities of these nuclides changed significantly.) For this study, a simplified fuel assembly was developed, using uniform fuel compositions in each fuel rod. The assembly chosen had a burnup of 45 /tU, an initial enrichment of 4%, and a cooling time of 5 years. Table 2 summarizes the results of this perturbation study. The individual masses of 238U, 235U, 239Pu, and 240Pu were reduced by 30%, one nuclide at a time, and the individual masses of 143Nd, 241Pu, 237Np, and 241Am were reduced by 60%, again one nuclide at a time. The amount of mass reduction of a particular nuclide was selected so as to be great enough to induce a sufficient change in count rate (and ratios). The reduced amounts for the latter four nuclides were larger because they were less abundant in the assembly. As shown, the changes in the ratio of (Gd Cd)/Bare (“ΔRatio”), generally speaking, were smaller than those for FFM/(Gd+Hf Cd), indicating (Gd-Cd)/ Bare is less sensitive to the change in mass. (One caveat to note is that for some cases, especially for the ratio of (Gd Cd)/Bare, the changes

in ratios might not be great enough relative to the uncertainties in the simulations (∼0.3%).) According to the column of “total wt.” (the overall impact of a particular nuclide), the three nuclides that affect the (Gd Cd)/Bare ratio most are 235U, 240Pu, and 239Pu, which partly explains the observed correlation between this ratio and 235U mass, as shown in Fig. 2(a) [7]. Note that the negative signs (in the columns “wt. coeff.” and “total wt.” of Table 2) mean the particular nuclide affected the ratio in the opposite direction than other nuclides. The weighting coefficient (sensitivity on a “per-gram” basis) of 235U for this ratio was 1.96 relative to 239Pu, meaning that a gram of 235U had a 1.96 times greater impact on the (Gd Cd)/Bare ratio than a gram of 239Pu (although adding more 239Pu would reduce the ratio). The three nuclides that affected the FFM/(Gd+Hf Cd) ratio the most were 239Pu, 235 U, and 238U, which partly explains the observed correlation between 239 Pu mass and the FFM/(Gd+Hf Cd) ratio, as shown in Fig. 2(b) [2].

2.2. Updated correlation based on the perturbation study results As shown in Table 2, the FFM/(Gd+Hf-Cd) ratio was predominantly affected by the 239Pu, 235U, and 238U masses. Because the relative change in 238U was small from one assembly to another, 238 U can be treated as a background for SINRD. Based on the findings of the perturbation study, 235U was included in the abscissa as well as 239Pu in the FFM/(Gd+Hf Cd) correlation. The SINRD count rate was simulated for each of the 64 virtual spent fuel assemblies from the NGSI spent fuel library [8]. The 64 assemblies have four different burnups (15, 30, 45, and 60 GWd/ tU), four different initial enrichments (2, 3, 4, and 5%), and four

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3. Neutron energy spectra before and after the filter materials As previously discussed, energy windows are created by the filtering materials of certain thickness (e.g., Gd, Cd, and Hf). It is insightful to visualize the energy spectrum of the neutron flux before and after it goes through these materials and also identify the energy cutoffs of these windows. Two FCs were selected for this study: Cd FC and Gd+Hf FC. In the MCNPX model, which includes the 3D fuel assembly model with the SINRD instrument next to it, neutron spectra were tallied at the outer (cylindrical) surface of each layer of the three aforementioned filter materials and the outer surface of the material beneath it. By examining the difference between these two spectra, the energy window created by this particular filtering material can be identified. Because the flux coming from the fuel assembly is of the most importance, only the portion of the flux entering the FC tubes (incoming) was counted in this tally, which was accomplished by using the F2 tally coupled with cosine bins (from 901 to 180○). Fig. 4 shows neutron energy spectra before and after the layer of 3-mm Cd that covers the Cd FC. (Note that the energy spectra shown in Figs. 4, 5, and 7 were normalized by lethargy to obtain “visually accurate area” plots, meaning the area under the curve is proportional to the quantity of the subject of interest, according to the MCNP5 manual [9].) As shown in Fig. 4(a), the Cd mainly absorbs neutrons below 1.0 eV, leaving the rest of the spectra almost intact. Fig. 4(b) zooms into the most affected area, showing that the Cd eliminates almost all the neutrons below 0.5 eV and part of the neutrons between 0.5 and 1.0 eV (∼66% of them in this range). Note that the thermal peak of the spectra before the Cd,

90

90

85

85

80

80

75 70 65 60

15 GWd/tU

55

30 GWd/tU

50

45 GWd/tU

45

60 GWd/tU

40 2.0

2.5

3.0

3.5

FFM/(Gd+Hf-Cd)

FFM/(Gd+Hf-Cd)

different cooling times (1, 5, 20, and 80 years). (More details about this library can be found in Ref. 8.) Fig. 3(a) shows the correlation between 239Pu and FFM/(Gd +Hf Cd) for all 64 assemblies. These results show very similar trends to those observed in Fig. 2(b) [2], although in Fig. 2(b) fewer data points were included, and 239Pu FCs were used instead of 235U FCs. (All FCs modeled in this work were 235U FCs because 239Pu FCs are scarce in reality.) In general, 239Pu scales with FFM/(Gd +Hf Cd), except for assemblies with high 235U content (i.e., all the 15 GWd/tU assemblies, and the 30 GWd/tU assemblies with 5% initial enrichment) [5]. As shown in this perturbation study, 235U also plays an important role in this ratio; thus, 235U was added to the abscissa with the weighting coefficient of 0.35 (as determined by the perturbation study). Fig. 3(b) shows the results of this new correlation. As shown, clear trends between the weighted sum of 239 Pu and 235U and the ratio can be observed within each burnup group, despite the scatter within each subgroup of four assemblies with different cooling times (but with the same burnup and initial enrichment). This result reaffirms that 235U should be included in this correlation. The different trends for different burnups can be attributed to the increasing amount of neutron absorbers (e.g., fission products and actinides such as 240Pu) accumulated in assemblies with higher burnups. More neutron absorbers will further depress the count rate of (Gd+Hf Cd), and thus make the ratio greater. The significant scatter within each subgroup of the four different cooling times indicates that further study is needed; these assemblies have the same amount of 235U and 239Pu but different amounts of cooling-time-dependent nuclides, which may have a non-negligible aggregate impact on this ratio.

75 70 65 60

Pu and FFM/(Gd+Hf

2

4

6

8

Mass of (0.348U235+Pu239) (kg)

Cd) for all 64 spent fuel assemblies; (b) (0.35235U+239Pu) and FFM/(Gd+Hf

0.15 0.10 0.05

1E-05

Cd) for all 64 spent fuel assemblies.

0.030

before Cd after Cd

0.20

0.00 1E-08

60 GWd/tU

40

0.30 0.25

45 GWd/tU

45

Normalized flux/lethargy

Normalized flux/lethargy

239

30 GWd/tU

50

Pu239 (kg) in the assembly Fig. 3. Correlations between (a)

15 GWd/tU

55

1E-02

1E+01

Neutron energy (MeV)

before Cd after Cd

0.025 0.020 0.015 0.010 0.005 0.000 1E-08

1E-07

1E-06

1E-05

1E-04

Neutron energy (MeV)

Fig. 4. Neutron energy spectra before and after a layer of 3-mm Cd: (a) the spectra over the entire energy range; (b) the spectra in the energy range of 0.01–100 eV.

J. Hu et al. / Nuclear Instruments and Methods in Physics Research A 729 (2013) 247–253

0.30

after Gd 0.25

after Gd and Hf

0.20 0.15 0.10 0.05 0.00 1E-08

before Gd and Hf after Gd after Gd and Hf

0.025 before Gd and Hf

Normalized flux/lethargy

Normalized flux/lethargy

0.35

1E-06

1E-04

1E-02

1E+00

1E+02

Neutron energy (MeV)

251

0.020

0.015

0.010

0.005

0.000 1E-08

1E-07

1E-06

1E-05

1E-04

Neutron energy (MeV)

Fig. 5. Neutron energy spectra before and after a layer of 0.025-mm Gd and an additional layer of 0.5-mm Hf: (a) the spectra over the entire energy range; (b) the spectra in the energy range of 0.01–100 eV.

which is formed by the neutrons directly coming out of the assembly before going through any absorbing material, is relatively low compared to the 2 MeV peak (considering the assembly is in water). This is because because the SINRD instrument itself displaces water (thus hardens the spectra), and there are absorbers in the instrument. Fig. 5 shows neutron energy spectra before and after a layer of 0.025-mm Gd and an additional layer of 0.5-mm Hf, which both cover the Gd+Hf FC. As shown in Fig. 5(a), the Gd mainly absorbs neutrons below 0.3 eV, leaving the rest of the spectra almost intact. Fig. 5(b) zooms into the most affected area, indicating the Gd removes almost all the neutrons below 0.05 eV and part of the neutrons between 0.05 and 0.3 eV (∼45% of them in this range). Hafnium mostly affects the neutrons around 1 eV (starting at ∼0.8 eV) and beyond. (Fortunately it has only slight impact on neutrons below 0.3 eV.) By taking the difference between the count rates from the Gd+Hf FC and the Cd FC, the count rate of (Gd +Hf Cd) can be mainly correlated to the neutrons with energies between 0.05 and 0.8 eV is created, although it has to be discounted for the range of [0.05, 0.3] eV and [0.5, 0.8] eV because Gd and Cd, respectively, partially block each range. The mathematical form of this energy window can be expressed as 0.55n [0.05, 0.3] eV+[0.3, 0.5] eV+0.34n[0.5, 0.8] eV. A nuclide that has a significant absorption cross section in this window will affect the count rate of (Gd+Hf Cd) and thus the ratio of FFM/(Gd+Hf Cd). On the other hand, as shown in both Figs. 4 and 5, SINRD makes use of only a small fraction of the entire neutron spectrum; therefore, long measurement time (hours) is needed to reduce counting uncertainties, especially for low-burnup spent fuels (weaker neutron source strength) [2]. Fig. 6 shows the absorption cross section of a few important nuclides (235U, 239Pu, 241Pu, 240Pu, 155Gd, 149Sm, and 241Am) in ranges around the [0.05, 0.8] eV energy window created by the Gd +Hf FC and the Cd FC. On a “per unit mass” basis, 155Gd and 149Sm would dominate the absorption in this window, but the quantity of each nuclide has to be factored into consideration. With use of the Hf filter, the majority of the large resonance absorption of 240 Pu around 1.0 eV was avoided in the window. It is also worth pointing out that given the way the SINRD instrument is designed, the front side (the side facing the fuel assembly) of the FCs detects more neutrons directly from the fuel (the neutrons that are detected without colliding with the materials outside the fuel assembly), while the back side of the FCs detects neutrons that are already affected by the absorbing materials in the back (e.g., B4C and Cd liner) before being detected. Thus, the back side of the FCs detects a weaker signal than the front side. Fig. 7 shows a comparison of neutron spectra (before

Fig. 6. The absorption cross section of a few important nuclides in ranges around the [0.05, 0.8] eV energy window created by the Gd+Hf FC and the Cd FC. Note that for fissile nuclides, fission cross section dominates the total absorption cross section.

and after the Cd filter) between the front side (a) and the back side (b) of the Cd FC. As shown, on the back side the Cd filter makes a much smaller difference on the neutrons with energies below 1.0 eV. Based on this observation, the performance of SINRD can be improved by “turning off” the back side of the FCs to ensure that the count rate is dominated by neutrons coming directly from the fuel, for example by coating an extra layer of absorbing material (e.g., Cd) onto the back side of the FCs.

4. Nuclides that cause cooling-time-dependent variations in the count rate Cooling time dependence in count rates and ratios was observed in the SINRD analysis; for example, it is shown in each subgroup of four assemblies in Fig. 3(b). It is important to identify the nuclides that are responsible for these variations. In this study, three sets of assemblies were chosen. The two assemblies in each set had the same burnup and initial enrichment but different cooling times. They were (1) 15 GWd/tU, 5%, 1 year vs. 80 years; (2) 30 GWd/tU, 5%, 1 year vs. 80 years; (3) 45 GWd/tU, 3%, 20 years vs. 80 years. The nuclides whose mass dramatically changed (e.g., over 20%) from one cooling time to another in each set were

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0.03

before Cd (the back side)

before Cd (the front side) aer Cd (the front side)

Normalized flux/lethargy

Normalized flux/lethargy

0.03

0.02

0.01

0.00 1E-8

1E-7

1E-6

1E-5

1E-4

aer Cd (the back side) 0.02

0.01

0.00 1E-8

1E-7

Neutron energy (MeV)

1E-6

1E-5

1E-4

Neutron energy (MeV)

Fig. 7. Neutron energy spectra before and after a layer of 3-mm Cd of the Cd FC: (a) the front side of the Cd FC (the side facing the fuel assembly); (b) the back side of the Cd FC.

Table 3 Nuclides that cause the largest changes in absorption in the energy window with cooling times (normalized to

241

Pu).

15 GWd/tU, 5%, 1 year vs. 80 years

30 GWd/tU, 5%, 1 year vs. 80 years

45 GWd/tU, 3%, 20 year vs. 80 years

Nuclide

Relative weight

Nuclide

Relative weight

Nuclide

Relative weight

Pu241 Am241 Sm147 U235 Pu238 Eu151 U234 Eu154 Cs137 Pd106 Sm151 Zr90

1.0 0.456243 0.048019 0.035491 0.017186 0.007962 0.006673 0.005101 0.004492 0.004185 0.003663 0.002706

Pu241 Am241 Pm147 Sm147 U234 Cs134 Eu154 Gd154 Eu151 Pd106 Zr90 Gd155

1.0 0.455645 0.026442 0.020411 0.013593 0.006926 0.006647 0.003105 0.003064 0.003015 0.001608 0.001386

Pu241 Am241 Pu238 U234 Cm244 Eu154 Cs137 Eu151 Zr90 Sm151 Cm243 Am242

1.0 0.391784 0.128135 0.048752 0.042304 0.004632 0.004061 0.002916 0.001737 0.00134 0.000651 0.000149

90 85 80 FFM/(Gd+Hf-Cd)

identified. These nuclides were then included on flux multiplication tallies (FM tallies) in the MCNPX model, with energy bins corresponding to the previously identified energy windows. With these tallies the total absorption rate in the energy window of each nuclide can be calculated by multiplying the cross section with the neutron flux in the fuel. After multiplying the change in mass of each of these nuclides between the two assemblies in each set, the nuclides that cause major changes in absorptions in the window among cooling times can be identified, and thus these nuclides are considered to be principally responsible for causing the cooling time variations. Table 3 lists the nuclides that cause the largest changes in absorption in the energy window with cooling times. “Relative weight” means the change in total absorption in the window between the two cooling times of a particular nuclide divided by that of 241Pu. As shown in this table, 241Pu (with a 14-year halflife), as expected, is the most important nuclide in the ranking followed by 241Am, which is about 39–45% as important as 241Pu. The rest of the nuclides make insignificant impacts except for 238 Pu in the 45 GWd/tU and 5% case (because more 238Pu builds up at higher burnup). Since 241Pu and 241Am were identified as the two most important nuclides responsible for cooling time variation, these two nuclides were included in the abscissa for the correlation with FFM/(Gd+Hf Cd). Fig. 8 shows the updated correlation. Compared to Fig. 3(b), Fig. 8 is almost identical except that 241Pu and 241Am were added to the abscissa. Again, the weighting coefficients for these two nuclides were determined through the perturbation study as discussed in Section 2. The four data points with different cooling times in each subgroup (with same burnup and initial enrichment) were essentially vertical in Fig. 3(b). In Fig. 8 some of

75 70 65 60

15 GWd/tU

55

30 GWd/tU

50

45 GWd/tU

45

60 GWd/tU

40 2

3

4

5

6

7

8

Mass of (0.35*U235+Pu239+0.6*Pu241+0.44*Am241) (kg) in the assembly Fig. 8. Correlation between the mass of (0.35235U+239Pu +0.6241Pu +0.44241Am) in the assembly (kg) and the FFM/(Gd+Hf Cd) ratio.

them were improved, such as the ones with a lower count rate ratio shifted to the left, while others became worse. This result suggests that some of the underlying causes of the cooling time dependence are yet to be determined, and future research is suggested on this matter. It is also speculated that the aggregated effects of all other “unimportant” nuclides may be playing a role as well. On the other hand, a wide range of cooling times, from 1to 80 years, was considered in this study, but in application one might only have to measure fuels that vary in a smaller range at on one particular occasion. It is also suggested that in the future this study be repeated at smaller intervals of cooling time (e.g., 5 years apart).

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5. Summary

Acknowledgments

This paper summarizes recent work to further understand the underlying physics of the SINRD technique. The perturbation method was shown to be a very useful method for understanding the SINRD signal and the impact of each nuclide. Based on the results of the perturbation study, the weighting coefficients of 239Pu and 235U were quantified and the weighted sum of 239Pu and 235U generally trends well with the FFM/(Gd+Hf Cd) count rate ratio within each burnup group. The individual mass of 239Pu and 235U in a spent fuel assembly can be quantified by combining with another instrument that has different sensitivities to 239Pu and 235U, such as the Californium Interrogation Prompt Neutron technique [10]. The spectra study visualized the energy windows created by Cd and Gd+Hf, and also demonstrated that SINRD makes use of only a small fraction of the entire neutron spectrum; therefore, long measurement time is needed to reduce counting uncertainties. Significant variations were observed in the FFM/(Gd+Hf Cd) correlation due to variations of cooling time. The nuclides responsible for the cooling variations were identified. A preliminary attempt was made to correct the cooling time dependence, but only minor improvements were achieved. More significant improvements are needed for this matter in future work. SINRD detects the reduction in the neutron flux in certain energy ranges caused by resonances present in the irradiated fuel. The degree of the flux depression is strongly related to the concentration of the resonance nuclides in the fuel, and thus the underlying physics are somewhat more complex than those of other NDA techniques. In summary, this work provides insights into some of the main factors that affect the performance of SINRD, and it should help improve the hardware design and interpretation of the SINRD signal. In addition, the modeling and simulation techniques used in this work can be easily adopted for analysis of other NDA systems, especially when spent nuclear fuel is involved.

The authors would like to acknowledge the support of the Next Generation Safeguards Initiative, Office of Nonproliferation and International Security, National Nuclear Security Administration. The authors would also like to thank Mr. Ian Gauld, Dr. Timothy Valentine, Dr. Ronald Ellis, and Mr. Stephen Bowman for their detailed reviews and valuable inputs to this manuscript.

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