EPJ Web of Conferences 146, 09041 (2017) DOI: 10.1051/epjconf/201714609041 ND2016
Precision requirement of the photoﬁssion cross section for the nondestructive assay
Rei Kimuraa, Hiroshi Sagara, and Satoshi Chiba
Tokyo Institute of Technology, 2-12-2 Ookayama Meguro-ku Tokyo, Japan
Abstract. Principle of the new NDA technique based on the photoﬁssion reaction rate ratio (PFRR) has been developed by Kimura et al for measurement of uranium enrichment by using the only relative measured counts of neutron produced by photoﬁssion reactions of 235Uand238U at different speciﬁc incident photon energies. In the past analysis, no attentions have been paid for relatively large uncertainty of photonuclear cross section of special nuclear materials around 10%. In the present paper, quantitative analysis was performed to reveal the impact of photonuclear cross section uncertainty to predicted value of the uranium enrichment by the PFRR methodology. And also, the requirement of photoﬁssion cross section precision was evaluated as less than 3%, to satisfy the uncertainty of PFRR methodology to within 5%.
1. Introduction photoﬁssion reaction rate ratio (PFRR) was validated by small scale numerical simulation with good reproducibility The nondestructive assay (NDA) techniques for quantify- of within 2% difference of predicted uranium enrichment ing special nuclear materials (SNMs) have been developed and reported by Kimura et al. . However, cross sections by many organizations and some of which have been of the photonuclear reaction of interested nuclides relating successfully applied to uranium enrichment measurement to PERR have, in general, around 10% uncertainty, which [1Ð9]. One of the recent projects is Next Generation may lead the huge impact to the accuracy of uranium Safeguards Initiative in the United States which has been enrichment measurement by the PFRR methodology. In examined in a spent fuel NDA technique . The other the present paper, quantitative analysis was performed to challenge of the NDA technique for quantiﬁcation or even reveal the impact of photonuclear cross section uncertainty detection of SNMs in unknown forms, such as unknown to predicted value of the uranium enrichment by the PFRR waste, debris or concealed and shielded highly enriched methodology. And also, the requirement of photonuclear uranium in containers, these have some technical difﬁculty cross section precision was evaluated as follows ;
(1) Few self-generated neutron or photon emissions because of shielding 2. Principle of the NDA technique based (2) Difﬁculty of measurement because of intensive on the Photoﬁssion reaction rate ratio gamma-ray backgrounds The PFRR methodology mechanism is based on the (3) Low measurement reliability due to impurities and difference of photonuclear cross section of different unknown information. nuclides and different incident photon energies, these functions of the incident photon energies for the typical Recently, the development of the compact and quasi- fertile and ﬁssile nuclides of ENDF/B-VII.1 are shown monochromatic photon (X-ray) source generator has in Fig. 1 . These differences of cross sections make proceeded, which is expected to be realized as portable the differences of neutron production rate at the target of photon generator device with higher energy than the SNMs, for example, as shown in Fig. 2 . photonuclear threshold energy [11Ð14]. Its application is The neutron production rates shown in Fig. 2 include expected to be one of the NDA techniques. the (γ ,n),(γ , 2n), (γ , ﬁssion), and other neutron A new NDA technique is aimed for uranium production reactions. In case of the maximum incident enrichment measurement, characterized by mathematical photon energy is under 11.27 MeV as threshold energy of process which represents the correlation of the target (γ , 2n) reaction at 238U and 235U target, (γ , ﬁssion) counts enrichment and relative measured counts of neutron can be extracted from the neutron counts by coincidence produced by the photoﬁssion reactions of 235U and counting. In the PFRR methodology, the information of 238U at different speciﬁc incident photon energies of photoﬁssion reactions is utilized to improve the precision 6 MeV and 11 MeV. Principle of the nuclear material by the simpliﬁed mathematical process as removal of other isotopic composition measurement method based on the reactions from the equation. The photoﬁssion reaction rate Ri (i represents the a e-mail: [email protected] speciﬁc incident photon energy spectrum) is described
c The Authors, published by EDP Sciences. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). EPJ Web of Conferences 146, 09041 (2017) DOI: 10.1051/epjconf/201714609041 ND2016 by Eq. (1), Ri = φi (E) Nnucσ f,nuc (E) dE, (1) nuc where E is the photon energy, φi (E)is the photon ﬂux, Nnucandσ f,nuc (E) are number density and microscopic photoﬁssion cross section of nuclide nuc. In addition, parameters i and nuc are deﬁned as 1, 2, 3 ...n and I, II, III···n. Further, Ai,nuc is deﬁned as Ai,nuc = φi (E) σ f,nuc (E)dE andR1 ∼ Rn−1are divided byRn, Eq. (1) for each iand nuc can be transformed as Eq. (2), where Ai,nuc is known. The PFRR methodology requires Figure 1. Photonuclear reaction cross sections versus the incident the measurement value of the photoﬁssion reaction rate photon energy. The cross section of each nuclides and reactions ratioRi Rn in order to calculateNnuc Nn. The isotopic are written as “nuclides(reaction)” [10,14]. composition IC of nuclide nuc is calculated from Nnuc Nn and Eq. (3).
−1 NI R1 R1 R1 R1 An,I − A1,I An,II − A1,II An,III − A1,III ··· An,n−1 − A1,n−1 Nn Rn Rn Rn Rn NII R2 R2 R2 R2 An,I − A2,I An,II − A2,II An,III − A2,III ··· An,n−1 − A2,n−1 Nn Rn Rn Rn Rn NIII R3 R3 R3 R3 An,I − A3,I An,II − A3,II An,III − A3,III ··· An,n−1 − A3,n−1 Nn = Rn Rn Rn Rn . . . . . . . . . . . . . . . . . .
Nn−1 Rn−1 Rn−1 Rn−1 Rn−1 An,I − An−1,I An,II − An−1,II An,III − An−1,III ··· An,n−1 − An−1,n−1 Nn Rn Rn Rn Rn R1 A1,n − An,n Rn R2 A2,n − An,n Rn R3 A3,n − An,n × Rn (2) . . .
Rn−1 An−1,n − An,n Rn
N IC = nuc nuc + + +···+ NI NII NIII Nn Figure 2. Difference in the neutron production for different photon energies and nuclides . Nnuc = Nn (3) NI + NII + NIII +···+ N N N 1 n n n where, NU235/NU238 and Rratio was Nnuc/Nn and Ri /Rn of Eq. (2), ε0,238U and ε0,235U were relative error of Hence, the PFRR methodology induces the isotopic 238 235 composition by only measuring relative value of the the photoﬁssion cross section of U and U. Other photoﬁssion reaction . parameters in the Eq. (4) were described as follows: MA = A238U,n − RratioA238U,i 3. Calculation model and methodology MB = RratioA235U,i − A235U,n MCNP6 as a Monte Carlo code and ENDF/B-VII.1 as an evaluated nuclear data library were used for simulating the 2 2 εA = ε0,238U A238U,n + ε0,238U RratioA238U,i photonuclear reaction in the target [14,15]. Figure 3 shows the calculation model of the present study. In this model, 2 2 εB = ε0,235U RratioA235U,i + ε0,235U A235U,n the photon beam is assumed to be injected to the center = σ φ , of the thin target. This target consists of metallic uranium A238U,i f,238U (E) i (E) 235 238 235 = σ φ ( U and U, U enrichment is 5Ð90%) which density A238U,n f,238U (E) n (E) is 19.1g/cm3. A235U,i = σ f,235U (E) φi (E), Incident photons from the pencil beam (108 histories A , = σ , (E) φ (E) . in this study) cause the photoﬁssion reaction at the target. 235U n f 235U n The ﬁssion reaction which occurred at the target is tallied as “Ri ”ofEq.(2). This ﬁssion reaction include (γ , ﬁssion) and (n, ﬁssion) because signal of (γ , ﬁssion) and (n, 4. Results and discussion ﬁssion) cannot be separated in the actual measurement by 235 coincidence counting. 4.1. Estimation of the U enrichment based on The error propagation formula of predicted 235U the PFRR method 235 238 enrichment in the UÐ U system was derived as Eq. (4), The results of the 235U enrichment prediction by PFRR method was shown in Fig. 4. The incident photon energies 2 2 ε = 1 1 ε + MA ε are 11 and 6 MeV that has the Gaussian shaped energy A B σ = . 2 M M2 distribution ( 0 5MeV). As shown in this ﬁgure, NU235 + 1 B B 235 NU238 the present method showed good reproducibility of U (4) enrichment, the principle of PFRR methodology was
2 EPJ Web of Conferences 146, 09041 (2017) DOI: 10.1051/epjconf/201714609041 ND2016
Figure 3. Calculation model on the MCNP code.
Figure 6. The predicted value of 235U enrichment and its uncertainty with 3% cross section uncertainty.
5. Conclusion The effect of the photoﬁssion cross section uncertainty to the predicted value of the 235U in the PFRR methodology was evaluated. This uncertainty was required to be 3% or less to keep less than 5% uncertainty of the predicted value of the 235U enrichment. 235 Figure 4. The predicted value of the U enrichment based on However, the current photonuclear cross section data the PFRR due the 11 MeV/6 MeV incident photon that has the of nuclear materials, namely, uranium and plutonium Gaussian shaped energy distribution . nuclides have generally 10% or more cross section uncertainty. Therefore, the photonuclear cross sections, especially photoﬁssion cross sections of uranium and plutonium, of these nuclides are strongly desired of precision improvement for uncertainty reduction of the PFRR methodology.
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