- Email: [email protected]
Verification and validation of the MCNPX-PoliMi code for simulations of neutron multiplicity counting systems
Nuclear Instruments and Methods in Physics Research A 700 (2013) 135–139
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Verification and validation of the MCNPX-PoliMi code for simulations of neutron multiplicity counting systems S.D. Clarke a,n, E.C. Miller a, M. Flaska a, S.A. Pozzi a, R.B. Oberer b, L.G. Chiang b a b
Department of Nuclear Engineering & Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109, USA Y-12 National Security Complex, P.O. Box 2009, Oak Ridge, TN 37831, USA
a r t i c l e i n f o
abstract
Article history: Received 22 May 2012 Received in revised form 14 August 2012 Accepted 5 October 2012 Available online 27 October 2012
Neutron coincidence counting is widely used in nuclear safeguards. Simulations of these systems can be performed using Monte Carlo codes such as MCNPX to aid in calibration or measurement design. However, the MCNPX coincidence-counting routines treat particle histories individually, therefore the dead time of the acquisition electronics is not treated. The MCNPX-PoliMi code provides the ability to model detailed effects such as data-acquisition electronics and system dead times. A specialized postprocessing code has been developed to interpret the collision-log file and determine the response of a 3 He multiplicity counter. The MCNPX-PoliMi simulation provides the full neutron multiplicity distribution measured by the 3He tubes. This distribution is used to compute the singles, doubles, and triples rates which are the quantities used to determine 235U mass. MCNPX-PoliMi has previously been validated with passive multiplicity measurements. In this study, a detailed analysis of the measurement system operating in active mode is presented for uranium-oxide standards ranging from 0.5 to 4.0 kg with a Canberra JCC-51 active well coincidence counter. MCNPX-PoliMi calculations are also compared with MCNPX. The two codes agree to within 1% for the cases with negligible dead times. The simulations are validated with measurements performed at the Y-12 National Security Complex. & 2012 Elsevier B.V. All rights reserved.
Keywords: 3He multiplicity Active well coincidence counter MCNPX-PoliMi
1. Introduction Neutron coincidence counting has been widely used in nuclear safeguards for many years [1–5]. In this method, correlated neutrons distinguish fission sources from (alpha, n) sources to establish a fissile mass. Historically, instruments based on 3He tubes have been used to perform these measurements. One such instrument is an active well coincidence counter (AWCC) [6]. The active source in this instrument is an Am-Li neutron source, which is most-commonly used when assaying uranium samples due to its low spontaneous fission rate. Even in the presence of the current 3He shortage, these instruments are still under investigation due to their ease of use and reliability of operation. There is a desire to replace the 3He that is currently used in AWCCs with other neutron-sensitive materials, such as 10B. Therefore, simulation of these systems is all the more important. Simulations are typically performed using Monte Carlo techniques; in fact, the widely applied MCNPX code has dedicated tallies, specially designed for
n
Corresponding author. Tel.: þ1 734 615 7830; fax: þ1 734 763 4540. E-mail addresses: [email protected] (S.D. Clarke), [email protected] (E.C. Miller), mfl[email protected] (M. Flaska), [email protected] (S.A. Pozzi), [email protected] (R.B. Oberer), [email protected] (L.G. Chiang). 0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2012.10.025
neutron coincidence counting. These tallies have proven accurate in the past when count rates are low and the neutrons from separate fission chains within the sample do not overlap. Under this condition there is negligible dead time. This is because the MCNPX routines treat particle histories individually. Therefore the dead time of the acquisition electronics cannot be treated. The MCNPX-PoliMi code has been developed, along with a module-based detector-response algorithm, to simulate various measurement systems. Recently, the capability has been added to simulate neutron multiplicity counting systems along with all of the associated coincidence acquisition electronics (effects are included such as dead time, pre-delay and shift register timing, etc.). This capability has been validated with passive multiplicity measurements through an ESARDA benchmark exercise with a range of weak and strong sources such as 252Cf and PuO2 [7]. In this work, the MCNPX-PoliMi code is verified and validated for an AWCC, operating in active mode. The verification is performed with calculations from both MCNPX-PoliMi and MCNPX code v. 2.7.0 and compared to experimental data.
2. Experimental setup The experimental data is from measurements performed at the Y-12 National Security Complex using an AWCC and a set of
136
S.D. Clarke et al. / Nuclear Instruments and Methods in Physics Research A 700 (2013) 135–139
93.18%-enriched uranium-oxide (U3O8) powder standards ranging from 0.5 to 4.0 kg made from New Brunswick Laboratory Certified Reference Material 149 [8,9]. These standards are wellcharacterized and the available information contains accurate values for net mass, total uranium mass, 235U mass, and enrichment. The 235U mass of these 93%-enriched standards ranges from 394 to 3151 g. The material is contained in thin-walled stainlesssteel cans with an inner radius of 6.1176 cm and an outer radius of 6.1976 cm. The height of the cans is 17.78 cm and the fill height of the U3O8 powder varies with mass. Table 1 summarizes the physical details of the CRM-149 standards. The results of these measurements were the singles, and doubles rates for each sample, as well as the empty AWCC. The measurements were performed using a Canberra, JCC-51 AWCC operating in active mode [10]. This counter contains 42 3 He tubes arranged in two concentric rings in a high-density polyethylene (density of 0.955 g/cm3) matrix around the sample cavity. Each sample was placed on a 10.16 cm tall stand in the base of the AWCC cavity. Fig. 1 shows an illustration of the MCNPX-PoliMi model of the AWCC. The source strength was calculated based on singles-rate measurement performed with an empty AWCC. This measurement resulted in an Am-Li source strength of 6.02 104 neutrons per second with both sources (upper and lower plugs) were assumed to as the same source strength. In the future, some sensitivity analysis may be done to assess the validity of this assumption. The samples were counted between 10 and 30 min, depending on the mass, and processed using standard shift register with a 4.5 ms pre-delay, a 64 ms counting window, and a 1024 ms accidental-gate delay. Table 1 Physical details of the CRM-149 U3O8 standards. Total mass (g)
235
500 1000 1500 2000 3000 4000
393.79 787.74 1181.62 1575.49 2363.31 3151.13
U mass (g)
Density (g/cm3)a
Fill height (cm)
2.35420 2.35468 2.37136 2.36301 2.36003 2.35896
1.8034 3.6068 5.4102 7.1882 10.7950 14.4018
a Exact density values were calculated in the simulations in order to preserve the specified 235U mass.
3. Description of the MCNPX-PoliMi code The MCNP-PoliMi code was originally developed in 2003 as an extension of the MCNP4c code to enable the simulation of correlated-particle measurements [11]. All previous versions of the MCNP code were incapable of simulating such measurements due to some simplifications and data-handling issues. For example, secondary gamma-ray production was uncorrelated to any individual interaction. Secondary gamma rays are sampled only from average production libraries. Also, the distributions used to sample neutrons produced from fission are simplified to include only two integer values on either side of the mean value. In addition, the MCNP-PoliMi code introduced the ability to write a collision-log file containing all information about the particle interactions inside of user-specified detector cells. It is these data that are used to calculate detector response using a module-based post-processing algorithm. In the years following the release of the MCNP4c code many of its simplifications and assumptions were addressed through the release of the MCNPX code. For example, the MCNPX code has the ability to treat the complete multiplicity distribution of the neutrons emitted from fission events. Furthermore, the MCNPX code has the capability of simulating more complex physics processes such as photonuclear interactions and heavy chargedparticle transport. In 2012 the MCNP-PoliMi modifications were incorporated in the MCNPX, combining all of the PoliMi extensions with the updated physics capabilities of the MCNPX code. This new version is designated MCNPX-PoliMi. A dedicated post-processing module has been developed for the AWCC and its associated acquisition electronics [12]. The detailed collision outputs from MCNPXPoliMi are used to generate a list of detector pulses and acquisition times similar to that obtained in a measurement, where individual detector dead times and electronic effects are explicitly accounted for. The dead times of the individual 3He tubes, amplifiers and the OR gate were assumed to have typical values of 2 ms, 500 ns, and 30 ns. This pulse list is processed with a simulated shift register to obtain the so-called Reals (R) and Reals-plus-Accidentals (Rþ A) frequency distributions which are used to calculate the singles, doubles, and triples count rates from the well-known Eq. (1), where P(n) is the RþA-gate distribution and Q(n) is the A-gate distribution, n is the multiplet, and t is the measurement time [13]. 1X S¼ PðnÞ
t
D¼ T¼
N
" 1 X
t
nUPðnÞ
N
" 1 X nðn1Þ
t
N
2
X
# nUQ ðnÞ
N
X nðn1Þ PðnÞ Q ðnÞ 2 N
!# P X X N nUQ ðnÞ nUPðnÞ nUQ ðnÞ P N Q ðnÞ N N
ð1Þ
3.1. MCNPX-PoliMi results
Fig. 1. Illustration of the MCNPX-PoliMi model of the AWCC.
Using MCNPX-PoliMi and the associated post-processor, detailed simulations of the shift register multiplicity analysis were performed for the U3O8 powder standards ranging in mass from 0.5 to 4.0 kg. Fig. 2 shows the resulting multiplicity distributions in the R þA and A gates for the 4.0 kg standards. The similarity in the two distributions is expected because the count rate is low therefore
S.D. Clarke et al. / Nuclear Instruments and Methods in Physics Research A 700 (2013) 135–139
137
Table 2 Multiplicity counting rates for 93% U3O8 standards ranging from 0.5 to 4.0 kg calculated using MCNPX-PoliMi and the post-processing algorithm (si are the statistical uncertainties calculated using the number of counts from the MCNPXPoliMi pulse-train analysis). Total mass (g)
S
sS
D
sD
T
sT
0 500 1000 1500 2000 3000 4000
13,229.7 13,837.5 14,117.4 14,351.0 14,546.7 14,910.7 15,233.8
4.0 4.1 4.1 4.2 4.2 4.2 4.3
1.7 135.1 202.7 262.4 316.0 422.4 531.1
7.0 7.5 7.7 7.9 8.1 8.3 8.6
2.3 17.6 28.0 39.2 48.5 68.7 91.2
8.4 9.3 9.8 10.3 10.6 11.3 12.0
Table 3 Multiplicity counting rates for 93% U3O8 samples ranging from 0.5 to 4.0 kg calculated using MCNPX v. 2.7.0 (si are the statistical uncertainties calculated by MCNPX). Fig. 2. Rþ A- and A-gate multiplicity distributions for the 4 kg standard of 93%-enriched U3O8; one-sigma statistical error bars are included.
Total mass (g)
S
sS
D
sD
T
sT
0 500 1000 1500 2000 3000 4000
13,253.1 13,864.6 14,148.4 14,380.5 14,584.7 14,947.4 15,299.9
5.3 69.3 58.0 53.2 49.6 44.8 41.3
0.0 135.9 204.7 264.9 320.3 431.6 549.3
0.0 0.8 1.0 1.2 1.3 1.6 1.8
0.0 16.3 26.7 38.1 48.7 72.4 96.9
0.0 0.3 0.4 0.6 0.7 0.9 1.0
4. Comparison with MCNPX
Fig. 3. Rþ A-gate multiplicity distributions for 93%-enriched U3O8 samples ranging from 0.5 to 4.0 kg calculated using MCNPX-PoliMi and the associated post-processing algorithm; one-sigma statistical error bars are included.
the accidentals contribute greatly to the total measured rates. Fig. 3 shows the RþA-gate distributions for all samples. The distributions peak at zero, which means that multiplicity windows containing only a single neutron are the most probable for all of the samples. The distributions then fall-off nearly exponentially until multiplets of nearly 10 (the A-gate distribution ends at 9 due to poor statistics). As expected, larger masses result in more counts at higher multiplets. The R þA-gate distribution is higher than that A-gate distribution at higher multiplets, illustrating the influence of the accidental background above the induced fission neutrons from the U3O8. The multiplicity distributions were used to calculate the multiplicity counting rates using Eq. (1). These rates are wellknown quantities that are closely correlated to fissile mass. In fact, the doubles-rate is used in nuclear safeguards applications to assay the fissile mass of unknown samples, or to verify the fissile mass of declared samples. Consequently, the ability to accurately simulate these rates is of great interest. Table 2 summarizes the multiplicity counting rates and the corresponding statistical uncertainties calculated by MCNPX-PoliMi for each of the U3O8 standards.
The most-recent versions of the MCNPX code have a specialized pulse height tally that can be used for correlated-particle counting [14]. This tally scores the number of capture reactions on a specific nuclide at the end of each history, with time gating and pre-delay windows available, making this tally easily applicable to neutron multiplicity counting. The MCNPX tally scores within each particle-history independently, making it a fundamentally different approach than the MCNPX-PoliMi post-processing algorithm discussed in Section 3. In particular, there is no consideration given to the accidental background as treated in the MCNPX-PoliMi code. Because of this, the MCNPX tally results can be understood as ideal multiplicity counting rates, in the absence of accidental background and detector dead time. In order to verify the results obtained from the MCNPX-PoliMi code, independent simulations were performed using MCNPX v. 2.7.0. Table 3 summarizes multiplicity counting rates calculated by MCNPX v. 2.7.0. Excellent agreement is observed between the codes implying that the difference between the simulated and experimental results is caused by the difference between the model and the physical AWCC. For this configuration the effects of accidental background and detector dead time are minimal. In other configurations where the effects are large, the results of the two codes are expected to differ. Table 4 shows the ratio of the multiplicity counting rates calculated by MCNPX-PoliMi to those calculated by MCNPX. The relative uncertainties of the codes were added in quadrature to compute the combined uncertainty displayed in Table 4.
5. Experimental validation 5.1. Comparison to simulated results The measurements described in Section 2 produced singles and doubles rates for the entire range of U3O8 masses. The triples
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S.D. Clarke et al. / Nuclear Instruments and Methods in Physics Research A 700 (2013) 135–139
Table 4 Ratio of the multiplicity counting rates calculated by MCNPX-PoliMi to those calculated by MCNPX (si are the combined statistical uncertainties calculated by the two codes). Total Mass (g)
S
sS
D
sD
T
sT
0 500 1000 1500 2000 3000 4000
0.998 0.998 0.998 0.998 0.997 0.998 0.996
0.001 0.005 0.004 0.004 0.003 0.003 0.003
– 0.994 0.990 0.991 0.987 0.979 0.967
– 0.056 0.038 0.030 0.025 0.020 0.016
– 1.085 1.048 1.029 0.996 0.949 0.942
– 0.576 0.368 0.270 0.219 0.157 0.124
Fig. 5. Comparison of simulated and measured doubles rates for various U3O8 masses.
Table 5 Sensitivity of the calculated doubles-rate with respect to the R þA- and A-gate distributions. 235
Fig. 4. Comparison of simulated and measured singles rates for various U3O8 masses.
rates were not recorded due to short counting times and low detection efficiency (singles are detected with efficiency e, doubles with efficiency e2, and triples with efficiency e3). Fig. 4 shows a comparison of singles rates calculated by MCNPX-PoliMi, MCNPX v. 2.6.0, and the experimental data. As noted earlier, the two Monte Carlo codes agree very well with one-another. There is a slight (less than 3.5%) positive bias in both codes relative to the experimental data for the entire range of 235 U masses. Furthermore, the bias is nearly a constant 340 counts per second for the entire range of 235U masses. This bias could be due to a number of factors: the polyethylene density, the 3 He density, the position of the AmLi sources within the plugs, and the relative strength of the AmLi sources. The contribution of these uncertainties to the observed agreement is difficult to predict; however, a rigorous sensitivity analysis could be done in the future. Fig. 5 shows a comparison of doubles rates calculated by MCNPX-PoliMi, MCNPX v. 2.7.0, and the experimental data. As noted earlier, the two Monte Carlo codes agree very well with one-another but again there is a positive bias in both codes relative to the experimental data. The bias is nearly a constant 60 counts per second for the entire range of 235U masses.
5.2. Sensitivity analysis The multiplicity counting rates are calculated as the difference of the moment of the RþA- and A-gate distributions, which are very similar to one-another as shown in Fig. 1. Table 4 shows the ratio of the number of counts in the A-gate to the number of counts in the RþA-gate (G) for both the measurement and the
U mass (g)
0 393.79 787.74 1181.62 1575.49 2363.31 3151.13
Gmeasured
Gsimulated
dG (%)
dD (%)
S
1.000 0.993 0.988 0.984 0.981 0.974 0.970
1.000 0.988 0.984 0.980 0.977 0.971 0.967
– 0.49 0.39 0.39 0.37 0.34 0.24
– 83.27 40.32 31.13 25.22 20.66 13.90
– 168.7 102.5 80.8 68.9 60.3 58.5
simulation.
G¼
NA NR þ A
ð2Þ
For the empty AWCC, G is equal to 1.000 because the counts are entirely accidentals. As samples of increasing mass are measured, G decreases to 0.970. In other words, the number of counts in the R þA-gate is at most 3% greater than the number of counts in the A-gate. A sensitivity coefficient, S, was defined as the ratio of the percent difference in the doubles-rate, dD to the percent difference in G, dG. The percent differences were computed as the MCNPX-PoliMi simulation results relative to the measured results.
dD S ¼ dG
ð3Þ
Table 5 contains the sensitivity coefficient for each of the U3O8 samples. At most, dG is 0.5% less in the simulation versus the measurement while dD can be as large as 83%. This shows that very small fluctuations in the A-gate counts can lead to a dramatic change in the calculated doubles-rate. Furthermore, it is conceivable that either the MCNP simulations or the measurements have A-gate errors on the order of 0.5%, which lead to the observed doubles-rate differences. For example, there could be slight discrepancies in the geometrical or material model of the AWCC leading to differing detection efficiency. Also, the assumption was made that the two AmLi sources have the same strength; in reality, this may not be the case.
S.D. Clarke et al. / Nuclear Instruments and Methods in Physics Research A 700 (2013) 135–139
6. Conclusions The full multiplicity distributions for New Brunswick National Laboratory CRM-149 HEU-oxide samples in an AWCC have been calculated using the MCNPX-PoliMi code. The resulting singles, doubles, and triples rates were also calculated and compared to results from MCNPX v. 2.7.0 for verification. The two codes agree well with one-another (within less than 1%) for all three multiplicity rates at each sample mass. It is expected that the MCNPXPoliMi and MCNPX multiplicity results would differ more for cases with non-negligible dead times. This is caused by the fact that the MCNPX tally scores within each history independently, making the multiplicity counting rates ideal (absence of accidental background and detector dead time). The singles and doubles rates were compared to experimental data from the Y-12 National Security Complex collected with a Canberra, JCC-51 AWCC. There were slight positive biases observed in both the singles and doubles rates: approximately 340 counts per second for the singles and approximately 60 counts per second for the doubles. These biases can be understood given the high sensitivity on the multiplicity rates to small fluctuation in the A-gate distributions. In fact, a change of less than 0.5% simulated A-gate distribution would correct the observed bias in the doubles count rates.
Acknowledgment The authors would like to thank Dr. B. Dahl from Chalmers University of Technology, Sweden for providing the initial MCNPX model upon which this work was based. This research was partially funded by the National Science Foundation and the Domestic Nuclear Detection Office of the
139
Department of Homeland Security through the Academic Research Initiative Award # CMMI 0938909.
References [1] N. Ensslin, W.C. Harker, M.S. Krick, D.G. Langner, M.M. Pockrell, J.E. Stewart, Application Guide to Neutron Multiplicity Counting, Los Alamos National Laboratory, LA-13422-M, 1998. [2] R. Dierckx, W. Hage, Nuclear Science and Engineering: The Journal of the American Nuclear Society 85 (1983) 325–338. [3] M.S. Krick, J.E. Swansen, Nuclear Instruments and Methods 219 (1984) 384–393. [4] P. Baeten, M. Bruggeman, R. Carchon, W. DeBoeck., Nuclear Instruments and Methods A 413 (1998) 333–340. [5] S.A. Pozzi, R.B. Oberer, L.G. Chiang Monte Carlo simulation of measurements with an active well coincidence counter (AWCC), in: Proceedings of the Institute of Nuclear Materials Management 45th Annual Meeting, Orlando, Florida, July 18–22, 2004. [6] Canberra JCC-51 Product Description, Canberra, Measurement Solutions for Nuclear Safety and Security, /http://www.canberra.com/products/715.aspS, 2010 (accessed 29.04.10). [7] P. Peerani, M. Swinhoe, A.-L. Weber, L.G. Evans, ESARDA Multiplicity Benchmark Exercise—Phases III and IV, ESARDA Bulletin, no. 42, Nov. 2009. [8] L. Chiang, R. Oberer, C. Gunn, E. Dukes, A. Akin, Comparison of the NDA of HEU Oxide Between AWCC and the HPGe Detector, Y-12 National Laboratory Internal Report, Y/EN-8311, December 2009. [9] Certified Reference Material 149, Report on Production and Characterization, New Brunswick Laboratory Report CRM-149, (not dated). [10] Canberra JCC-51 Product Description, Canberra, Measurement Solutions for Nuclear Safety and Security, /http://www.canberra.com/products/715.aspS, 2010 (accessed 29.04.10). [11] S.A. Pozzi, E. Padovani, M. Marseguerra, Nuclear Instruments and Methods A 513 (2003) 550. [12] E.C. Miller, S.D. Clarke, M. Flaska, S. Prasad, S.A. Pozzi, E. Padovani, Journal of Nuclear Materials Management XL (Number 2) (2012). [13] P. Peerani, M. Swinhoe, ESARDA Multiplicity Benchmark Exercise—Final Report, ESARDA Bulletin, no. 34, Feb. 2006. [14] D.B. Pelowitz (Ed.), MCNPX Manual, Version 2.7.0, LA-CP-11-00438, April 2011.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Verification and validation of the MCNPX-PoliMi code for simulations of neutron multiplicity counting systems S.D. Clarke a,n, E.C. Miller a, M. Flaska a, S.A. Pozzi a, R.B. Oberer b, L.G. Chiang b a b
Department of Nuclear Engineering & Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109, USA Y-12 National Security Complex, P.O. Box 2009, Oak Ridge, TN 37831, USA
a r t i c l e i n f o
abstract
Article history: Received 22 May 2012 Received in revised form 14 August 2012 Accepted 5 October 2012 Available online 27 October 2012
Neutron coincidence counting is widely used in nuclear safeguards. Simulations of these systems can be performed using Monte Carlo codes such as MCNPX to aid in calibration or measurement design. However, the MCNPX coincidence-counting routines treat particle histories individually, therefore the dead time of the acquisition electronics is not treated. The MCNPX-PoliMi code provides the ability to model detailed effects such as data-acquisition electronics and system dead times. A specialized postprocessing code has been developed to interpret the collision-log file and determine the response of a 3 He multiplicity counter. The MCNPX-PoliMi simulation provides the full neutron multiplicity distribution measured by the 3He tubes. This distribution is used to compute the singles, doubles, and triples rates which are the quantities used to determine 235U mass. MCNPX-PoliMi has previously been validated with passive multiplicity measurements. In this study, a detailed analysis of the measurement system operating in active mode is presented for uranium-oxide standards ranging from 0.5 to 4.0 kg with a Canberra JCC-51 active well coincidence counter. MCNPX-PoliMi calculations are also compared with MCNPX. The two codes agree to within 1% for the cases with negligible dead times. The simulations are validated with measurements performed at the Y-12 National Security Complex. & 2012 Elsevier B.V. All rights reserved.
Keywords: 3He multiplicity Active well coincidence counter MCNPX-PoliMi
1. Introduction Neutron coincidence counting has been widely used in nuclear safeguards for many years [1–5]. In this method, correlated neutrons distinguish fission sources from (alpha, n) sources to establish a fissile mass. Historically, instruments based on 3He tubes have been used to perform these measurements. One such instrument is an active well coincidence counter (AWCC) [6]. The active source in this instrument is an Am-Li neutron source, which is most-commonly used when assaying uranium samples due to its low spontaneous fission rate. Even in the presence of the current 3He shortage, these instruments are still under investigation due to their ease of use and reliability of operation. There is a desire to replace the 3He that is currently used in AWCCs with other neutron-sensitive materials, such as 10B. Therefore, simulation of these systems is all the more important. Simulations are typically performed using Monte Carlo techniques; in fact, the widely applied MCNPX code has dedicated tallies, specially designed for
n
Corresponding author. Tel.: þ1 734 615 7830; fax: þ1 734 763 4540. E-mail addresses: [email protected] (S.D. Clarke), [email protected] (E.C. Miller), mfl[email protected] (M. Flaska), [email protected] (S.A. Pozzi), [email protected] (R.B. Oberer), [email protected] (L.G. Chiang). 0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2012.10.025
neutron coincidence counting. These tallies have proven accurate in the past when count rates are low and the neutrons from separate fission chains within the sample do not overlap. Under this condition there is negligible dead time. This is because the MCNPX routines treat particle histories individually. Therefore the dead time of the acquisition electronics cannot be treated. The MCNPX-PoliMi code has been developed, along with a module-based detector-response algorithm, to simulate various measurement systems. Recently, the capability has been added to simulate neutron multiplicity counting systems along with all of the associated coincidence acquisition electronics (effects are included such as dead time, pre-delay and shift register timing, etc.). This capability has been validated with passive multiplicity measurements through an ESARDA benchmark exercise with a range of weak and strong sources such as 252Cf and PuO2 [7]. In this work, the MCNPX-PoliMi code is verified and validated for an AWCC, operating in active mode. The verification is performed with calculations from both MCNPX-PoliMi and MCNPX code v. 2.7.0 and compared to experimental data.
2. Experimental setup The experimental data is from measurements performed at the Y-12 National Security Complex using an AWCC and a set of
136
S.D. Clarke et al. / Nuclear Instruments and Methods in Physics Research A 700 (2013) 135–139
93.18%-enriched uranium-oxide (U3O8) powder standards ranging from 0.5 to 4.0 kg made from New Brunswick Laboratory Certified Reference Material 149 [8,9]. These standards are wellcharacterized and the available information contains accurate values for net mass, total uranium mass, 235U mass, and enrichment. The 235U mass of these 93%-enriched standards ranges from 394 to 3151 g. The material is contained in thin-walled stainlesssteel cans with an inner radius of 6.1176 cm and an outer radius of 6.1976 cm. The height of the cans is 17.78 cm and the fill height of the U3O8 powder varies with mass. Table 1 summarizes the physical details of the CRM-149 standards. The results of these measurements were the singles, and doubles rates for each sample, as well as the empty AWCC. The measurements were performed using a Canberra, JCC-51 AWCC operating in active mode [10]. This counter contains 42 3 He tubes arranged in two concentric rings in a high-density polyethylene (density of 0.955 g/cm3) matrix around the sample cavity. Each sample was placed on a 10.16 cm tall stand in the base of the AWCC cavity. Fig. 1 shows an illustration of the MCNPX-PoliMi model of the AWCC. The source strength was calculated based on singles-rate measurement performed with an empty AWCC. This measurement resulted in an Am-Li source strength of 6.02 104 neutrons per second with both sources (upper and lower plugs) were assumed to as the same source strength. In the future, some sensitivity analysis may be done to assess the validity of this assumption. The samples were counted between 10 and 30 min, depending on the mass, and processed using standard shift register with a 4.5 ms pre-delay, a 64 ms counting window, and a 1024 ms accidental-gate delay. Table 1 Physical details of the CRM-149 U3O8 standards. Total mass (g)
235
500 1000 1500 2000 3000 4000
393.79 787.74 1181.62 1575.49 2363.31 3151.13
U mass (g)
Density (g/cm3)a
Fill height (cm)
2.35420 2.35468 2.37136 2.36301 2.36003 2.35896
1.8034 3.6068 5.4102 7.1882 10.7950 14.4018
a Exact density values were calculated in the simulations in order to preserve the specified 235U mass.
3. Description of the MCNPX-PoliMi code The MCNP-PoliMi code was originally developed in 2003 as an extension of the MCNP4c code to enable the simulation of correlated-particle measurements [11]. All previous versions of the MCNP code were incapable of simulating such measurements due to some simplifications and data-handling issues. For example, secondary gamma-ray production was uncorrelated to any individual interaction. Secondary gamma rays are sampled only from average production libraries. Also, the distributions used to sample neutrons produced from fission are simplified to include only two integer values on either side of the mean value. In addition, the MCNP-PoliMi code introduced the ability to write a collision-log file containing all information about the particle interactions inside of user-specified detector cells. It is these data that are used to calculate detector response using a module-based post-processing algorithm. In the years following the release of the MCNP4c code many of its simplifications and assumptions were addressed through the release of the MCNPX code. For example, the MCNPX code has the ability to treat the complete multiplicity distribution of the neutrons emitted from fission events. Furthermore, the MCNPX code has the capability of simulating more complex physics processes such as photonuclear interactions and heavy chargedparticle transport. In 2012 the MCNP-PoliMi modifications were incorporated in the MCNPX, combining all of the PoliMi extensions with the updated physics capabilities of the MCNPX code. This new version is designated MCNPX-PoliMi. A dedicated post-processing module has been developed for the AWCC and its associated acquisition electronics [12]. The detailed collision outputs from MCNPXPoliMi are used to generate a list of detector pulses and acquisition times similar to that obtained in a measurement, where individual detector dead times and electronic effects are explicitly accounted for. The dead times of the individual 3He tubes, amplifiers and the OR gate were assumed to have typical values of 2 ms, 500 ns, and 30 ns. This pulse list is processed with a simulated shift register to obtain the so-called Reals (R) and Reals-plus-Accidentals (Rþ A) frequency distributions which are used to calculate the singles, doubles, and triples count rates from the well-known Eq. (1), where P(n) is the RþA-gate distribution and Q(n) is the A-gate distribution, n is the multiplet, and t is the measurement time [13]. 1X S¼ PðnÞ
t
D¼ T¼
N
" 1 X
t
nUPðnÞ
N
" 1 X nðn1Þ
t
N
2
X
# nUQ ðnÞ
N
X nðn1Þ PðnÞ Q ðnÞ 2 N
!# P X X N nUQ ðnÞ nUPðnÞ nUQ ðnÞ P N Q ðnÞ N N
ð1Þ
3.1. MCNPX-PoliMi results
Fig. 1. Illustration of the MCNPX-PoliMi model of the AWCC.
Using MCNPX-PoliMi and the associated post-processor, detailed simulations of the shift register multiplicity analysis were performed for the U3O8 powder standards ranging in mass from 0.5 to 4.0 kg. Fig. 2 shows the resulting multiplicity distributions in the R þA and A gates for the 4.0 kg standards. The similarity in the two distributions is expected because the count rate is low therefore
S.D. Clarke et al. / Nuclear Instruments and Methods in Physics Research A 700 (2013) 135–139
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Table 2 Multiplicity counting rates for 93% U3O8 standards ranging from 0.5 to 4.0 kg calculated using MCNPX-PoliMi and the post-processing algorithm (si are the statistical uncertainties calculated using the number of counts from the MCNPXPoliMi pulse-train analysis). Total mass (g)
S
sS
D
sD
T
sT
0 500 1000 1500 2000 3000 4000
13,229.7 13,837.5 14,117.4 14,351.0 14,546.7 14,910.7 15,233.8
4.0 4.1 4.1 4.2 4.2 4.2 4.3
1.7 135.1 202.7 262.4 316.0 422.4 531.1
7.0 7.5 7.7 7.9 8.1 8.3 8.6
2.3 17.6 28.0 39.2 48.5 68.7 91.2
8.4 9.3 9.8 10.3 10.6 11.3 12.0
Table 3 Multiplicity counting rates for 93% U3O8 samples ranging from 0.5 to 4.0 kg calculated using MCNPX v. 2.7.0 (si are the statistical uncertainties calculated by MCNPX). Fig. 2. Rþ A- and A-gate multiplicity distributions for the 4 kg standard of 93%-enriched U3O8; one-sigma statistical error bars are included.
Total mass (g)
S
sS
D
sD
T
sT
0 500 1000 1500 2000 3000 4000
13,253.1 13,864.6 14,148.4 14,380.5 14,584.7 14,947.4 15,299.9
5.3 69.3 58.0 53.2 49.6 44.8 41.3
0.0 135.9 204.7 264.9 320.3 431.6 549.3
0.0 0.8 1.0 1.2 1.3 1.6 1.8
0.0 16.3 26.7 38.1 48.7 72.4 96.9
0.0 0.3 0.4 0.6 0.7 0.9 1.0
4. Comparison with MCNPX
Fig. 3. Rþ A-gate multiplicity distributions for 93%-enriched U3O8 samples ranging from 0.5 to 4.0 kg calculated using MCNPX-PoliMi and the associated post-processing algorithm; one-sigma statistical error bars are included.
the accidentals contribute greatly to the total measured rates. Fig. 3 shows the RþA-gate distributions for all samples. The distributions peak at zero, which means that multiplicity windows containing only a single neutron are the most probable for all of the samples. The distributions then fall-off nearly exponentially until multiplets of nearly 10 (the A-gate distribution ends at 9 due to poor statistics). As expected, larger masses result in more counts at higher multiplets. The R þA-gate distribution is higher than that A-gate distribution at higher multiplets, illustrating the influence of the accidental background above the induced fission neutrons from the U3O8. The multiplicity distributions were used to calculate the multiplicity counting rates using Eq. (1). These rates are wellknown quantities that are closely correlated to fissile mass. In fact, the doubles-rate is used in nuclear safeguards applications to assay the fissile mass of unknown samples, or to verify the fissile mass of declared samples. Consequently, the ability to accurately simulate these rates is of great interest. Table 2 summarizes the multiplicity counting rates and the corresponding statistical uncertainties calculated by MCNPX-PoliMi for each of the U3O8 standards.
The most-recent versions of the MCNPX code have a specialized pulse height tally that can be used for correlated-particle counting [14]. This tally scores the number of capture reactions on a specific nuclide at the end of each history, with time gating and pre-delay windows available, making this tally easily applicable to neutron multiplicity counting. The MCNPX tally scores within each particle-history independently, making it a fundamentally different approach than the MCNPX-PoliMi post-processing algorithm discussed in Section 3. In particular, there is no consideration given to the accidental background as treated in the MCNPX-PoliMi code. Because of this, the MCNPX tally results can be understood as ideal multiplicity counting rates, in the absence of accidental background and detector dead time. In order to verify the results obtained from the MCNPX-PoliMi code, independent simulations were performed using MCNPX v. 2.7.0. Table 3 summarizes multiplicity counting rates calculated by MCNPX v. 2.7.0. Excellent agreement is observed between the codes implying that the difference between the simulated and experimental results is caused by the difference between the model and the physical AWCC. For this configuration the effects of accidental background and detector dead time are minimal. In other configurations where the effects are large, the results of the two codes are expected to differ. Table 4 shows the ratio of the multiplicity counting rates calculated by MCNPX-PoliMi to those calculated by MCNPX. The relative uncertainties of the codes were added in quadrature to compute the combined uncertainty displayed in Table 4.
5. Experimental validation 5.1. Comparison to simulated results The measurements described in Section 2 produced singles and doubles rates for the entire range of U3O8 masses. The triples
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Table 4 Ratio of the multiplicity counting rates calculated by MCNPX-PoliMi to those calculated by MCNPX (si are the combined statistical uncertainties calculated by the two codes). Total Mass (g)
S
sS
D
sD
T
sT
0 500 1000 1500 2000 3000 4000
0.998 0.998 0.998 0.998 0.997 0.998 0.996
0.001 0.005 0.004 0.004 0.003 0.003 0.003
– 0.994 0.990 0.991 0.987 0.979 0.967
– 0.056 0.038 0.030 0.025 0.020 0.016
– 1.085 1.048 1.029 0.996 0.949 0.942
– 0.576 0.368 0.270 0.219 0.157 0.124
Fig. 5. Comparison of simulated and measured doubles rates for various U3O8 masses.
Table 5 Sensitivity of the calculated doubles-rate with respect to the R þA- and A-gate distributions. 235
Fig. 4. Comparison of simulated and measured singles rates for various U3O8 masses.
rates were not recorded due to short counting times and low detection efficiency (singles are detected with efficiency e, doubles with efficiency e2, and triples with efficiency e3). Fig. 4 shows a comparison of singles rates calculated by MCNPX-PoliMi, MCNPX v. 2.6.0, and the experimental data. As noted earlier, the two Monte Carlo codes agree very well with one-another. There is a slight (less than 3.5%) positive bias in both codes relative to the experimental data for the entire range of 235 U masses. Furthermore, the bias is nearly a constant 340 counts per second for the entire range of 235U masses. This bias could be due to a number of factors: the polyethylene density, the 3 He density, the position of the AmLi sources within the plugs, and the relative strength of the AmLi sources. The contribution of these uncertainties to the observed agreement is difficult to predict; however, a rigorous sensitivity analysis could be done in the future. Fig. 5 shows a comparison of doubles rates calculated by MCNPX-PoliMi, MCNPX v. 2.7.0, and the experimental data. As noted earlier, the two Monte Carlo codes agree very well with one-another but again there is a positive bias in both codes relative to the experimental data. The bias is nearly a constant 60 counts per second for the entire range of 235U masses.
5.2. Sensitivity analysis The multiplicity counting rates are calculated as the difference of the moment of the RþA- and A-gate distributions, which are very similar to one-another as shown in Fig. 1. Table 4 shows the ratio of the number of counts in the A-gate to the number of counts in the RþA-gate (G) for both the measurement and the
U mass (g)
0 393.79 787.74 1181.62 1575.49 2363.31 3151.13
Gmeasured
Gsimulated
dG (%)
dD (%)
S
1.000 0.993 0.988 0.984 0.981 0.974 0.970
1.000 0.988 0.984 0.980 0.977 0.971 0.967
– 0.49 0.39 0.39 0.37 0.34 0.24
– 83.27 40.32 31.13 25.22 20.66 13.90
– 168.7 102.5 80.8 68.9 60.3 58.5
simulation.
G¼
NA NR þ A
ð2Þ
For the empty AWCC, G is equal to 1.000 because the counts are entirely accidentals. As samples of increasing mass are measured, G decreases to 0.970. In other words, the number of counts in the R þA-gate is at most 3% greater than the number of counts in the A-gate. A sensitivity coefficient, S, was defined as the ratio of the percent difference in the doubles-rate, dD to the percent difference in G, dG. The percent differences were computed as the MCNPX-PoliMi simulation results relative to the measured results.
dD S ¼ dG
ð3Þ
Table 5 contains the sensitivity coefficient for each of the U3O8 samples. At most, dG is 0.5% less in the simulation versus the measurement while dD can be as large as 83%. This shows that very small fluctuations in the A-gate counts can lead to a dramatic change in the calculated doubles-rate. Furthermore, it is conceivable that either the MCNP simulations or the measurements have A-gate errors on the order of 0.5%, which lead to the observed doubles-rate differences. For example, there could be slight discrepancies in the geometrical or material model of the AWCC leading to differing detection efficiency. Also, the assumption was made that the two AmLi sources have the same strength; in reality, this may not be the case.
S.D. Clarke et al. / Nuclear Instruments and Methods in Physics Research A 700 (2013) 135–139
6. Conclusions The full multiplicity distributions for New Brunswick National Laboratory CRM-149 HEU-oxide samples in an AWCC have been calculated using the MCNPX-PoliMi code. The resulting singles, doubles, and triples rates were also calculated and compared to results from MCNPX v. 2.7.0 for verification. The two codes agree well with one-another (within less than 1%) for all three multiplicity rates at each sample mass. It is expected that the MCNPXPoliMi and MCNPX multiplicity results would differ more for cases with non-negligible dead times. This is caused by the fact that the MCNPX tally scores within each history independently, making the multiplicity counting rates ideal (absence of accidental background and detector dead time). The singles and doubles rates were compared to experimental data from the Y-12 National Security Complex collected with a Canberra, JCC-51 AWCC. There were slight positive biases observed in both the singles and doubles rates: approximately 340 counts per second for the singles and approximately 60 counts per second for the doubles. These biases can be understood given the high sensitivity on the multiplicity rates to small fluctuation in the A-gate distributions. In fact, a change of less than 0.5% simulated A-gate distribution would correct the observed bias in the doubles count rates.
Acknowledgment The authors would like to thank Dr. B. Dahl from Chalmers University of Technology, Sweden for providing the initial MCNPX model upon which this work was based. This research was partially funded by the National Science Foundation and the Domestic Nuclear Detection Office of the
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Department of Homeland Security through the Academic Research Initiative Award # CMMI 0938909.
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