Analytical Validation of Uncertainty in Reactor Physics Parameters for Nuclear Transmutation Systems

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1 Journal of Nuclear Science and Technology ISSN: (Print) (Online) Journal homepage: Analytical Validation of Uncertainty in Reactor Physics Parameters for Nuclear Transmutation Systems Takanori SUGAWARA, Kenji NISHIHARA, Kazufumi TSUJIMOTO, Toshinobu SASA & Hiroyuki Oigawa To cite this article: Takanori SUGAWARA, Kenji NISHIHARA, Kazufumi TSUJIMOTO, Toshinobu SASA & Hiroyuki Oigawa (21) Analytical Validation of Uncertainty in Reactor Physics Parameters for Nuclear Transmutation Systems, Journal of Nuclear Science and Technology, 47:6, To link to this article: Published online: 5 Jan 212. Submit your article to this journal Article views: 25 View related articles Citing articles: 8 View citing articles Full Terms & Conditions of access and use can be found at

2 Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 47, No. 6, p (21) ARTICLE Analytical Validation of Uncertainty in Reactor Physics Parameters for Nuclear Transmutation Systems Takanori SUGAWARA, Kenji NISHIHARA, Kazufumi TSUJIMOTO, Toshinobu SASA y and Hiroyuki OIGAWA Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki , Japan (Received November 13, 29 and accepted in revised form February 12, 21) To confirm the reliability of calculated reactor physics parameters for the nuclear transmutation systems, the uncertainty deduced from the covariance data prepared in JENDL-3.3 is compared with the differences in the reactor physics parameters in the Monte-Carlo calculation using different nuclear data libraries, ENDF/B-VII. and JEFF The Accelerator-Driven System (ADS) and the Minor Actinide (MA)-loaded Fast Reactor (FR) are selected as the representative transmutation systems. The criticality and void reactivity of these systems are discussed. The results show that the uncertainties deduced from the JENDL-3.3 covariance data are smaller than the differences in the reactor physics parameters among the nuclear data libraries. The cause of this discrepancy is that the covariance data of main nuclides and reactions in JENDL-3.3 are smaller than the relative differences in the cross sections among the nuclear data libraries. It is required to verify the uncertainty of the reactor physics parameters by integral experiments and to discuss the uncertainty utilization for the nuclear design accuracy. KEYWORDS: nuclear design accuracy, nuclear data library, covariance data, sensitivity coefficient, transmutation system, accelerator-driven system, fast reactor, JENDL-3.3, ENDF/B-VII., JEFF I. Introduction Research and Development (R&D) for transmutation systems such as Accelerator-Driven System (ADS) and Minor Actinide (MA)-loaded Fast Reactor (FR) has been performed worldwide. Since uncertainties of the current MA nuclear data are supposed to be larger than those of other major nuclides, it is considered that the analyzed reactor physics parameters of transmutation systems should have much larger design margins than those of conventional nuclear reactors. Therefore, it is one of the most important issues in R&D to discuss the nuclear design accuracy of the transmutation system. Recently, the uncertainty analysis using covariance data prepared in a nuclear data library and sensitivity coefficients has been carried out and discussed. 1 4) Since this procedure is available to estimate the uncertainty deduced from the covariance data quantitatively, it has been used for the discussion of target accuracies of nuclear systems, 1,2) criticality safety assessment, 3) and evaluation of the effect of hypothetical MA-loaded critical experiments for a reduction of the uncertainty. 4) In these analyses, the reliability of the results was based on the covariance data used. However, Corresponding author, sugawara.takanori@jaea.go.jp y Present address: Atomic Energy Commission of Japan, Kasumigaseki, Chiyoda-ku, Tokyo 1-897, Japan ÓAtomic Energy Society of Japan verifications of the uncertainty deduced from the covariance data have not been performed comprehensively. In this paper, the uncertainty deduced from the covariance data and Monte-Carlo calculation results are compared to verify the reliability of the uncertainty for transmutation systems. As the transmutation systems, an ADS and an MA-loaded FR were employed as the representative systems. In the Monte-Carlo calculation, differences in reactor physics parameters among nuclear data libraries were employed for the comparison. Although calculation results and the uncertainty deduced from the covariance data should normally be discussed based on the experimental data, it is difficult to obtain the experimental data for the transmutation systems due to a treatment of MA fuels. Thus, the comparisons with the Monte-Carlo calculation results were performed to discuss the reliability of the uncertainty for transmutation systems. II. Calculation Condition 1. Core Specification (1) ADS As a transmutation system, the ADS investigated in the Japan Atomic Energy Agency (JAEA) was employed. In Ref. 5), various concepts of the ADS core were investigated to achieve the power flattening. In the present paper, the basic ADS concept in Ref. 5) was selected; namely, an 8 MWt lead-bismuth eutectic (LBE) cooled single-zone 521

3 522 T. SUGAWARA et al. Table 1 Main parameter of transmutation systems ADS MA-loaded FR Fuel (MA+Pu)N MOX Coolant LBE Na Thermal Power [GWt] Operation period [EFPDs] a) Pu ratio [wt%] b) /21.6 c) MA ratio [wt%] b) a) Effective Full Power Day. For FR, 8[EFPDs] 4 batch. b) Weight ratio to heavy metal c) Inner/Outer core Table 2 Isotopic composition (Pu) ADS MA-loaded FR Pu % 2.7% Pu % 54.9% Pu % 3.7% Pu % 1.5% Pu % 1.2% Table 3 Isotopic composition (MA) ADS a) MA-loaded FR Np % 35.4% Am % 54.5% Am-242m.6% Am % 9.6% Cm-243.3% Cm %.5% Cm % Cm-246.4% a) Due to the half adjust, the total is not 1% Fig. 1 RZ calculation model for the ADS ADS with nitride fuel, which can transmute about 25 kg of MA per year. The main parameters of the ADS are shown in Table 1. The isotopic compositions of Pu and MA were based on the PWR spent fuel of 45 GWd/tHM burnup with 7 years of cooling. The compositions of Pu and MA are summarized in Tables 2 and 3, respectively. The RZ calculation model is employed in both the uncertainty analysis and Monte-Carlo calculation. The model is shown in Fig. 1. Other detailed conditions were described in Ref. 5). (2) MA-Loaded FR As another transmutation system, an MA-loaded FR based on the concept investigated in the feasibility study in Japan 6) was selected. It is a 3,6 MWt sodium-cooled FR core with MOX fuel. The RZ calculation model of the FR is shown in Fig. 2. In the feasibility study, some core concepts were discussed to transmute MA discharged from various fuel cycles. As the extreme case of the transition phase in the fast reactor cycle, the composition 6) mixing three spent fuels was employed, namely, LWR-MOX spent fuel of GWd/HMt burnup after 11 years of cooling, LWR spent fuel of GWd/HMt burnup after 9 years of cooling, and Advanced Light Water Reactor (ALWR) spent fuel of Fig. 2 RZ calculation model for the MA-loaded FR 6 GWd/HMt burnup after 4 years of cooling. The reason for selecting the extreme case was that it was expected that the uncertainty of this case was larger than that of other typical cases for the transition phase. These compositions are also summarized in Tables 2 and 3. The weight ratio of MA to heavy metal was 5.% in both inner and outer core regions. Other detailed conditions were described in Ref. 6). JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

4 Analytical Validation of Uncertainty in Reactor Physics Parameters for Nuclear Transmutation Systems 523 Table 4 (FR) Current status of covariance data prepared in JENDL-3.3 Table 5 Current status of covariance data prepared in JENDL-3.3 (ADS inherent nuclides) Nuclide Capture Fission Elastic Inelastic -bar U-235 J33 J33 J33 J33 J33 J33 J33 U-238 J33 J33 J33 J33 J33 J33 J33 Pu-238 J33 J33 Prov. Prov. Prov. x x Pu-239 J33 J33 J33 J33 J33 J33 J33 Pu-24 J33 J33 J33 J33 J33 J33 J33 Pu-241 J33 J33 J33 J33 J33 x J33 Pu-242 J33 J33 Prov. Prov. Prov. x x Np-237 J33 J33 J33 Prov. Prov. x x Am-241 J33 J33 J33 Prov. Prov. x x Am-243 J33 J33 J33 Prov. Prov. x x Cm-244 J33 J33 Prov. Prov. Prov. x x O J33 J33 J33 J33 Fe J33 J33 J33 J33 Cr J33 J33 J33 J33 Ni J33 J33 J33 J33 Na J33 J33 J33 J33 is the fission spectrum. -bar is the direction cosine of elastic scattering. J33 means that the data are prepared in JENDL-3.3. Prov. means the provisional data. x means no data. Nuclide Capture Fission Elastic Inelastic -bar Am-242m J33 J33 Prov. Prov. Prov. x x Cm-243 Prov. Prov. Prov. Prov. Prov. x x Cm-245 Prov. Prov. Prov. Prov. Prov. x x Cm-246 Prov. Prov. Prov. Prov. Prov. x x N-15 Prov. J33 Prov. x Zr-9 J33 Prov. J33 x Zr-91 Prov. Prov. Prov. x Zr-92 Prov. Prov. Prov. x Zr-94 Prov. Prov. Prov. x Zr-96 Prov. Prov. Prov. x Pb-24 Prov. Prov. Prov. x Pb-26 Prov. Prov. J33 x Pb-27 Prov. Prov. J33 x Pb-28 Prov. Prov. J33 x Bi-29 Prov. Prov. J33 x is the fission spectrum. -bar is the direction cosine of elastic scattering. J33 means that the data are prepared in JENDL-3.3. Prov. means the provisional data. x means no data. The ADS contains Pu isotopes, MA isotopes, and structure material nuclides (Fe, Cr, Ni) presented in Table Uncertainty Analysis Using Covariance Data The uncertainty analysis was performed by using the covariance data matrix M prepared in JENDL ) and a sensitivity coefficient matrix G. In the uncertainty analysis, the uncertainty deduced from the covariance data is calculated using GMG t (t means a transposition). 11,12) For the covariance data, although the data for many nuclides and reactions for the FR analysis were prepared, the data for the ADS such as Pb and Bi isotopes were not prepared sufficiently in JENDL-3.3. In the present study, provisional covariance data 13) of these nuclides and reactions were employed. Table 4 summarizes the current status of the covariance data for the MA-loaded FR, and Table 5 presents the covariance data for ADS inherent nuclides. By adding the provisional data, covariance data of almost all the nuclides and reactions required in this study were considered. Sensitivity coefficients for the criticality and void reactivity (the coolant volume fraction at the core region was changed to %) were calculated using the SAGEP code 14) with 18-energy group structure from 1 ev to 1 MeV. This calculation code can be used to calculate the sensitivity coefficient for static characteristics such as the criticality or a reactivity change on the basis of the diffusion theory. In the SAGEP calculation, SLAROM code 15) was employed for the generation of the effective cross sections, where JAERI Fast Set (JFS-3) 16) based on JENDL-3.3 was used as the nuclear data library. 3. Monte-Carlo Calculation For the Monte-Carlo Calculation, the MCNPX code 17) (version 2.7a) was employed. The RZ calculation models shown in Figs. 1 and 2 were also employed in these calculations. As the nuclear data library, JENDL-3.3, ENDF/ B-VII., 18) and JEFF ) were used. The criticality and Table 6 void reactivity (the coolant volume fraction was % at the core region) of each system were calculated with each nuclear data library. III. Results and Discussion Uncertainty analysis result k eff GMG t a) Void reactivity [k=k] GMG t a) ADS % 5: % MA-loaded FR % 3: % FR Target Accuracy b) :3%k (1) 1. Uncertainty Analysis Result The results of the uncertainty analysis are summarized in Table 6. In this table, the k eff values and void reactivity are shown with their uncertainties deduced from the JENDL-3.3 covariance data (shown as GMG t ). This table also presents the target accuracy for the FR nuclear design investigated in Ref. 2). The uncertainties of the criticality were 1.3 and 1.1% for the ADS and MA-loaded FR, respectively. These values were larger than the FR target value. However, it was confirmed that the uncertainty for the MA-loaded FR would be reduced below the target accuracy by the cross-section adjustment method 11,12) and MA-loaded critical experiments. 4) For the void reactivity, the uncertainties were 6.9 and 2.6% for the ADS and FR, respectively. These results satisfied the FR target value. 2% (2) a) Uncertainty deduced from the covariance data (JENDL-3.3) (confidence interval: 1) b) From Ref. 2). Confidence interval is shown in parentheses. VOL. 47, NO. 6, JUNE 21

5 524 T. SUGAWARA et al. Uncertainty deduced from covariance data [%] Inelastic Elastic ν Fission Capture ADS: Criticality Pu 24 Pb 24 Pb 26 Pb 27 Pb 28 Bi 29 N 15 Uncertainty deduced from covariance data [%] U 235 U 238 Pu 24 FR: Criticality Inelastic Elastic ν Fission Capture Na 23 Fe Fig. 3 Uncertainty deduced from the covariance data for the criticality of the ADS Fig. 5 Uncertainty deduced from the covariance data for the criticality of the MA-loaded FR Uncertainty deduced from covariance data [%] Inelastic Elastic ν Fission Capture ADS: Void reactivity Pu 24 Pb 24 Pb 26 Pb 27 Pb 28 Bi 29 N 15 Uncertainty deduced from covariance data [%] U 235 U 238 Inelastic Elastic ν Fission Capture Pu 24 FR: Void reactivity Na 23 Fe Fig. 4 Uncertainty deduced from the covariance data for the void reactivity of the ADS Fig. 6 Uncertainty deduced from the covariance data for the void reactivity of the MA-loaded FR Figures 3 and 4 show details of the uncertainties of the criticality and void reactivity of the ADS, respectively. For the criticality, the contributions of MA nuclides were significant. The contributions of 239 Pu fission and 29 Bi and 15 N elastic scattering reaction were also confirmed for the ADS criticality. For the void reactivity, 239 Pu fission reaction, capture reactions of MA isotopes, and inelastic scattering reactions of Pb isotopes and 29 Bi were the main causes of the uncertainty. The details of the criticality and void reactivity of the MA-loaded FR are illustrated in Figs. 5 and 6. For the criticality of the FR, 238 U inelastic scattering and 239 Pu fission reaction were the main causes of the uncertainty. It was also observed that 238 Pu, 24 Pu, and 242 Pu values, and 241 Am capture and nat Fe inelastic scattering reactions contributed to the uncertainty. Figure 6 indicates that 238 U inelastic scattering, 239 Pu fission, and 241 Am capture reactions were the main causes of the void reactivity uncertainty. It was also confirmed that the contributions of 23 Na and nat Fe were also large in this case. 2. Monte-Carlo Calculation Result (1) Comparison of Uncertainty with Difference in Reactor Physics Parameter among Nuclear Data Libraries Table 7 presents the MCNPX calculation results for the ADS. Standard deviations as the statistical error were very small in all the cases; on the other hand, there were clear differences between the results with each nuclear data library. The difference (ðiþ) from the result calculated with JENDL-3.3 was estimated using the following equation: JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

6 Analytical Validation of Uncertainty in Reactor Physics Parameters for Nuclear Transmutation Systems 525 Table 7 MCNPX calculation result (ADS) Table 9 MCNPX calculation result (MA-loaded FR) k eff SD a) Void reactivity [k=k] SD a) JENDL : : :1 1 4 ENDF/B-VII : : :2 1 4 JEFF : : :3 1 4 a) Standard deviation (confidence interval: 1) k eff SD a) Void reactivity [k=k] SD a) JENDL : 1 5 2: :2 1 5 ENDF/B-VII : 1 5 2: :2 1 5 JEFF : 1 5 2: :2 1 5 a) Standard deviation (confidence interval: 1) Table 8 Difference from JENDL-3.3 result in MCNPX calculation (ADS) k eff Void reactivity (ENDF/B-VII.) 2.2% 28.7% (JEFF-3.1.1) 2.8% 23.9% GMG t a) 1.3% 6.9% a) Uncertainty shown in Table 6 Table 1 Difference from JENDL-3.3 result in MCNPX calculation (MA-loaded FR) k eff Void reactivity (ENDF/B-VII.).5% 5.8% (JEFF-3.1.1) 1.3% 5.4% GMG t a) 1.1% 2.6% a) Uncertainty shown in Table 6 ðiþ ¼ absðx i x j33 Þ ; ð1þ x j33 where i is the nuclear data library (ENDF/B-VII. or JEFF ), x i is the value of k eff or the void reactivity calculated using library i, and x j33 is the value of k eff or the void reactivity calculated with JENDL-3.3. Table 8 shows ðiþ values for the ADS. This table also presents the uncertainties deduced from the JENDL-3.3 covariance data. From this table, it was found that the uncertainties deduced from the JENDL-3.3 covariance data were smaller than the differences in the reactor physics parameters among the nuclear data libraries. For the criticality, the difference by using JEFF was more than twice as large as the uncertainty deduced from the JENDL-3.3 covariance data. The difference by using ENDF/B-VII. was about 4.2 times larger than the uncertainty deduced from the JENDL- 3.3 covariance data for the void reactivity. The differences in the void reactivity did not satisfy the FR target accuracy shown in Table 6, although the uncertainty deduced from the JENDL-3.3 covariance data satisfied it. Table 9 presents the MCNPX calculation results for the MA-loaded FR, and Table 1 indicates their ðiþ values. The same tendency described above was confirmed in the FR case. From Table 1, the differences in the criticality and void reactivity by using JEFF were about 1.2 and 2.1 times larger than the uncertainties deduced from the JENDL-3.3 covariance data, respectively. For the void reactivity, the difference by using ENDF/B-VII. was about 2.2 times larger than the uncertainty deduced from the JENDL-3.3 covariance data, although the difference satisfied the FR target accuracy. (2) Investigation into the Cause of Difference in MCNPX Calculation To investigate the cause of those differences among the nuclear data libraries in the MCNPX calculations, calculations with changing the nuclear data library from JENDL-3.3 to ENDF/B-VII. or JEFF for each nuclide were performed. Figure 7 presents the calculation results of the ADS criticality for dominant nuclides. In this figure, Pu-238 keff ENDF/B VII. JEFF ADS: Criticality JENDL 3.3 Pu 24 Pb 24 Pb 26 Pb 27 Pb 28 Bi 29 N 15 Fig. 7 Effective multiplication factor by changing the nuclear data library from JENDL-3.3 to ENDF/B-VII. or JEFF for the ADS. Pu-238 means the result by using the input data whose nuclear data library was JENDL-3.3 except 238 Pu. Then, as the nuclear data library of 238 Pu, ENDF/B-VII. or JEFF was employed. corresponds to the result shown in Table 7. means the result by using the input data whose nuclear data library was JENDL-3.3 except 238 Pu. Then, as the nuclear data library of 238 Pu, ENDF/B-VII. or JEFF was employed. The results in Fig. 7 correspond to the results shown in Table 7. These calculation results indicated that 26 Pb, 27 Pb, and 15 N were the main causes in both ENDF/B-VII. and JEFF cases. The difference was about :7%k when the nuclear data library of 26 Pb was changed to ENDF/B-VII. or JEFF In the ENDF/ B-VII. case, 243 Am was also the main cause and the difference was about :3%k. In the JEFF case, the contributions of 237 Np and 241 Am were large and the differences were about :3%k and :7%k, respectively. The results of the ADS void reactivity are shown in Fig. 8. From this figure, it was found that the contributions of Pb iso- VOL. 47, NO. 6, JUNE 21

7 526 T. SUGAWARA et al. 5.5x1 2 JENDL 3.3 ADS: Void reactivity 3.1x1 2 3.x1 2 FR: Void reactivity JENDL 3.3 Reactivity [ k/k] 5.x x1 2 4.x1 2 ENDF/B VII. JEFF Reactivity [ k/k] 2.9x x1 2 ENDF/B VII. JEFF x1 2 Pu 24 Pb 24 Pb 26 Pb 27 Pb 28 Bi 29 N 15 U 235 U 238 Pu 24 Na 23 Fe 56 Fig. 8 Void reactivity by changing the nuclear data library from JENDL-3.3 to ENDF/B-VII. or JEFF for the ADS keff ENDF/B VII. JEFF FR: Criticality JENDL 3.3 U 235 U 238 Pu 24 Na 23 Fe 56 Fig. 9 Effective multiplication factor by changing the nuclear data library from JENDL-3.3 to ENDF/B-VII. or JEFF for the MA-loaded FR topes were very large in both ENDF/B-VII. and JEFF cases. The maximum difference was about :65%k=k for 26 Pb. For other nuclides, 24 Pu and 237 Np showed a significant effect in the ENDF/B-VII. case. In the JEFF case, 239 Pu, 241 Am, and 29 Bi were the main causes and the maximum difference was about :13%k=k in the 29 Bi case. Figures 9 and 1 show the calculation results for the criticality and void reactivity of the FR, respectively. In the calculation of the criticality, Table 1 shows that the difference by using ENDF/B-VII. was small. On the other hand, that by using JEFF was large. Then, Fig. 9 indicates that the differences by changing 238 Pu, 239 Pu, 24 Pu, and 241 Am were the main causes of the difference in the JEFF case. It was also confirmed that there were the contributions of 23 Na and 56 Fe in both library cases. Figure 1 shows that the contribution of 23 Na was very large in both ENDF/B-VII. and JEFF cases. Additionally, 239 Pu and 56 Fe were also remarkable in the JEFF case. Fig. 1 Void reactivity by changing the nuclear data library from JENDL-3.3 to ENDF/B-VII. or JEFF for the MA-loaded FR 3. Discussion (1) Difference by Changing Nuclear Data Library The cross section data of seven nuclides were compared to discuss the causes of the differences among the nuclear data shown above. The seven nuclides, 241 Am, 24 Pu, 26 Pb, 15 N, 239 Pu, 23 Na, and 56 Fe, were selected as the main responsible nuclides from the results in Figs. 7 through 1. The reactions for these nuclides were decided based on the results in Figs. 3 through 6. The differences by changing 241 Am and 24 Pu nuclear data library were large in the calculation for the criticality of both the ADS and FR. Figure 11 shows relative changes in the 241 Am capture cross section between JENDL-3.3 and ENDF/B-VII. or JEFF Figure 12 presents the relative changes in the 24 Pu fission cross section. The relative change (RC) was calculated as RC ¼ ð i j33 Þ ; ð2þ j33 where i is the nuclear data library (ENDF/B-VII. or JEFF ), i is the cross section in the library i, and j33 is the cross section in JENDL-3.3. These figures also illustrate the sensitivity coefficients for the criticality of the ADS and FR calculated using the SAGEP code and the relative standard deviation of the covariance data prepared in JENDL-3.3. Since the contribution of the capture reaction was large in Figs. 3 and 5, the capture reaction was selected for the discussion of 241 Am. Although the contribution of the value was large in Figs. 3 and 5 for 24 Pu, the fission reaction was chosen because the relative change in the 24 Pu value was small but that of the fission reaction was very large. For the 241 Am capture reaction, the sensitivity coefficients for the ADS and FR criticality were negative values in the whole energy range. It means that the k eff value decreases (increases) when a summation of the relative change is positive (negative). In terms of JEFF-3.1.1, the cross section was the same as that of JENDL-3.3 from 4 kev to 2 MeV, and JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

8 Analytical Validation of Uncertainty in Reactor Physics Parameters for Nuclear Transmutation Systems 527 Sensitivity coeff. [x1 4 ] Rel. change (ENDF/B VII.) : Capture ADS criticality 12 FR criticality Fig. 11 Relative changes in the 241 Am capture cross section between JENDL-3.3 and ENDF/B-VII. or JEFF and sensitivity coefficients for the criticality of the ADS and MA-loaded FR. SD means the relative standard deviation of the covariance data prepared in JENDL-3.3. Sensitivity coefficients were calculation results by the SAGEP code. Sensitivity coeff. [x1 4 ] ADS criticality FR criticality Pu 24: Fission Rel. change (ENDF/B VII.) Fig. 12 Relative changes in the 24 Pu fission cross section between JENDL-3.3 and ENDF/B-VII. or JEFF and sensitivity coefficients for the criticality of the ADS and MA-loaded FR Sensitivity coeff. [x1 4 ] Rel. change (ENDF/B VII.) ADS criticality ADS void reactivity Pb 26: Inelastic Fig. 13 Relative changes in the 26 Pb inelastic scattering cross section between JENDL-3.3 and ENDF/B-VII. or JEFF and sensitivity coefficients for the criticality and void reactivity of the ADS Sensitivity coeff. [x1 4 ] Rel. change (ENDF/B VII.) ADS criticality ADS void reactivity N 15: Elastic Fig. 14 Relative changes in the 15 N elastic scattering cross section between JENDL-3.3 and ENDF/B-VII. or JEFF and sensitivity coefficients for the criticality and void reactivity of the ADS the relative change in this energy range was zero. The relative change below 4 kev was roughly negative. This is the main reason why the k eff values for 241 Am in Figs. 7 and 9 were larger than that of JENDL-3.3. It was also observed that the relative standard deviation in JENDL-3.3 covered the relative changes. For the 24 Pu fission reaction, it was found from Fig. 12 that the sensitivity coefficients for the ADS and FR criticality were positive values in the whole energy range. The relative changes were larger than the relative standard deviation below the hundreds of kev region. It seemed that the relative change for JEFF was positive totally in the tens to hundreds of kev region, which had the unignorable sensitivity. Hence, the k eff values for 24 Pu in Figs. 7 and 9 were larger than that of JENDL-3.3, especially in the JEFF case. Figures 7 and 8 indicate that typical nuclides for the ADS such as Pb isotopes and 15 N also affected the differences in the ADS criticality and void reactivity. For the discussion, 26 Pb inelastic scattering and 15 N elastic scattering reactions were selected as typical nuclides and reactions. Figures 13 and 14 present the relative changes in the cross sections, relative standard deviations, and sensitivity coefficients for the 26 Pb inelastic scattering and 15 N elastic scattering reactions, respectively. It was observed for the 26 Pb inelastic scattering reaction that the same data were employed in ENDF/B-VII. and JEFF-3.1.1, and the absolute value of the relative change was larger than the relative standard deviation in JENDL-3.3 at a MeV region. The maximum change was about 35% in the MeV region, and the sensitivities were large in this energy region. It was guessed that the large differences in VOL. 47, NO. 6, JUNE 21

9 528 T. SUGAWARA et al. Sensitivity coeff. [x1 4 ] Rel. change (ENDF/B VII.) FR criticality 4 FR void reactivity : Fission Fig. 15 Relative changes in the 239 Pu fission cross section between JENDL-3.3 and ENDF/B-VII. or JEFF and sensitivity coefficients for the criticality and void reactivity of the MA-loaded FR Sensitivity coeff. [x1 4 ] Rel. change (ENDF/B VII.) FR criticality FR void reactivity Na 23: Elastic Fig. 16 Relative changes in the 23 Na elastic scattering cross section between JENDL-3.3 and ENDF/B-VII. or JEFF and sensitivity coefficients for the criticality and void reactivity of the MA-loaded FR the MCNPX calculations were caused by these reasons. The same tendency was observed for Pb-27, which also led to the large differences in the MCNPX calculations for the ADS. From Fig. 14, it was found that the same data were also used in ENDF/B-VII. and JEFF for the 15 N elastic scattering reaction. The relative change was beyond the relative standard deviation in JENDL-3.3 in almost all energy regions. It was considered that this large discrepancy in the 15 N elastic scattering reaction caused the differences in the 15 N case in Figs. 7 and 8. For the FR, the cases for 238 Pu, 239 Pu, 23 Na, and 56 Fe were remarkable from Figs. 9 and 1 except for 24 Pu and 241 Am, which were mentioned above. In this study, the discussion was focused on 239 Pu fission, 23 Na elastic scattering, and 56 Fe inelastic scattering reactions. In the case of 238 Pu, the same tendency discussed in the case of 24 Pu was observed; namely, the relative changes in the fission reaction, which were larger than the relative standard deviation in JENDL- 3.3, were the major cause. Figure 15 shows the comparison of the relative change in the cross section and the relative standard deviation with the sensitivity coefficients for the 239 Pu fission reaction. It was found that the sensitivity coefficients of the 239 Pu fission reaction were much larger than those of other nuclides and reactions. Hence, even if the relative changes in the cross section for the nuclear data libraries were small, there would be the possibility of causing a large difference with a small change in the cross section. Figure 15 shows that the relative changes in the Pu-239 fission cross section were very small above 3 kev and those were the same in the 2 3 kev region for ENDF/B-VII. and JEFF-3.1.1, and a large change was observed in the 1 2 kev region for ENDF/ B-VII.. As the result, the differences in the case of 239 Pu shown in Figs. 9 and 1 were very small for the criticality and void reactivity for ENDF/B-VII.. On the other hand, the differences were large in both results for JEFF It Sensitivity coeff. [x1 4 ] Rel. change (ENDF/B VII.) FR criticality FR void reactivity Fe 56: Inelastic Fig. 17 Relative changes in the 56 Fe inelastic scattering cross section between JENDL-3.3 and ENDF/B-VII. or JEFF and sensitivity coefficients for the criticality and void reactivity of the MA-loaded FR is, therefore, required to improve the cross section accuracy of the 239 Pu fission reaction in the 1 3 kev region. Figures 5 and 6 indicate that all the reactions, namely, capture, elastic scattering, and inelastic scattering, were important for 23 Na. Figure 16 is an example to comprehend the changes in the 23 Na elastic reaction between the nuclear data libraries. This figure shows that the relative changes were larger than the relative standard deviation in JENDL-3.3 partially between the latest nuclear data libraries for the 23 Na elastic reaction. It is also necessary to improve the accuracy of 23 Na cross section data. Figure 17 illustrates the relative change in the cross section and the relative standard deviation with the sensitivity coefficients for the 56 Fe inelastic scattering reaction. It was also observed that the relative changes were larger than the JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

10 Analytical Validation of Uncertainty in Reactor Physics Parameters for Nuclear Transmutation Systems 529 relative standard deviation in the MeV region, which had the significant sensitivity coefficients. It was guessed that this discrepancy was one of the causes of the differences in the 56 Fe case shown in Figs. 5 and 6. The comparisons of the cross section data between the latest nuclear data libraries showed that obvious discrepancies existed for main nuclides and reactions. The discrepancies were sometimes larger than the relative standard deviations in JENDL-3.3. This was the reason why the differences between the MCNPX calculation results were larger than the uncertainties calculated using the covariance data prepared in JENDL-3.3. (2) Uncertainty Deduced from Covariance Data For the ADS calculation, k eff ¼ :97 was aimed as the subcritical system, and the result of JENDL-3.3 almost achieved the target value. However, the k eff value calculated using JEFF was.995 ((JEFF-3.1.1) = 2.8%). This result indicates that the system designed using JEFF is hardly the subcritical system. Meanwhile, the uncertainty deduced from the JENDL-3.3 covariance data was 1.3%, and it meant that the maximum k eff considered the uncertainty as.987. For the void reactivity, about 29% difference was obtained by using ENDF/B-VII.. It is very important to comprehend the uncertainty of the void reactivity since it is related to the safety of the system. However, the uncertainty deduced from the JENDL-3.3 covariance data indicated only about 6.9% difference. The same conclusion can also be derived from the results for the MA-loaded FR. The uncertainties deduced from the JENDL-3.3 covariance data were lower than the differences among the nuclear data libraries in both the criticality and void reactivity cases. The main reason for these discrepancies was discussed earlier, that is, the covariance data prepared in JENDL-3.3 are smaller than the relative changes among the latest nuclear data libraries for many nuclides and reactions. The covariance data prepared in JENDL-3.3 were obtained by two methods mainly. The first one was the method based on experimental data of cross section measurements. The covariance data of nuclides and reactions whose experimental data were enough were calculated in a process of nuclear data evaluation by using the least-squares method employed in a code system such as GMA code. 21,22) The second one was the method employed in the covariance evaluation system, KALMAN. 23) KALMAN can produce the covariance data of nuclides and reactions whose experimental data do not exist by using the parameter dependences of nuclear reaction models. The covariance data prepared in JENDL ) were obtained by these two methods, basically. It is supposed that the logics of these evaluation methods are right, but it is necessary to discuss whether the covariance data itself can be used for the reliability assessment of the nuclear design. However, benchmark calculations and verifications of the uncertainty have not been performed comprehensively, although it is the current trend that the uncertainty deduced from the covariance data is utilized for the discussion of the nuclear design accuracy or the criticality safety assessment as described in the Introduction. When the nuclear design accuracy is discussed, the uncertainty should indicate the difference from the true value. Particularly, the reliability of the uncertainty is important to estimate the nuclear design accuracy of the transmutation systems because it is very difficult to confirm their true values by mockup experiments, which need a certain amount of MA. In this work, however, it was verified that the uncertainty deduced from the covariance data prepared in JENDL-3.3 may partly underestimate the errors in the nuclear design of the transmutation systems, particularly in the ADS. In consideration of these results, two directions are presented for the succeeding discussions on the nuclear design. The first one is the direction to use the uncertainty deduced from the covariance data with a safety factor. After the calculation of the uncertainty, the safety factor is added to the uncertainty by nuclear designers to ensure the nuclear design accuracy. In this case, the uncertainty itself should not be employed for the discussion of the nuclear design accuracy. The second one is the direction to construct a new nuclear data error library based on the current covariance data. This direction required a lot of discussions but a new uncertainty calculated using the new nuclear data error library is available to discuss the nuclear design accuracy appropriately. IV. Conclusions To confirm the reliability of the uncertainty deduced from the covariance data, the comparison between the uncertainty and the differences in the reactor physics parameters among the nuclear data library in the Monte-Carlo calculation was performed for the ADS and MA-loaded FR. The comparison results showed that the uncertainties deduced from the JENDL-3.3 covariance data were smaller than the differences among the nuclear data libraries for the criticality and void reactivity. These results confirmed that the covariance data in JENDL-3.3 may partly underestimate the uncertainty in the nuclear design of the transmutation systems. It was also considered from the investigations of the 23 Na and 56 Fe cross sections that the underestimation would occur in the nuclear design of conventional nuclear reactors. The cause of the underestimation was that the covariance data in JENDL-3.3 were smaller than the relative changes in the cross sections between the latest nuclear data libraries for main nuclides and reactions. The covariance data prepared in JENDL-3.3 are obtained by adequate methods from the viewpoint of the science, but a discussion is required as to whether the covariance data can be employed for the nuclear design. Although no verifications of the uncertainty deduced from the covariance data have been performed comprehensively, it is utilized for the discussion of the nuclear design accuracy or the criticality safety assessment. It is required to verify the uncertainty of the reactor physics parameters by integral experiments and to discuss the uncertainty utilization for the nuclear design accuracy. It is also necessary to prepare covariance data for the provisional data shown in Tables 4 and 5, in consideration of the results of this study. VOL. 47, NO. 6, JUNE 21

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