Faculty Profiles - ENDO Tomohiro

Other Link： https://doi.org/10.1080/00223131.2015.1126541

Data Assimilation Using Subcritical Measurement of Prompt Neutron Decay Constant Invited Reviewed International journal Open Access

Tomohiro Endo, Akio Yamamoto

Nuclear Science and Engineering Vol. 194 ( 11 ) page： 1089 - 1104 2020.11

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The prompt neutron decay constant α in a steady-state subcritical system can be directly measured using a reactor noise analysis method such as the Feynman-α method. To reduce the nuclear data-induced uncertainty of keff for a target system, this study investigates the applicability of data assimilation techniques, i.e., the bias factor method and the cross-section adjustment method, based on a subcritical measurement of α conducted at Kyoto University Critical Assembly (KUCA). The sensitivity coefficients of keff and α with respect to the nuclear data were efficiently estimated using a deterministic SN transport code with first-order perturbation theory. As a result, the a priori relative uncertainty of keff due to the 56-group SCALE covariance data can be reduced if there is strong correlation between the measured α and the target keff. The experimental value of α contributes to improving the nuclear data of total fission spectrum χ and total fission neutron number ν via strong correlations between χ and prompt χp and between ν and prompt νp , by utilizing the sensitivity coefficients of α with respect to prompt χp and νp.

DOI： 10.1080/00295639.2020.1720499

Other Link： https://doi.org/10.1080/00295639.2020.1720499

Theoretical Derivation of a Unique Combination Number Hidden in the Higher-Order Neutron Correlation Factors Using the Pál-Bell Equation Invited Reviewed International journal

Tomohiro Endo, Fuga Nishioka, Akio Yamamoto, Kenichi Watanabe, Cheol Ho Pyeon

Nuclear Science and Engineering Vol. 197 ( 2 ) page： 176 - 188 2023.2

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The Pál-Bell equation is a backward-type master equation that describes the probability generating function (PGF) of neutron counts in a neutron multiplication system. Thanks to the Pál-Bell equation with the two-forked and the fundamental mode approximations, an analytical solution of PGF of neutron counts in a source-driven subcritical system can be theoretically derived. This theoretical derivation clarifies that the unique combination number of double factorial (2n−3)!! does exist in the ratio of the higher-order neutron correlation factors measured in a critical state even for any kind of fissile and moderator materials. Additionally, the unique combination numbers are experimentally validated for the order 3 ≤ n ≤ 6 through reactor noise measurements in actual subcritical systems. This knowledge can be used to judge whether a target system is in a deep subcritical state or to roughly estimate the magnitude of subcriticality, based on the factorial moments of the measured reactor noise in a zero-power state.

DOI： 10.1080/00295639.2022.2049992

Sensitivity Analysis of Prompt Neutron Decay Constant using Perturbation Theory Reviewed International journal Open Access

Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 55 ( 11 ) page： 1245 - 1254 2018.11

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Experimental results of prompt neutron decay constant α is useful information to validate numerical results of ω-eigenvalue for spatial and energetic fundamental mode. In order to accomplish the data assimilation technique using α, it is desirable to establish an efficient numerical calculation method for sensitivity coefficient analysis of α. For this purpose, the numerical calculation method using the first-order perturbation theory is investigated. A specific theoretical formula is derived to evaluate the sensitivity coefficient of α to nuclear data. The derived rigorous formula utilizes forward and adjoint eigenfunctions which consist of neutron flux and delayed neutron precursor densities. Using the prompt approximation, the derived formula can be simplified without the term involving the delayed neutron precursor densities. By calculating α using the multi-energy-group neutron transport code for an ICSBEP benchmark problem, the derived formula for sensitivity analysis using the perturbation theory is verified by comparing with the reference results using the direct method. Consequently, the efficient numerical procedures for uncertainty quantification of α can be established by the aid of the sensitivity coefficients based on the perturbation theory.

DOI： 10.1080/00223131.2018.1491902

Comparison of theoretical formulae and bootstrap method for statistical error estimation of Feynman-α method Reviewed International journal Open Access

Tomohiro Endo, Akio Yamamoto

Annals of Nuclear Energy Vol. 124 page： 606 - 615 2019.2

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

This paper discusses the statistical error of the variance-to-mean ratio, or the Y value in the Feynman-α method, from a single measurement of reactor noise. As a theoretical approach, two practical theoretical formulae are derived to estimate the statistical error of Y: one is based on the propagation of uncertainty with unbiased estimators for the third-and fourth-order central moments; the other is a simplified formula that reuses the Y value under the fundamental mode approximation, where the subcriticality is approximately less than 10,000 pcm. As a numerical approach, the bootstrap method is improved to efficiently estimate the correlations of Y between different counting gate widths, or covariance matrix Σ_Y , due to the bunching method. Through an actual reactor noise experiment at the Kyoto University Criticality Assembly, the statistical errors of Y using the theoretical formulae and the bootstrap method are validated by comparing the reference statistical errors that are estimated from the multiple experiments of reactor noise. Furthermore, the impact of Σ_Y on the statistical error of the prompt neutron decay constant α is numerically investigated. Consequently, in the case of this experimental analysis, it was confirmed that the bootstrap method with the correlations of Y seems to be slightly better from the viewpoint of the coverage probability of the estimated confidence intervals of α, although the fitting error method without the correlation of Y could be useful for the order estimation of the statistical error of α.

DOI： 10.1016/j.anucene.2018.10.032

Other Link： https://doi.org/10.1016/j.anucene.2018.10.032

Application of dynamic mode decomposition to Rossi-α method in a critical state using file-by-file moving block bootstrap method Reviewed International journal Open Access

Tomohiro Endo, Fuga Nishioka, Akio Yamamoto, Kenichi Watanabe, Cheol Ho Pyeon

Journal of Nuclear Science and Technology Vol. 59 ( 9 ) page： 1117 - 1126 2022.9

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

Prompt neutron decay constant α in a critical state is useful information to validate the numerically predicted ratio of the point kinetics parameters βeff/ℓ, where βeff and ℓ are the effective delayed neutron fraction and prompt neutron lifetime, respectively. To directly measure α in a target critical system, this study proposes the application of the dynamic mode decomposition (DMD) to the reactor noise analysis based on the Rossi-α method. The DMD-based Rossi-α method enables us to robustly estimate the fundamental mode component of α from the Rossi-α histograms measured using multiple neutron detectors. Furthermore, the file-by-file moving block bootstrap method is newly proposed for the statistical uncertainty quantification of α to prevent huge memory usage when the neutron count rate is high and/or the total measurement time is long. A critical experiment has been conducted at Kyoto University Critical Assembly to demonstrate the proposed method. As a result, the proposed method can uniquely determine the α value of which the statistical uncertainty is smallest. By utilizing this experimental result of α, numerical results of βeff/ℓ ratio using the continuous energy Monte Carlo code MCNP6.2 with recent nuclear data libraries, which are processed by the nuclear data processing code FRENDY, are validated.

DOI： 10.1080/00223131.2022.2030260

Deterministic sampling method using simplex ensemble and scaling method for efficient and robust uncertainty quantification Reviewed International journal

Tomohiro Endo, Shuhei Maruyama, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 61 ( 3 ) page： 363 - 374 2024.3

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

Uncertainty quantification (UQ) of the neutron multiplication factor is important to investigate the appropriate safety margin for a target system. Although the random sampling method is a practical and useful UQ method, a large computational cost is required to reduce the statistical error of the estimated uncertainty. Furthermore, if an input variable follows a normal distribution with a large standard deviation, the perturbed input variable by the random sampling method may become a physically inappropriate or negative value. To address these issues for the efficient and robust UQ, a modified deterministic sampling method using the simplex ensemble and the scaling method is proposed. The features of the proposed method are summarized as follows: The sample size is (r+2), where r corresponds to the effective rank of the covariance matrix between the input variables; depending on a situation of target UQ, the amounts of perturbations for the input parameters can be arbitrarily given by the scaling factor method; the scaling factor can be updated to avoid physically inappropriate in the perturbed input variables. The effectiveness of the proposed method is demonstrated through the UQ of the neutron multiplication factor due to fuel manufacturing uncertainties for a typical PWR pin-cell burnup calculation.

DOI： 10.1080/00223131.2023.2231931

Experimental validation of unique combination numbers for third- and fourth-order neutron correlation factors of zero-power reactor noise Reviewed International journal

Tomohiro Endo, Akio Yamamoto, Masao Yamanaka, Cheol Ho Pyeon

Journal of Nuclear Science and Technology Vol. 56 ( 4 ) page： 322 - 336 2019.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Zero-power reactor noise is useful for subcriticality measurements. Based on the nuclear reactor physics and the theory of neutron detection, this paper theoretically clarifies that the third- and fourth-order neutron correlation factors Y_3 and Y_4 can be expressed as functions of the second-order neutron correlation factor Y. In particular, if the neutron-counting gate width is sufficiently large, the saturation values Y_3⁄Y^2 and Y_4⁄Y^3 are almost equal to the unique combination numbers, ‘3’ and ‘15,’ for a source-driven subcritical system, where the subcriticality is less than 10000 pcm. These unique combination numbers, ‘3’ and ‘15,’ for Y_3⁄Y^2 and Y_4⁄Y^3 were validated using actual zero-power reactor noise measurements carried out at the Kyoto University Criticality Assembly. In this study, the estimation of statistical errors and correlations between different gate widths owing to the bunching method was achieved by the moving block bootstrap method. For a sufficiently long measured reactor noise in a steady and unperturbed state, a statistical test for the evaluation of the critical state and the absolute measurement of subcriticality can be carried out by statistically quantifying the difference between the measurement value of Y_3⁄Y^2 and the unique combination number.

DOI： 10.1080/00223131.2019.1580625

Other Link： https://doi.org/10.1080/00223131.2019.1580625

Confidence interval estimation by bootstrap method for uncertainty quantification using random sampling method Invited Reviewed International journal

Tomohiro Endo, Tomoaki Watanabe, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 52 ( 7-8 ) page： 993 - 999 2015.8

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Confidence interval estimation by the bootstrap method is investigated for the uncertainty quantification of neutronics calculation using the random sampling method. The random sampling method is a simple and practical technique to quantify an uncertainty (standard deviation) of the target parameter calculated by a core analysis code. It is noted that a statistical error is inevitably included in the estimated uncertainty because of the probabilistic method using random numbers. In order to estimate the statistical error of uncertainty, we focus on the bootstrap method. The bootstrap method is one of the resampling techniques to evaluate variance and confidence interval of a sample estimate (e.g. variance) without the assumption of normality. Through a lattice burnup calculation for a simplified boiling water reactor (BWR) fuel assembly, it is verified that the bootstrap method can reasonably estimate the confidence interval of uncertainty of infinite neutron multiplication factor (k(inf)) due to covariance data of JENDL-4.0. In the case of this problem, the distribution of k(inf) is well approximated by a normal distribution; thus, the confidence interval of uncertainty can be also estimated by the aid of chi-squared distribution. The merit using the bootstrap method is to simply estimate the confidence interval of uncertainty without the assumption of normality.

DOI： 10.1080/00223131.2015.1034216

Detected-neutron multiplication factor measured by neutron source multiplication method Reviewed International journal

Tomohiro Endo, Akio Yamamoto, Yoshihiro Yamane

Annals of Nuclear Energy Vol. 38 ( 11 ) page： 2417 - 2427 2011.11

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

An alternative definition of neutron multiplication factor measured by the neutron source multiplication (NSM) method is newly proposed. This newly defined neutron multiplication factor, kdet, is derived on the basis of neutron detection process in a subcritical system with an external neutron source. The definition of kdet is expressed as a ratio of total number of detected fission-neutrons to total number of detected all neutrons. In this paper, a heuristic derivation of kdet is presented, and another interpretation of kdet is explained by using the detector importance function. Based on the idea of kdet, the measurement principle of NSM method is reinterpreted, and the correction factors in the NSM method are clarified. In order to verify our proposed NSM method, numerical analysis of the NSM method is carried out. The numerical results suggest that target neutron multiplication factors of the NSM method can be well estimated even without any corrections by putting a neutron detector where the effective neutron multiplication factor keff is well approximated by kdet.

DOI： 10.1016/j.anucene.2011.01.007

Development of new solid angle quadrature sets to satisfy even- and odd-moment conditions Reviewed International journal

Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 44 ( 10 ) page： 1249 - 1258 2007.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

In this paper, we propose new solid angle quadrature sets named EON for the SN method. The EON quadrature sets are developed for the 3-D xyz geometry, and satisfy not only even-moment conditions but also odd-moment conditions for direction cosines over an octant of the sphere. We can accurately calculate the numerical integration of the polynomial of direction cosines using EON. We verify the effectiveness of EON through the 2-D bulk shield problem and the 3-D neutron transport benchmark problems. The verification results indicate that the angular discretization error of EON is much smaller than that of the conventional level symmetric quadrature set.

DOI： 10.1080/18811248.2007.9711368

Hybrid data assimilation methods for nuclear-data-induced uncertainties Reviewed International journal

Shuhei Maruyama, Akio Yamamoto, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. xx ( xx ) page： xx - xx 2025.5

Authorship：Last author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

This study proposes new hybrid data assimilation (DA) methods to effectively use experimental data represented in two different ways in the DA process for reducing nuclear-data-induced uncertainties. Conventional DA methods often assume a linear model, where data in a DA database are represented by their differential coefficients, i.e. nuclear data sensitivity coefficients. In contrast, more rigorous and versatile DA methods based on sampling techniques have been proposed recently. These sampling-based DA methods describe data for DA using results derived from direct transport calculations performed with perturbed nuclear data samples. The proposed hybrid DA methods simultaneously use both types of data described by sensitivity coefficients and sampling results and thus are called ‘hybrid.’ Two hybrid DA methods are proposed herein: the simple hybrid DA and efficient hybrid DA methods. Among these, the simple method is based on a straightforward concept that uses a random sampling technique. In contrast, the efficient method employs a more technical method that effectively combines a new deterministic sampling technique with sensitivity coefficients to reduce statistical uncertainties associated with the simple method. The efficient method is expected to be a candidate to achieve high precision and rigorous DA with a realistic sample size.

DOI： 10.1080/00223131.2025.2500579

Treatment of corner crossing ray-traces in CMFD acceleration of MOC Reviewed International journal

Akio Yamamoto, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. xxx ( xx ) page： xx - xx 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

Treatment of corner crossing ray traces in the coarse-mesh finite-difference (CMFD) acceleration of a method of characteristics (MOC) transport calculation is discussed. The contribution of the corner crossing ray trace at a CMFD mesh is independently tallied as partial current at the corner of the CMFD mesh to reduce computational burden during transport sweeps in MOC. The tallied partial current at the corner is distributed to the partial currents at the sides of CMFD meshes. Some details of implementations in rectangular and triangular CMFD meshes are explained. The present method is implemented to the GENESIS neutron transport code, and its validity is confirmed through the 3×3 square cells and the hexagonal cell geometries. The calculation results indicate that the present method resolves the issue of corner crossing ray trace in the CMFD acceleration of MOC.

DOI： 10.1080/00223131.2025.2490832

Impact of nuclear data updates from JENDL-4.0 to JENDL-5 on burnup calculations of light-water reactor fuels Reviewed International journal

Tomoaki Watanabe, Kenichi Tada, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. xx ( xx ) page： xxx - xxx 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

This study investigated the impact of nuclear data updates from JENDL-4.0 (J4) to JENDL-5 (J5) on the light-water reactor fuel burnup calculations. Burnup calculations were conducted with J4 and J5 for pressurized water reactor pin-cell and boiling water reactor (BWR) fuel assembly geometries. The calculation results revealed significant burnup-dependent differences in the neutron multiplication factor (kinf). Across the burnup range of 0–50 GWd/t, kinf values of J5 were consistently smaller than those of J4 and the difference gradually increased as burnup progressed. Direct sensitivity calculations, in which each nuclide data was replaced from J4 to J5, indicated that updates to the cross-sections of U-235, U-238, and Pu-239 and the thermal scattering law data of H in H2O notably impacted the kinf differences. For the BWR assembly geometry containing Gd fuels, large kinf differences were observed in the burnup range of 10–15 GWd/t. This difference was primarily attributed to updates in the cross-sections of U-235, Gd-155, Gd-157, and thermal scattering law data of H in H2O. Furthermore, we investigated how the nuclear data updates affected the kinf differences by examining nuclide number densities, the energy-dependent sensitivities, and the neutron spectra.

DOI： 10.1080/00223131.2025.2486798

Development of Multigroup Monte Carlo Neutron Transport Method with Regionwise Even-Parity Discontinuity Factor Reviewed International journal

Yoshiki Oshima, Tomohiro Endo, Akio Yamamoto

Nuclear Science and Engineering Vol. 199 ( 4 ) page： 586 - 598 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The multigroup Monte Carlo (MC) neutron transport method with a regionwise even-parity discontinuity factor (REPDF), i.e. the discontinuity factor (DF)–MC method, is developed with the aim to provide a reference solution for deterministic transport calculations with DF. Applying the analogy with optics, neutrons are transmitted or reflected at a region surface during random walks. The probability of transmission or reflection is determined by REPDFs in adjacent regions. The DF is traditionally used in deterministic neutron transport methods to reduce the discretization error due to spatial homogenization and energy condensation. The DF-MC method can treat DF in the framework of the multigroup MC method.
In this paper, the weight cancellation technique based on the closest pair of points using the divide-and-conquer algorithm is used because negative weights appear due to the neutron reflection. The REPDF is calculated by the method of characteristics (MOC). The verification calculations are carried out in the pin-by-pin homogenized and assembly homogenized KAIST-2A core geometry. The DF-MC calculation can reproduce the results of the MOC with the REPDF. These results demonstrate the principle of the DF-MC method and extend the application of the DF to the probabilistic neutron transport method.

DOI： 10.1080/00295639.2024.2383102

Reduced order SP3 core calculation based on Local/Global iterations using proper orthogonal decomposition Reviewed International journal

Masato Ito, Tomohiro Endo, Akio Yamamoto, Taichi Takeishi, Yasuhiro Kodama, Hideaki Hyoudou

Journal of Nuclear Science and Technology Vol. 62 ( 4 ) page： 366 - 378 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

For an efficient heterogeneous neutron transport calculation, this study newly proposes a reduced order core calculation method by applying proper orthogonal decomposition (POD) to the simplified P3 (SP3) calculation with the local/global iterations. The fine mesh SP3 calculation (local calculation) for each single assembly can be efficiently solved using POD, thanks to the matrix form-based SP3 equation and the relatively small system of linear equations. By reconstructing the fine mesh distribution of neutron flux and partial neutron currents from the POD bases and the expansion coefficients estimated by the local calculation, the partial current-based coarse mesh finite difference (p-CMFD) calculation is applied to the coarse mesh calculation (global calculation). Using the global calculation results, each local boundary condition can be updated. These local and global calculations are iterated until convergence. Through a two-dimensional UO2-MOX whole core calculation with different fuel loading patterns, the proposed method is verified in comparison with the reference result by the conventional fine mesh SP3 calculation. The calculation results show that the proposed method accurately reconstructs the fine mesh distribution of neutron flux.

DOI： 10.1080/00223131.2024.2436958

Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations Reviewed International journal

Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 61 ( 12 ) page： 1536 - 1545 2024.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution.

DOI： 10.1080/00223131.2024.2365445

Limited linear source approximation with Edge Detection for Convergence Stability of Method of Characteristics Reviewed International journal Open Access

Akio Yamamoto, Tomohiro Endo, Go Chiba

Journal of Nuclear Science and Technology Vol. 61 ( 11 ) page： 1405 - 1414 2024.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

A new implementation of the limited linear source approximation (LLSA) is proposed. The LLSA was previously proposed to eliminate local negative source in flux regions to mitigate numerical instability of the method of characteristics (MOC) with linear source approximation (LSA). In the present LLSA implementation, the convex edges of flux regions are used to check the local negative source to decrease the computational load. The present method is implemented in the transport code GENESIS and its effectiveness is verified through the two dimensional C5G7 benchmark problem and the simplified two-dimensional high-temperature engineering test reactor core. The calculation results indicate that the present LLSA implementation efficiently mitigates the numerical instability of MOC with LSA. Additional computational time is less than 1% of total computation time.

DOI： 10.1080/00223131.2024.2341776

Quantifying uncertainty induced by scattering angle distribution using maximum entropy method Reviewed International journal

Shuhei Maruyama, Akio Yamamoto, Tomohiro Endo

Annals of Nuclear Energy Vol. 205 page： 110591 2024.9

Authorship：Last author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

This study developed a new method for evaluating the uncertainty in reactor core/shielding characteristics attributable to the scattering angle distribution in the combined method of the continuous energy Monte Carlo (CEMC) transport calculations and the random sampling (RS) technique based on nuclear data covariances. Recent advances in computer performance have made it possible to evaluate the nuclear data-induced uncertainty with high accuracy using the Monte Carlo method. The total Monte Carlo (TMC) method is a typical uncertainty quantification method that relies entirely on the Monte Carlo method. Another representative Monte Carlo-based uncertainty quantification method is the combination method of the RS technique based on nuclear data covariances and CEMC transport calculations (CEMC-RS). CEMC-RS has the advantage that the uncertainty can be quantified even if one is not familiar with nuclear data measurement and evaluation, as long as the nuclear data covariances are available. However, no method has been established to quantify the uncertainty in CEMC-RS, despite the fact that the uncertainty due to the scattering angle distribution is non-negligible in fast reactor core analysis and shielding analysis. This study introduces a new approach for uncertainty quantification related to scattering angle distribution in CEMC-RS, utilizing the maximum entropy method. The effectiveness of this method was verified through comparison with results from the classical deterministic uncertainty quantification approach based on generalized perturbation theory. Overall, this method offers a more accurate tool for nuclear engineers and researchers in evaluating and managing uncertainties in reactor design and safety analysis.

DOI： 10.1016/j.anucene.2024.110591

Simplified Treatment of Coating Layers in TRISO Fuel in Statistical Geometry Method in Monte Carlo Calculation Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Satoshi Takeda, Kazuya Yamaji, Hiroki Koike, Koji Asano

Nuclear Science and Engineering Vol. xxx ( xx ) page： xx - xx 2024.8

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

An improved sampling method for flight distance is proposed for Monte Carlo analysis of TRISO fuel particles using the statistical geometry (STG) method. The statistically uniform distribution of fuel particles, which is usually assumed as a default sampling method of flight distance of a neutron between fuel particles, shows considerable bias on k-infinity when coating layers of a TRISO fuel particle are homogenized with a graphite matrix. The proposed new sampling method almost resolves the difference between the no-coating-layer model (coating layers are homogenized with a graphite matrix) and the explicit-coating-layer model (explicitly considers coating layers, reference). By adopting the present method, the no-coating-layer model can be used without significant loss of accuracy in the STG method of a Monte Carlo analysis. The computation time with a continuous energy Monte Carlo code for a typical fuel compact cell of a high-temperature gas-cooled reactor is reduced to one-seventh of the explicit-coating-layer model when the no-coating-layer model is used.

DOI： 10.1080/00295639.2024.2384236

Impact of Uncertainty Reduction on Lead-Bismuth Coolant in Accelerator-Driven System Using Sample Reactivity Experiments Reviewed International journal

Ryota Katano, Akito Oizumi, Masahiro Fukushima, Cheol Ho Pyeon, Akio Yamamoto, Tomohiro Endo

Nuclear Science and Engineering Vol. 198 ( 6 ) page： 1215 - 1234 2024.6

Authorship：Last author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

In this study, we have demonstrated that data assimilation (DA) using lead and bismuth sample reactivities measured in the Kyoto University Critical Assembly A-core can successfully reduce the uncertainty of the coolant void reactivity in accelerator-driven systems (ADSs) derived from inelastic scattering cross sections of lead and bismuth. We reevaluated and highlighted the experimental uncertainties and correlations of the sample reactivities for the DA formula. We used the MCNP6.2 code to evaluate the sample reactivities and their uncertainties and performed DA using the reactor analysis code system MARBLE. The high-sensitivity coefficients of the sample reactivities to lead and bismuth allowed us to reduce the cross-section–induced uncertainty of the void reactivity of the ADS from 6.3% to 4.8%, achieving a provisional target accuracy of 5% in this study. Furthermore, we demonstrated that the uncertainties arising from other dominant factors, such as minor actinides and steel, can be effectively reduced by using integral experimental data sets for the unified cross-section dataset ADJ2017.

DOI： 10.1080/00295639.2023.2246779

Development of nuclear data processing code FRENDY version 2 Reviewed International journal

Kenichi Tada, Akio Yamamoto, Satoshi Kunieda, Chikara Konno, Ryoichi Kondo, Tomohiro Endo, Go Chiba, Michitaka Ono, Masayuki Tojo

Journal of Nuclear Science and Technology Vol. 61 ( 6 ) page： 830 - 839 2024.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Nuclear data processing is important to connect evaluated nuclear data libraries and radiation transport codes. The nuclear data processing code FRENDY version 1 was released in 2019 to generate ACE formatted cross section files with simple input data. After we released FRENDY version 1, many functions were developed, e.g., neutron multi-group cross section generation, explicit consideration of the resonance interference effect among different nuclides in a material, adaptive setting of the background cross sections, consideration of the resonance upscattering, ACE file perturbation, statistical uncertainty quantification of probability table, and modification of ENDF-6 formatted file. FRENDY version 2 was released including these new functions. It generates GENDF and MATXS formatted neutron multi-group cross section files from an ACE formatted cross section file or an evaluated nuclear data file. This paper explains the features of the new functions implemented in FRENDY version 2 and the verification of the neutron multigroup cross section generation function of this code.

DOI： 10.1080/00223131.2023.2278600

Deterministic Transport Calculation Method for Statistical Geometry with Small Fuel Particles Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Satoshi Takeda, Hiroki Koike, Kazuya Yamaji, Koji Asano

Nuclear Science and Engineering Vol. 198 ( 5 ) page： 981 - 992 2024.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A deterministic transport calculation method is proposed for the treatment of dispersed fuel particles in a fuel compact/fuel pebble of a typical high-temperature gas-cooled reactor fuel. The random distribution of fuel particles was considered using the statistical geometry (STG) method, which is widely used in the Monte Carlo method. A long-ray trace, which represents a neutron flight path, was considered, and the segment lengths and material distributions on the ray trace were randomly sampled using STG. Then a conventional transport sweep, as used in the method of characteristics, was performed along the ray trace. The proposed deterministic statistical geometry (DSTG) method can calculate the flux spatial distribution in a heterogeneous geometry containing randomly dispersed fuel particles and the surrounding graphite matrix, which is consistent with the STG in a Monte Carlo method. The validity of the DSTG method was confirmed through sensitivity calculations and comparisons with a multigroup Monte Carlo method that utilizes STG. The proposed method can be used for the homogenization of heterogeneous structures inside a fuel compact or fuel pebble as an alternative to conventional deterministic unit cell calculations that consider fuel particles and the surrounding matrix in high-temperature gas-cooled reactor fuels.

DOI： 10.1080/00295639.2023.2230414

Application of neutron current method for Dancoff factor estimation of fuel particles in double-heterogeneous fuel Reviewed International journal

Akio Yamamoto, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. 61 ( 3 ) page： 354 - 362 2024.3

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

An evaluation method of Dancoff factors of fuel particles in a typical fuel element of a high-temperature gas-cooled reactor (HTGR) is proposed based on the neutron current method that is widely used for lattice physics calculations of light water reactors. The first level of heterogeneity, i.e. dispersed fuel particles in graphite matrix, is treated by the deterministic statistical geometry (DSTG) method. The homogenized cross-sections of dispersed fuel particles are provided to the second level of heterogeneity, i.e. fuel compacts in a fuel element or a fuel pebble. The validity of the present method is confirmed through the comparison with the reference Dancoff factor obtained by the Monte Carlo and the neutron current methods, which explicitly treats the double heterogeneity. The comparison is carried out for a fuel element simulating the High Temperature Engineering Test Reactor (HTTR), which adopts a typical prismatic fuel element. The numerical results indicate that the present method well reproduces the reference Dancoff factor under various packing fractions. Since the present method can handle flexible geometry and its computation time is short, the present method will be a candidate for the Dancoff factor evaluation method in design calculations of HTGR.

DOI： 10.1080/00223131.2023.2231462

Uncertainty reduction of sodium void reactivity using data from a sodium shielding experiment Reviewed International journal

Shuhei Maruyama, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 61 ( 1 ) page： 31 - 43 2024.1

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

This study investigated the feasibility of reducing the uncertainty associated with fast-reactor-core design by sharing an experimental database between different fields (e.g. reactor physics and radiation shielding) using data assimilation techniques. As the first step in this study, we focused on the ORNL sodium shielding experiment and investigated the possibility of using the experimental data to reduce the uncertainty in sodium void reactivity (SVR), which is the most important safety parameter for sodium-cooled fast reactors. A sensitivity analysis based on the Generalized Perturbation Theory was performed for the sodium shielding experiment. Using the sensitivity coefficients evaluated here and those of the sodium void reactivity previously evaluated by the JAEA, we showed that sodium shielding experimental data can contribute to the uncertainty reduction of SVR by adopting the cross-section adjustment method. Based on this study, the uncertainty reduction effect is expected to be significant, especially for SVR dominated by neutron-leakage phenomena. Although new reactor physics experimental data on SVR may be difficult to obtain, the results of this study suggest that data from sodium shielding experiments can partially substitute for this role. This study demonstrated the value of the mutual use of integral experimental data in fast reactor designs.

DOI： 10.1080/00223131.2023.2244512

Sensitivity analysis of risk assessment for continuous Markov process Monte Carlo method using correlated sampling method Reviewed International journal

Yuki Morishita, Akio Yamamoto, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. 60 ( 12 ) page： 1573 - 1585 2023.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The correlated sampling method is applied to the continuous Markov-chain Monte-Carlo (CMMC) method to efficiently perform sensitivity analysis of input parameters such as the failure rate of safety components. In the correlated sampling method, the original and the perturbed samples are assumed to trace an identical accident sequence, but the weight of the perturbed sample is adjusted to incorporate the variation of input data. The present method is applied to the sensitivity analysis of the safety evaluation of spent fuel pools. The result indicates that the sensitivity analysis for the CMMC coupling method can be efficiently carried out using the correlated sampling method.

DOI： 10.1080/00223131.2023.2231464

An estimation method for an unknown covariance in cross-section adjustment based on unbiased and consistent estimator Reviewed International journal

Shuhei Maruyama, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 60 ( 11 ) page： 1372 - 1385 2023.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

A new estimation method of an unknown covariance in the cross-section adjustment method for the development of an application library is proposed. The unknown covariance is defined by the difference between the true covariance (the population covariance) and a prior covariance assumed by an analyst. The unknown covariance is estimated using an empirical covariance consistent with the observed data. To estimate the unknown covariance, an unbiased and consistent estimator in regression analysis has been incorporated into the conventional cross-section adjustment. This estimator does not require assumptions for the probability distribution of the observation data. The statistical properties of this estimator were numerically verified. In addition, the effectiveness of the proposed method was confirmed by another numerical test using actual integral experimental data. In the second numerical test, the modeling uncertainty (covariance) due to the deterministic analysis method was assumed to be unknown. The results showed that the proposed method could practically estimate the unknown covariance and adjusted cross-sections using only prior information on covariances.

DOI： 10.1080/00223131.2023.2203707

Impact of nuclear data revised from JENDL-4.0 to JENDL-5 on PWR spent fuel nuclide composition Reviewed International journal

Tomoaki Watanabe, Kenichi Tada, Tomohiro Endo, Akio Yamamo

Journal of Nuclear Science and Technology Vol. 60 ( 11 ) page： 1386 - 1396 2023.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The burnup calculations for estimating the nuclide composition of the spent fuel are highly dependent on nuclear data. Many nuclides in the latest version of the Japanese Evaluated Nuclear Data Library JENDL-5 were modified from JENDL-4.0 and the modification affects the burnup calculations. This study confirmed the validity of JENDL-5 in the burnup calculations. The PIE data of Takahama-3 was used for the validation. The effect of modifications of the parameters, e.g., cross sections and fission yields, from JENDL-4.0 to JENDL-5 on the nuclide compositions was quantitatively investigated. The calculation results showed that JENDL-5 has a similar performance to JENDL-4.0. The calculation results also revealed that the modifications of the cross sections of actinide nuclides, fission yields, and thermal scattering low data of hydrogen in H2O affected the nuclide compositions of PWR spent fuels.

DOI： 10.1080/00223131.2023.2201603

Convergence behavior of statistical uncertainty in probability table for cross section in unresolved resonance region Reviewed International journal

Kenichi Tada, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. 60 ( 11 ) page： 1397 - 1405 2023.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The probability table method is a well-known method for addressing self-shielding effects in the unresolved resonance region. A long computational time is required to generate the table. The effective way to reduce the generation time is the reduction of the number of ladders. The purpose of this study is the estimation of the optimal number of ladders using the statistical uncertainty in the probability table. To this end, the statistical uncertainty quantification method of the probability table was developed and the convergence behavior of the statistical uncertainty was investigated. The product of the probability and the average cross section was considered the target of the statistical uncertainty. The convergence behavior was investigated by using Sr-90, U-235, and U-238 from JENDL-4.0. The calculation results revealed that the convergence rate of the statistical uncertainty was different in each nuclide and it was affected by the average level spacing and the average reduced neutron width. The generation time of the probability table was less than half when the input parameter for the iteration condition was changed from the number of ladders to the tolerance value. The developed method leads to the efficient generation of probability tables and the reduction of processing time.

DOI： 10.1080/00223131.2023.2204102

Comparison of internal boundary conditions for optical diffusion calculations considering reflection and refraction Reviewed International journal

Toranosuke Amano, Tomohiro Endo, Akio Yamamoto

Optics Continuum Vol. 2 ( 7 ) page： 1540 - 1560 2023.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Optica Publishing Group

A method to treat the internal boundary condition in an optical diffusion calculation is proposed and is compared with the conventional methods. One of the existing internal boundary conditions is Haskel's method, which uses the effective reflection coefficient for partial currents. However, Haskel's method ignores incoming partial currents from the adjacent mesh in its derivation. As a result, the accuracy at the internal boundary is lower. This paper proposes a method to improve the accuracy by iteratively updating the effective reflection coefficient for partial current. The proposed method was applied to the benchmark calculations on a one-dimensional slab geometry and its accuracy was confirmed by comparing it with the reference solution obtained by the Monte Carlo code MCML, along with the previously proposed Haskel's method and Aronson's method. As a result, it was confirmed that the proposed method is more accurate than Haskel's method at the internal boundary and gives the same result as Aronson's method. The convergence of the effective reflection coefficient using iterative calculations in the proposed method was good.

DOI： 10.1364/optcon.492445

A Feynman-α analysis ranging over time constants of delayed neutrons based on time-sequence counting data consecutively acquired for a very long time Reviewed International journal

Sin-Ya Hohara, Tomohiro Endo, Kazuki Takahashi, Kunihiro Nakajima, Atsushi Sakon, Tadafumi Sano, Kengo Hashimoto

Journal of Nuclear Science and Technology Vol. 60 ( 6 ) page： 724 - 730 2023.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

Time-sequence counting data of a neutron counter were acquired for 17 consecutive days at shutdown state of UTR-KINKI reactor and then a Feynman-α analysis over a very wide gate width range was carried out to give light on a delayed-neutron contribution of all precursors, where statistical error of the correlation amplitude Y was estimated using the bootstrap method. A first plateau of the Y could be observed in a gate width range of several hundred milliseconds. With an enlargement of gate width beyond a time constant of prompt neutrons, the Y monotonically increased above the first plateau of prompt neutrons. Enlarging gate width beyond 100 s, the Y seemed to approach a second plateau of delayed neutrons. The second plateau originated from the delayed neutrons released from the longest-life Br87. In the gate width range beyond 100 s, however, the statistical error increased sharply. The increasing error indicates a statistical limit resulting from the present measurement time. A value Yp of the first plateau of prompt neutrons was determined from another Feynman- analysis confined to a short gate width range and the Y was divided by the plateau’s value Yp to eliminate an unknown detection efficiency. The Y-to-Yp ratio was calculated using several sets of delayed-neutron group parameters for thermal fission of U235 nuclide, to validate these sets by comparing with the measured ratio to which all precursors contributed. The ratios calculated using Keepin’s 6-group and Spriggs’ 8-group parameters agreed very well with the measured ratio in a gate width range up to 100 s and consequently these parameters could be validated. However, the ratios calculated using the other sets were in a very poor agreement with the measured ratio in the gate width range.

DOI： 10.1080/00223131.2022.2138601

Development of ACE file perturbation tool using FRENDY Reviewed International journal

Kenichi Tada, Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 60 ( 6 ) page： 624 - 631 2023.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The sensitivity analysis and the uncertainty quantification play an important role in improving the evaluated nuclear data library. The current computational performance enables us to perform sensitivity analysis and uncertainty quantification using continuous energy Monte Carlo calculation codes. The ACE file perturbation tool was developed for these calculations using modules of FRENDY. This tool perturbs the microscopic cross section, the number of neutrons per fission, and the fission spectrum. The uncertainty quantification using the random sampling method is also available if the user prepares the covariance matrices. The uncertainty of k eff using the ACE file perturbation tool was compared to the current sensitivity analysis codes SCALE/TSUNAMI and MCNP/KSEN. The comparison results indicated that the random sampling method using this tool accurately estimates the uncertainty of k eff. The ACE file perturbation tool is included in the current version of FRENDY.

DOI： 10.1080/00223131.2022.2130463

Efficient reduced order model based on the proper orthogonal decomposition for time-dependent MOC calculations Reviewed International journal

Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 60 ( 3 ) page： 343 - 357 2023.3

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

An efficient reduced order model (ROM) for time-dependent transport calculations using the method of characteristics (MOC) is proposed. In the present ROM, the flux distributions and the net neutron currents between the adjacent unstructured mesh regions are taken from the MOC solution. Then, the coefficient matrices for the MOC-equivalent diffusion equation are reconstructed from them. The proper orthogonal decomposition (POD) is applied for the MOC-equivalent diffusion equation to reduce the degree of freedoms (DOFs) using the orthogonal bases obtained by the singular value decomposition (SVD) for the sampled MOC solution. The accuracy and computation time of the present ROM are verified in the C5G7-TD 2D benchmark problem. The calculation results show that the present ROM enables us approximately 5000–6000 times faster computation than the full order model (FOM) for kinetic calculations itself in the present calculation condition. The present method can be substituted as real-time simulations without the spatial homogenization when typical flux distributions and the net neutron currents of a target problem can be precalculated.

DOI： 10.1080/00223131.2022.2097963

Nuclear data adjustment using a deterministic sampling method with unscented transformation Reviewed International journal

Yuhei Fukui, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 60 ( 3 ) page： 238 - 250 2023.3

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

A nuclear data adjustment method using a deterministic sampling method based on an unscented transform was developed, and its validity was confirmed through a twin experiment using a critical benchmark problem. Conventional nuclear data adjustment methods require sensitivity analysis using generalized perturbation theory or many forward calculations using stochastically sampled nuclear data. To address this issue, this study focused on unscented transform-based sampling (UTS), which is used in uncertainty quantification. Based on the UTS, perturbed nuclear data can be deterministically sampled to reproduce the population covariance matrix with minimum sample size. Therefore, UTS can significantly reduce the computational cost compared to conventional nuclear data adjustment using random sampling (RS). Furthermore, the UTS was improved to prevent the sampling of negative nuclear data while accurately reproducing the population covariance matrix. The proposed method was applied to the numerical experiment of Godiva, and the adjusted nuclear data were compared with those obtained using conventional methods. Consequently, it was demonstrated that UTS can adjust nuclear data at a lower computational cost than RS.

DOI： 10.1080/00223131.2022.2095051

Implementation of Resonance Upscattering Treatment in FRENDY Nuclear Data Processing System Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Go Chiba, Kenichi Tada

Nuclear Science and Engineering Vol. 196 ( 11 ) page： 1267 - 1279 2022.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The resonance upscattering effect (the thermal agitation effect) is implemented in the generation capability of multigroup neutron cross sections of the FRENDY nuclear data processing system. The resonance upscattering effect is considered by (1) the variation of self-shielding factors (effective cross sections) due to the change in the ultra-fine group spectrum and (2) the variation of group-to-group elastic scattering cross sections. Since the upscattering effect is considered in the ultra-fine group spectrum calculation, an iteration calculation is necessary to consider the upscattering. The impacts of the iteration strategy (Jacobi or Gauss-Seidel), as well as the number of iterations, are discussed. In the verification calculations, impacts on the ultra-fine group spectrum, effective cross sections, and neutronics characteristics (the Doppler effect) are confirmed. The effect of energy group structure and the impact of resonance upscattering treatments on the Doppler effect through the variation of effective cross sections and the elastic scattering matrix are investigated. The results indicate that FRENDY can provide appropriate multigroup cross sections considering the resonance upscattering effect.

DOI： 10.1080/00295639.2022.2087833

Sensitivity Coefficient Evaluation of an Accelerator-Driven System Using ROM-Lasso Method Invited Reviewed International journal

Ryota Katano, Akio Yamamoto, Tomohiro Endo

Nuclear Science and Engineering Vol. 196 ( 10 ) page： 1194 - 1208 2022.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

We propose the use of reduced-order modeling to improve the sensitivity coefficient evaluation method based on Lasso-type penalized linear regression. In this method, cross sections of interest are uniformly randomly sampled, and corresponding perturbed core analyses are performed. The sensitivity coefficients of the higher-dimensional model are expanded by the active subspace (AS) attained by the lower-dimensional model, and the expansion coefficients are estimated by the Lasso regression. In addition, AS bases can be flexibly chosen according to neutronics parameters of interest. We conducted a verification calculation for an accelerator-driven system and clarified that the proposed method successfully reduces the calculation cost by a couple of orders of magnitude compared with the direct method. The proposed method can be used to practically evaluate the sensitivity coefficients of various parameters.

DOI： 10.1080/00295639.2022.2067447

Improvements in Computational Efficiency for Resonance Calculation Using Energy Spectrum Expansion Method Reviewed International journal

Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto, Satoshi Takeda, Hiroki Koike, Kazuya Yamaji, Koji Asano

Nuclear Science and Engineering Vol. 196 ( 7 ) page： 769 - 791 2022.7

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Improvements in computational efficiency for the Resonance calculation using energy Spectrum Expansion (RSE) method are proposed in order to increase the applicability of the method for core nuclear analyses. First, efficient treatment of the neutron source for the RSE method has been newly developed. This is a balanced approach from the viewpoints of computation time and memory size, in comparison with the other approaches mentioned in a previous study [R. KONDO et al., “A New Resonance Calculation Method Using Energy Expansion Based on a Reduced Order Model,” Nucl. Sci. Eng., 195, 694 (2021)]. Second, low-rank approximation has been applied to the RSE method considering the deficit ratio of the singular value for the orthogonal basis. Computation time was reduced by ~68% while maintaining sufficient accuracy of effective cross sections. Third, the impacts of the discretization parameters in the method of characteristics on the RSE method have been investigated, and coarser conditions of the parameters were found to be appropriate from the viewpoints of computation time and accuracy of effective cross sections. Finally, RSE calculations with these improvements have been performed for the fuel assembly geometry of a light water reactor. The computation time was reduced by ~70%, and the data size of the scattering cross-section moments was approximately 3900 times smaller in comparison with the RSE calculation without the improvements.

DOI： 10.1080/00295639.2021.2025297

Impact of Angular and Spatial Source Distribution Approximations on Convergence Performance of Nonlinear Acceleration Methods for MOC in Slab Geometry Reviewed International journal

Yoshiki Oshima, Tomohiro Endo, Akio Yamamoto

Nuclear Science and Engineering Vol. 196 ( 4 ) page： 379 - 394 2022.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The convergence performance of nonlinear acceleration methods for the method of characteristics (MOC) with flat source (FS) approximation (FS MOC) or linear source (LS) approximation (LS MOC) is numerically investigated by focusing on the spatial and angular approximations in the acceleration calculations. The convergence of nonlinear acceleration depends on the consistency of the calculation models between the higher-order and lower-order (acceleration) methods. The convergence of four acceleration methods is evaluated to clarify the relationship between model consistency and convergence performance. These methods consist of FS or LS for the spatial source distribution and P1 or discrete angle for the angular distribution, i.e., (1) FS analytic coarse mesh finite difference (ACMFD) acceleration (FS ACMFD), (2) LS ACMFD, (3) FS angular-dependent discontinuity factor MOC (ADMOC) acceleration (FS ADMOC), and (4) LS ADMOC. The ACMFD and ADMOC accelerations are based on P1 and discrete angle approximations, respectively. The FS MOC and LS MOC are considered higher-order methods. The FS MOC and LS MOC with five acceleration methods, i.e., the aforementioned four acceleration methods and the conventional coarse mesh finite difference acceleration method, are used to perform fixed-source calculations in one-group one-dimensional homogeneous slab geometry, and the spectral radii are numerically evaluated. The numerical results indicate that (1) the nonlinear acceleration methods that are unconditionally stable for FS MOC also show similar convergence properties for LS MOC in one-dimensional slab geometry; (2) better convergence is observed when the consistency of higher- and lower-order models is high; and (3) when a coarse mesh is optically thick, the spatial homogenization degrades the convergence performance, even if spatial and angular approximations are consistent between the higher- and lower-order models.

DOI： 10.1080/00295639.2021.1982549

Applicability of Dynamic Mode Decomposition to Estimate Fundamental Mode Component of Prompt Neutron Decay Constant from Experimental Data Reviewed International journal

Fuga Nishioka, Tomohiro Endo, Akio Yamamoto, Masao Yamanaka, Cheol Ho Pyeon

Nuclear Science and Engineering Vol. 196 ( 2 ) page： 133 - 143 2022.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

To robustly estimate the fundamental mode component of prompt neutron decay constant α in a subcritical system, dynamic mode decomposition (DMD) is applied to time-series data obtained by the pulsed-neutron source (PNS) and Rossi-α methods. For the statistical uncertainty quantification of α by DMD, randomly sampled virtual data are used for the DMD procedure. The applicability of DMD is demonstrated by analyzing the experimental results by the PNS and Rossi-α methods, which are performed at the Kyoto University Critical Assembly (KUCA). When applying the DMD to the PNS and Rossi-α experimental data, a constant signal was added to the experimental data to remove the background constant component. The application results indicate that DMD enables one to robustly estimate the fundamental mode component of α in the PNS and Rossi-α methods.

DOI： 10.1080/00295639.2021.1968225

Adaptive setting of background cross sections for generation of effective multi-group cross sections in FRENDY nuclear data processing code Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Kenichi Tada

Journal of Nuclear Science and Technology Vol. 58 ( 12 ) page： 1343 - 1350 2021.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

An adaptive setting method of background cross sections is implemented to FRENDY/MG, which is a multi-group neutron cross section generation module, for accurate interpolation of self-shielding factors with a minimum number of background cross sections. Since the dependence of self-shielding factors on background cross section is significantly different among energy group, reaction type, and nuclide, appropriate setting of background cross sections usually requires considerable works. In the present adaptive setting method, the range of background cross section is initially divided into 10 equal intervals and unnecessary background cross section points are eliminated. Then interpolation accuracy at each interval is tested. If the interpolation accuracy in an interval is not sufficient, the interval is successively halved until sufficient interpolation accuracy is obtained. For accurate interpolation of self-shielding factor or reaction rates, the monotone cubic interpolation is used. Verification calculations are carried out for all isotopes in JENDL-4.0. Calculation results indicate that the present method provides an appropriate set of background cross sections while satisfying input error tolerance for self-shielding factors or reaction rates. Typical numbers of background cross sections are from 10 to 25 when the monotone cubic interpolation and error tolerance of 0.01 for self-shielding factors are used.

DOI： 10.1080/00223131.2021.1944930

Application of continuous Markov-chain Monte-Carlo method to multi-unit risk evaluations considering interdependence of accident progression among multiple units Reviewed International journal

Kento Sawada, Akio Yamamoto, Tomohiro Endo, Chikahiro Sato, Keisuke Maeda, Sunghyon Jang

Journal of Nuclear Science and Technology Vol. 58 ( 12 ) page： 1308 - 1317 2021.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The accident in Fukushima Dai-ichi nuclear power plants reconfirms the necessity of the safety assessment considering multiple nuclear reactor units. However, consideration of the interdependency among safety systems or events in multiple units as well as the time dependency of accident progressions is difficult in the conventional event tree method, which is widely used in probabilistic risk assessments. Recently, the continuous Markov-chain Monte-Carlo (CMMC) method coupled with a plant safety analysis or a severe accident analysis code has been paid attention to address these issues. In the present study, the CMMC coupling method is applied to the risk assessment of multiple units to clarify the benefits and issues to be resolved of this method. Since the CMMC coupling method requires many executions of an accident analysis code, a meta-model that simplifies systems and physical phenomena in accidents is used in this study to reduce computational cost. Furthermore, the inverse transform sampling method is newly adapted. Numerical analyses of BWR accident under station blackout with loss of cooling capability are carried out considering the correlation among the availabilities of mitigation systems. The results suggested that the CMMC coupling method can quantitatively treat the interdependency and time dependency among events in multiple units.

DOI： 10.1080/00223131.2021.1940341

Multi-group neutron cross section generation capability for FRENDY nuclear data processing code Reviewed International journal

Akio Yamamoto, Kenichi Tada, Go Chiba, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. 58 ( 11 ) page： 1165 - 1183 2021.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The multi-group cross-section generation capability for neutrons is implemented in the FRENDY nuclear data processing code. ACE-formatted files are used as the source of nuclear data instead of ENDF-formatted files since FRENDY already has the capability to generate pointwise cross sections in the ACE format. The several distinguished features are implemented for the multi-group generation capability, e.g. explicit consideration of resonance interference effect among nuclides, enhanced resonance treatment for various nuclear reactions, and accurate numerical integration of thermal cross sections. Verification calculations of the newly implemented capability are carried out through the comparison with the NJOY nuclear data processing code. Cross-section generations for all nuclides in JENDL-4.0, -4.0u, -5α4, ENDF/B-VII.1, -VIII.0, JEFF-3.3, and TENDL-2019 are carried out without unexpected processing issues, except for Pu-238 of TENDL-2019 that includes inconsistent data. The verification results indicate that the multi-group cross sections generated by FRENDY are consistent with those generated by NJOY. Now FRENDY can generate not only the pointwise cross sections for continuous energy Monte-Carlo codes but also the multi-group cross sections for deterministic neutronics analysis codes.

DOI： 10.1080/00223131.2021.1921631

Proposal and applicability of estimated criticality lower-limit multiplication factor using the bootstrap method Reviewed International journal

Takuto Hayashi, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 58 ( 9 ) page： 1008 - 1017 2021.9

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

To judge whether an application system is a subcritical state or not based on numerical results of the effective neutron multiplication factor keff, an evaluation method of the estimated criticality lower-limit multiplication factor (ECLLMF) using the bootstrap method is newly proposed. By utilizing numerical results of keff for critical benchmark-problems that are selected depending on neutronic similarity to the application system, the ECLLMF should be carefully and conservatively estimated based on uncertainties of keff due to a criticality safety analysis code, experimental uncertainty, and covariance matrix of the nuclear data library. Furthermore, the frequency distribution of keff for these problems does not necessarily obey an ideal normal distribution. Using a resampling technique called ‘bootstrap method,’ the proposed method can reasonably estimate the ECLLMF considering the uncertainties and nuclear data-induced correlation between each critical benchmark-problem without the assumption of normality. To investigate the applicability of the proposed method, the approach-to-criticality experiment was carried out at the Kyoto University Critical Assembly (KUCA). Comparison of numerical results of keff and the ECLLMF using the bootstrap method indicated that the proposed method was able to judge an actual subcritical core as subcritical state.

DOI： 10.1080/00223131.2021.1902416

A New Resonance Calculation Method Using Energy Expansion Based on a Reduced Order Model Reviewed International journal

Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto, Satoshi Takeda, Hiroki Koike, Kazuya Yamaji, Daisuke Sato

Nuclear Science and Engineering Vol. 195 ( 7 ) page： 694 - 716 2021.7

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A Resonance calculation using energy Spectrum Expansion (RSE) method is newly proposed in this paper. In this method, ultra-fine-group (UFG) spectra appearing in a resonance calculation are expanded by orthogonal bases on energy, which are extracted from the UFG spectra obtained in homogeneous geometry with various background cross sections using singular value decomposition and low-rank approximation. Namely, this method is based on the concept of a reduced order model. A neutron transport equation for flux moments (expansion coefficients) similar to the conventional one is derived and is numerically solved. This method applies to two benchmark problems in which a resonance interference effect and spatial self-shielding effect can appear. The results indicate that this method accurately predicts the reference effective cross sections and reaction rates obtained from direct UFG calculation in heterogeneous geometry.

DOI： 10.1080/00295639.2020.1863066

Fast reproduction of time-dependent diffusion calculations using the reduced order model based on the proper orthogonal and singular value decompositions Reviewed International journal

Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 58 ( 2 ) page： 173 - 183 2021.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

An efficient reduced order model (ROM) for time-dependent diffusion calculations using the proper orthogonal decomposition (POD) is proposed. Employing the singular value decomposition (SVD) and low-rank approximation (LRA) for the flux distributions sampled from the detail full order model (FOM) solutions, the orthogonal basis suitable for a target problem is numerically obtained. In the present ROM, flux distribution is expanded with an orthogonal basis on space. Then, the dimensionality reduction is performed for the neutron diffusion equation using the orthogonal basis, and the equation for the expansion coefficients is obtained. Since any flux distributions can be used to construct the orthogonal bases, different orthogonal bases calculated from different flux distribution sets are tested. The accuracy and computation time of the present ROM are verified in the TWIGL benchmark problem. The calculation results show that the present ROM is approximately 100 times faster than the FOM for kinetic calculations in the present conditions. The present method can be substituted as real-time FOM simulations when typical flux distributions of a target problem can be precalculated to represent the solution space with less degree of freedom (DOF).

DOI： 10.1080/00223131.2020.1814891

Compression of Cross-Section Data Size for High-Resolution Core Analysis Using Dimensionality Reduction Technique Reviewed International journal

Masato Yamamoto, Tomohiro Endo, Akio Yamamoto

Nuclear Science and Engineering Vol. 195 ( 1 ) page： 33 - 49 2021.1

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Compression of cross-section data used for high-resolution core analysis is performed using a dimensionality reduction technique based on the singular value decomposition (SVD) and low-rank approximation. The size of cross-section data can be a significant issue in high-resolution core analysis using detailed energy and spatial resolutions. This study addresses this issue focusing on the similarity of multigroup cross sections among different spatial regions. A data compression method using the SVD and low-rank approximation is applied for the multigroup microscopic cross sections of heterogeneous material regions obtained by a lattice physics calculation with burnup and branch calculations. Weighting by nuclide number densities and neutron spectra is considered to improve the efficiency of compression for cross sections. Single-assembly transport calculations with the method of characteristics are carried out using the original cross sections and the reconstructed cross sections after data compression. The accuracy of data compression for cross sections is evaluated by comparing the multiplication factor and multigroup scalar fluxes. The results indicate that the present data compression for microscopic cross sections can reduce approximately 99.7% of the original cross-section data size under the present calculation condition.

DOI： 10.1080/00295639.2020.1781482

Neutron Generation Time in Highly-Enriched Uranium Core at Kyoto University Critical Assembly Reviewed International journal

Cheol Ho Pyeon, Masao Yamanaka, Tomohiro Endo, Go Chiba, Willem F. G Van Rooijen, Kenichi Watanabe

Nuclear Science and Engineering Vol. 194 ( 12 ) page： 1116 - 1127 2020.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

At the Kyoto University Critical Assembly experiments on kinetics parameters are carried out at near-critical configurations, supercritical and subcritical states, in the thermal neutron spectrum made with a highly enriched uranium fuel. The main calculated kinetics parameters, the effective delayed neutron fraction (βeff) and the neutron generation time (Ʌ), are used effectively for the estimation of experimental parameters, and the accuracy of experiments on prompt neutron decay constant (α) and subcriticality (ρ_dollar) in dollar units is attained by the numerical results of βeff and Ʌ. Furthermore, the value of βeff/Ʌ is experimentally deduced with the use of the experimental results of α and ρ_dollar, ranging between 250 and −80 pcm. Thus, the experimentally deduced values of βeff/Ʌ that reveal good accuracy through a comparison with those by the MCNP6.1 calculations with JENDL-4.0 are then taken as an index of Ʌ by introducing an acceptable assumption of βeff at near-critical configurations. From the results of experimental and numerical analyses, the experimental value of βeff/Ʌ is important for the validation of Ʌ since kinetics parameters are successfully obtained from the clean cores of near-critical configurations in the thermal neutron spectrum.

DOI： 10.1080/00295639.2020.1774230

Applicability of a reduced order model for a safety analysis code to statistical safety analysis Reviewed International journal

Masaki Matsushita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 57 ( 12 ) page： 1307 - 1318 2020.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A reduced order model (ROM) for a safety analysis code (RELAP/SCDAPSIM) is developed and is applied to the statistical safety analysis in order to reduce computational load. The ROM that reproduces output of the safety analysis code (e.g., the peak cladding temperature) is constructed using the singular value decomposition and the low-rank approximation for time-series data of a safety analysis code. A sampling method that incorporates dissimilarity among input data is tested to generate training data for the ROM. A loss of coolant accident with multiple failures of safety functions in a BWR is considered as an accident scenario. Statistical results such as the average, the standard deviation, and the 95% cumulative probability value of safety parameters obtained by the ROM and those obtained by the safety analysis code are compared. The reference results obtained by the direct random sampling method with the safety analysis code are within the 95% confidence interval of the results obtained by ROM. Thus the applicability and effectiveness of the ROM to the statistical safety analysis are confirmed through numerical analysis.

DOI： 10.1080/00223131.2020.1783382

Implementation of the unscented transformation with low rank approximation in uncertainty analysis during large-break loss of coolant accident Reviewed International journal

Basma Foad, Akio Yamamoto, Tomohiro Endo

Annals of Nuclear Energy Vol. 146 page： 107614 2020.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

The Low Rank Approximation (LRA) and Unscented Transform (UT) are integrated to produce a new algorithm having the capability to decrease the time required for the uncertainty quantification during Loss of coolant accident (LOCA) in Pressurized Water Reactors (PWR). The LRA is an efficient technique used in reducing computational cost due to its ability to perform dimensionality reduction by revealing the active or important degrees of freedom and calculate the basis of the so-called active subspace basing on the Singular Value Decomposition (SVD). For further reduction in the computational time; the UT algorithm is also implemented to generate a set of sigma points, these sigma points are the representatives of the whole probability distribution (the UT is restricted to Gaussian distribution). The main safety parameter is the maximum cladding temperatures during the accident which are computed by ATHLET thermal-hydraulic code. The reactivity coefficients and the covariance matrix are calculated using the SCALE 6.2 code. The present calculation model has 14-dimensions, therefore the number of sigma points needed for the SVD/UT technique is 29, and can be minimized to 5 sigma points only if the LRA/UT is used where two singular values are sufficient to reproduce/span the space thanks to the strong correlations between the reactivity coefficients.

DOI： 10.1016/j.anucene.2020.107614

Uncertainty and regression analysis of the MSLB accident in PWR based on unscented transformation and low rank approximation Reviewed International journal

Basma Foad, Akio Yamamoto, Tomohiro Endo

Annals of Nuclear Energy Vol. 143 page： 107493 2020.8

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

The present studies focus on the quantification of uncertainty during the main steam line break accident scenario (MSLB) in PWR, assuming that there is a failure on the feed-water regulating valve of the broken steam generator. The scenario is characterized by the associated positive Doppler and coolant density reactivities which bring the core back to critical (return-to-power). Accordingly, the input uncertainty parameters are the Doppler and coolant density reactivities taking into account the correlation matrix among the input parameters, which is calculated by SCALE 6.2 code. The main safety parameters are the maximum cladding surface temperatures and average core power during the accident which are computed by ATHLET thermal-hydraulic code. The sampling-based uncertainty technique is considered to be the most dependable technique which can be applicable to any code, however it is computationally expensive. Therefore, it is important to develop efficient techniques which are capable of reducing the calculation time. The first approach is the SVD-UT where the Unscented Transform (UT) algorithm and singular value decomposition (SVD) are combined to generate a minimal sample points. In addition, due to the strong correlation between the input reactivities, the computational time can be further reduced by implementing the Low Rank Approximation (LRA) and revealing the active subspace.

DOI： 10.1016/j.anucene.2020.107493

Efficient uncertainty quantification for PWR during LOCA using unscented transform with singular value decomposition Reviewed International journal

Basma Foad, Akio Yamamoto, Tomohiro Endo

Annals of Nuclear Energy Vol. 141 page： 107341 2020.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

This paper discusses one of the most important issues facing the regulatory body while performing the uncertainty analysis of the nuclear reactor parameter during accident conditions. This problem is the long computational time required by the statistical sampling methods to compute the uncertainty. We overcome this problem by introducing the Unscented Transform (UT) algorithm and singular value decomposition (SVD). Where both algorithms are combined (SVD/UT) to generate a set of sigma points, these sigma points are the representatives of whole probability distribution. The uncertainty quantification is performed during Loss of coolant accident in Pressurized Water Reactor (PWR), where the input variable of uncertainty is the coolant density reactivity. The SCALE 6.2 code is used for calculating the reactivity coefficients and the covariance matrix. The response variables are the peak cladding temperatures during the accident which are computed by ATHLET thermal-hydraulic code. The results obviously confirm the efficiency of the SVD/UT sampling in predicting the new mean values, and assure its ability to reduce the sampling size leading to a dramatic reduction of computational cost.

DOI： 10.1016/j.anucene.2020.107341

Impact of Various Parameters on Convergence Performance of CMFD Acceleration for MOC in Multigroup Heterogeneous Geometry Reviewed International journal

Yoshiki Oshima, Tomohiro Endo, Akio Yamamoto, Yasuhiro Kodama, Yasunori Ohoka, Hiroaki Nagano

Nuclear Science and Engineering Vol. 194 ( 6 ) page： 477 - 491 2020.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The impact of various parameters in the coarse mesh finite difference (CMFD) acceleration method on overall convergence behavior is investigated through numerical calculations using the method of characteristics (MOC). Four parameters appearing in the CMFD acceleration with MOC, i.e., scalar flux distribution in flat flux regions (FFRFlux), the scalar flux distribution in CMFD meshes (CMFDFlux), homogenized cross sections (HXSs) in CMFD meshes, and current correction factors (CCFs), are considered. Parts of these four parameters are fixed to the converged values throughout iterations in order to estimate their impact on convergence. Numerical calculations are carried out for Korea Advanced Institute of Science and Technology’s (KAIST’s) benchmark problem KAIST-2A, which is a heterogeneous and multigroup problem, and the number of outer iterations to reach convergence is evaluated. The impact of geometric heterogeneity and cross-section homogenization in the CMFD acceleration has not been considered in linearized Fourier analysis so far. The calculation results indicate that (1) convergence of HXS has little impact on the overall convergence, (2) convergence of FFRFlux is dominant followed by CCF when a CMFD mesh is optically thin, and (3) convergence of FFRFlux is dominant when a CMFD mesh is optically thick and contains many flat flux regions.

DOI： 10.1080/00295639.2020.1722512

Application of the multigrid amplitude function method for time-dependent MOC based on the linear source approximation Reviewed International journal

Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 57 ( 6 ) page： 646 - 662 2020.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

An efficient numerical scheme for time-dependent MOC calculations is proposed. In the present scheme, one of the most successful factorization method, the multigrid amplitude function (MAF) method, is employed to achieve faster computation with the minimum degradation for the temporal integration of the scalar flux. In addition, the MAF method is re-derived based on the linear source approximation, which is not applied for time-dependent MOC calculations in the past studies as far as the authors’ knowledge, to reduce the spatial discretization error with the coarser flux region separation. The accuracy and computational time of the present scheme are evaluated through the calculation of the TWIGL and the C5G7-TD 2D benchmark problems. The present calculation results show that the present scheme is 6.2 times faster than the conventional method while achieving the same accuracy in the C5G7-TD benchmark problem.

DOI： 10.1080/00223131.2019.1709993

Development of a reduced order model for severe accident analysis codes by singular value decomposition aiming probabilistic safety margin analysis Reviewed International journal

Masaki Matsushita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 57 ( 5 ) page： 573 - 589 2020.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Severe accident codes (e.g. MAAP, RELAP, and MELCORE) model various physical phenomena during severe accidents. Many analyses using these codes for safety margin evaluation are impractical due to large computational costs. Surrogate models have an advantage of quickly reproducing multiple results with a low computational cost. In this study, we apply the singular value decomposition to the time-series results of a severe accident code to develop a reduced order modeling (ROM). Using the ROM, the probabilistic safety margin analysis for the station blackout with a total loss of feedwater capabilities at a boiling water reactor is carried out. The dominant parameters to the accident progression are assumed to be the down-time and the recovery-time of the reactor core isolation cooling system, and decay heat. To reduce the number of RELAP5/SCDAPSIM analyses while maintaining the prediction accuracy of ROM, we develop a data sampling method based on adaptive sampling, which selects the new sampling data based on the dissimilarity with the existing training data for ROM. Our ROM can rapidly reproduce the time-series results and can estimate core conditions. By reproducing multiple results by ROM, a time-dependent core damage probability distribution is calculated instead of the direct use of RELAP5/SCDAPSIM.

DOI： 10.1080/00223131.2019.1699190

Subcriticality Measurement using Time-Domain Decomposition-Based Integral Method for Simultaneous Reactivity and Source Changes Reviewed International journal

Tomohiro Endo, Asahi Nonaka, Sho Imai, Akio Yamamoto, Atsushi Sakon, Kengo Hashimoto

Journal of Nuclear Science and Technology Vol. 57 ( 5 ) page： 607 - 616 2020.5

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

To estimate the subcriticality in dollar units for an arbitrary state-change, the time-domain decomposition-based integral method (TDDI) is proposed using the point kinetics theory based on the fundamental mode approximation. In a general transient subcritical system, reactivity, neutron source intensity, and point kinetics parameters can vary simultaneously. Furthermore, the state-change may not necessarily be a stepwise change. For such a transient, the TDDI method can estimate the subcriticality after the transient using only the time variation of the neutron count rate. Therefore, the proposed method is useful to approximately estimate the subcriticality in a system where a detailed core configuration is unknown. To investigate the applicability of the TDDI method, transient experiments with simultaneous reactivity and source changes or to two successive safety rods dropping were performed at the Kindai University Training and Research Reactor (UTR-KINKI). By comparing with reference values using excess reactivity and control rod worth, it was validated that the subcriticality values obtained by the TDDI method better agree with the reference values than the previous integral method.

DOI： 10.1080/00223131.2019.1706658

Other Link： https://doi.org/10.1080/00223131.2019.1706658

Loading pattern optimization for a PWR using Multi-Swarm Moth Flame Optimization Method with Predator Reviewed International journal

Satomi Ishiguro, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 57 ( 5 ) page： 523 - 536 2020.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

This paper aims to propose a new methodology for optimizing fuel loading pattern in a nuclear reactor which is important for its higher safety and economic efficiency. Previous researches have proposed various methodologies to decide better loading patterns automatically. However, the processes still require manual operations of engineers to automatically design actual loading patterns. Swarm intelligence algorithm has currently gained interest as a solution to seek the patterns. Although these methodologies generate better patterns, they sometimes struggle with getting out from local optima and fails to complete the optimization. Large and multimodal solution space sometimes captures worse solutions due to local optima. The conventional methodologies struggle with setting proper parameters to get out from local optima. This research focuses on Multi-Swarm Moth Flame Optimization with Predator (MSMFO-P), an improved Moth Flame Optimization (MFO) by applying the concepts of predator and multi-swarm, as new methodologies. The method of MSMFO-P was applied to solve a loading pattern problem and compared with the conventional optimization methods such as simulated annealing (SA), Hybrid genetic algorithm (GA), and particle swarm optimization (PSO). The results of our experimental works indicated that MSMO-P generates better loading patterns than the conventional methodologies.

DOI： 10.1080/00223131.2019.1700844

Nuclear data-induced uncertainty quantification of prompt neutron decay constant based on perturbation theory for ADS experiments at KUCA Reviewed International journal

Tomohiro Endo, Kenichi Watanabe, Go Chiba, Masao Yamanaka, Willem Frederik Geert, van Rooijen, Cheol Ho Pyeon

Journal of Nuclear Science and Technology Vol. 57 ( 2 ) page： 196 - 204 2020.2

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

In experimental benchmarks of the accelerator-driven system (ADS) conducted at the Kyoto University Critical Assembly (KUCA), the prompt neutron decay constant α was measured using two types of pulsed neutron sources, i.e. a D-T neutron source and a spallation neutron source driven by a 100-MeV proton beam. The measurement results of α are useful information to validate the numerical results predicted by the prompt ω-eigenvalue calculation. In this study, the numerical analysis of α using a multi-energy group SN neutron transport code was carried out for the uranium-lead zoned experimental cores. To reduce the discretization error owing to the deterministic code, the KUCA geometry was modelled in detail as a three-dimensional heterogeneous plate-by-plate geometry, and an improved variant of EON quadrature was utilized. In addition, the sensitivity coefficients of α with respect to nuclear data were efficiently evaluated by first-order perturbation theory, followed by nuclear data-induced uncertainty quantification based on the 56 neutron-energy group SCALE covariance library. Consequently, the numerical results of α were validated successfully by the experimental results of the pulsed neutron source method, compared with the range of the nuclear data-induced uncertainties.

DOI： 10.1080/00223131.2019.1647893

Numerical benchmark problem of solid-moderated enriched-uranium-loaded core at Kyoto university critical assembly Reviewed International journal

Go Chiba, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. 57 ( 2 ) page： 187 - 195 2020.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Useful and valuable measurement data obtained at the solid-moderated core for the development of accelerator-driven systems (ADSs) have been accumulated at the Kyoto University Critical Assembly (KUCA), and some of them have been open to the public. In order to efficiently utilize these data, experimental analyses with deterministic calculation procedures are helpful. In the present manuscript, a numerical benchmark problem is established. This benchmark problem can be utilized by users of the ADS-related measurement data obtained at the KUCA A-core to verify their own numerical tools devoted to experimental analyses. Material and geometrical specifications with reference solutions obtained by a continuous-energy Monte Carlo code MVP-II are provided.<br />
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In addition, numerical results obtained by a deterministic code system CBZ are also presented as an example. Through careful investigation about discretization on space and angle, guideline for proper discretization is provided. The CBZ results tend to underestimate the reference Monte Carlo solutions about 0.5%∆k/kk', and calculations of simplified core models suggest that this is caused by neutron leakage treatment in finite systems or resonance self-shielding treatment in CBZ.

DOI： 10.1080/00223131.2019.1647892

Real-time subcriticality monitoring system based on a highly sensitive optical fiber detector in an accelerator-driven system at the Kyoto University Critical Assembly Reviewed International journal

Watanabe Kenichi, Yamanaka Masao, Endo Tomohiro, Pyeon Cheol Ho

Journal of Nuclear Science and Technology Vol. 57 ( 2 ) page： 136 - 144 2020.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A real-time subcriticality monitoring system for accelerator-driven system (ADS) is developed at the Kyoto University Critical Assembly (KUCA). The monitoring system consists of a highly sensitive optical fiber-based neutron detector, which combines a large number of small pieces of LiF/Eu:CaF2 eutectic scintillators with a wavelength-shifting fiber, and a digital signal processing system. The fabricated detector is sufficiently small for insertion into slight gaps between the fuel assemblies of the KUCA core and clearly reveals a peak shape indicating neutron signals in the pulse height spectrum. As subcriticality determination procedures, the system employs the Rossi-α, α-fitting, and area ratio methods. The subcriticality experimental results and their related parameters are compared with numerical results. Although the area ratio method slightly underestimates the parameters, overall, the estimated parameters agree well with the calculated ones. Finally, the developed system is found to evaluate the subcriticality within an accuracy of approximately 20% for the effective neutron multiplication factor keff ranges between 0.97 and 0.93, which are used in typical ADS experiments.

DOI： 10.1080/00223131.2019.1647895

Experimental analyses of βeff/Λ in accelerator-driven system at Kyoto University Critical Assembly Reviewed International journal

Masao Yamanaka, Cheol Ho Pyeon, Tomohiro Endo, Kenichi Watanabe, Go Chiba, Willem Frederik Geert van Rooijen

Journal of Nuclear Science and Technology Vol. 57 ( 2 ) page： 205 - 215 2020.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The capability of βeff/Λ obtained by λ-mode and ω-mode calculations is examined for target subcriticality in the accelerator-driven system through a comparison with that obtained in the pulsed-neutron source (PNS) experiments at the Kyoto University Critical Assembly. Directly measured results of βeff/Λ, α and ρ_$ in the PNS experiments are validated by varying the experimental conditions: the external neutron source, detector position, detector type and subcriticality ranging between 500 and 7500 pcm. The numerical analyses of βeff/Λ are conducted by using MCNP6.1 together with ENDF/B-VII.1 for λ-mode calculations and PARTISN (SCALE6.2.2 with ENDF-VII.1 for the effective cross sections) for both the λ-mode and the ω-mode calculations. The comparison between calculated and measured βeff/Λ with varying subcriticality shows good agreement between the experiments and the ω-mode calculations, although a difference is observed between the experiments and the λ-mode calculations.

DOI： 10.1080/00223131.2019.1666057

A New Interpretation of Discontinuity Factor Reviewed International journal

Akio Yamamoto, Tomohiro Endo

Nuclear Science and Engineering Vol. 193 ( 9 ) page： 991 - 997 2019.9

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A new interpretation of the discontinuity factor (DF) for scalar flux, partial current, and angular flux is discussed. Conventionally, the DF is considered as the discontinuous condition of scalar flux, partial current, or angular flux at an interface. In the new interpretation, the DF is considered as the refractive index of materials for partial current or angular flux that conserves odd-parity or odd-moment angular flux at an interface of different materials. It is related to the transmission and reflection of partial current or angular flux at an interface where different materials are adjacent. Using the present interpretation, a fundamental issue of neutron balance (i.e., artificial loss or production of neutrons at an interface due to discontinuous condition), which would appear in the conventional interpretation of DF, can be resolved.

DOI： 10.1080/00295639.2019.1579514

First nuclear transmutation of Np237 and Am241 by accelerator-driven system at Kyoto University Critical Assembly Reviewed International journal

Cheol Ho Pyeon, Masao Yamanaka, Akito Oizumi, Masahiro Fukushima, Go Chiba, Kenichi Watanabe, Tomohiro Endo, Wilfred G. Van Rooijen, Kengo Hashimoto, Atsushi Sakon, Naoto Aizawa, Yasutoshi Kuriyama, Tomonori Uesugi, Yoshihiro Ishi

Journal of Nuclear Science and Technology Vol. 56 ( 8 ) page： 684 - 689 2019.8

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

This study demonstrates, for the first time, the principle of nuclear transmutation of minor actinide (MA) by the accelerator-driven system (ADS) through the injection of high-energy neutrons into the subcritical core at the Kyoto University Critical Assembly. The main objective of the experiments is to confirm fission reactions of neptunium-237 (Np237) and americium-241 (Am241), and capture reactions of Np237. Subcritical irradiation of Np237 and Am241 foils is conducted in a hard spectrum core with the use of the back-to-back fission chamber that obtains simultaneously two signals from specially installed test (Np237 or Am241) and reference (uranium-235) foils. The first nuclear transmutation of Np237 and Am241 by ADS soundly implemented by combining the subcritical core and the 100 MeV proton accelerator, and the use of a lead-bismuth target, is conclusively demonstrated through the experimental results of fission and capture reaction events.

DOI： 10.1080/00223131.2019.1618406

Transport consistent diffusion coefficient for CMFD acceleration and comparison of convergence properties Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Akinori Giho

Journal of Nuclear Science and Technology Vol. 56 ( 8 ) page： 716 - 723 2019.8

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A diffusion coefficient for the coarse mesh finite difference (CMFD) acceleration is derived from the semi-analytic solution of one-group, one-dimensional, even-parity transport equation. The derived diffusion coefficient, i.e., the transport consistent diffusion coefficient (TCD), depends on the optical length of a mesh and shows similar behavior with the artificial grid diffusion (AGD) and the effective diffusion (EffD) coefficients for an optically thick mesh. Convergence properties of typical diffusion coefficients are evaluated using the linearized Fourier analysis. Analyses of the C5G7 3D benchmark problems with and without voided region are carried out to compare the convergence properties. The number of transport sweeps to reach convergence using TCD is smaller than that using EffD or AGD.

DOI： 10.1080/00223131.2019.1618405

A simple treatment of increased gap due to fuel assembly bowing through correction of cross sections Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Hiroaki Nagano, Yasunori Ohoka, Kento Yamamoto

Journal of Nuclear Science and Technology Vol. 56 ( 6 ) page： 471 - 478 2019.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Increased fuel assembly gap due to bowing in commercial light-water reactors (LWRs) has an impact on local pin-power distribution due to increased local moderation. In order to consider the effect of increased assembly gap without explicit consideration of increased gap width, a correction method of cross sections in the gap region is proposed. In this cross section correction method, the average chord length of gap region is preserved to capture the effect of increased gap width. The validity of the present method is confirmed by verification calculations in a single assembly and 5 × 5 assembly geometries using the GENESIS code, which is a transport code based on the method of characteristics.

DOI： 10.1080/00223131.2019.1598509

Utilization of Regionwise Even-Parity Discontinuity Factor to Reduce Discretization Error of MOC Reviewed International journal

Yamamoto Akio, Giho Akinori, Endo Tomohiro

Nuclear Science and Engineering Vol. 193 ( 3 ) page： 253 - 268 2019.3

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

To reduce angular and spatial discretization error of the method of characteristics with a coarse calculation condition, the regionwise even-parity discontinuity factor (EPDF) for transport calculations is evaluated through an iterative procedure using only the regionwise scalar flux, i.e., without the odd-parity angular flux, the partial current, or the net current at the region boundary. The regionwise EPDF is evaluated in a single-assembly geometry with the reflective boundary condition. The evaluated EPDF is applied to a 2 × 2 colorset assembly and core configurations, and the performance is compared to that of the conventional superhomogenization (SPH) method. The calculation results indicate that (1) no convergence issue is observed during the iteration process to estimate the EPDF, (2) the performance of the regionwise EPDF is better than that of the conventional SPH method, and (3) the normalization of the EPDF is necessary to incorporate different surface scalar flux levels among different types of fuel assemblies.

DOI： 10.1080/00295639.2018.1516961

Inverse estimation methods of unknown radioactive source for fuel debris search Invited Reviewed International journal

Shinji Sugaya, Tomohiro Endo, Akio Yamamoto

Annals of Nuclear Energy Vol. 124 page： 49 - 57 2019.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

To identify the distribution of fuel debris remaining in the reactor vessel and/or the containment vessel of Fukushima Daiichi NPS, we focused on the inverse estimation of radioactive source distribution using the measured radiation counts. The Maximum Likelihood-Expectation Maximization (ML-EM) and the Moore-Penrose Matrix Inverse (MPMI) methods are examined. The ML-EM method has been used for the image reconstruction of computed tomography, and the MPMI method is one of the solution methods for simultaneous linear equations with the underdetermined condition. A simple calculation model simulating a containment vessel was constructed including detectors and radiation sources. In an actual situation, a sufficient number of radiation measurement positions would not be available owing to the complexity of structures inside the containment vessel. Thus, the number of radiation measurement points (number of constraints) is smaller than that of radiation source positions. It means that an underdetermined inverse problem should be solved. The detection probability of radiation (neutron or photon) is calculated by the adjoint transport calculation since the detection probability is used as the coupling coefficient between radiation counts at a detector and a radioactive source. The result of estimation using the ML-EM or the MPMI method indicates that the accuracy of estimation depends on the distance between a radiation source and a detector, and measurement positions of radiation count. The ML-EM and the MPMI methods show different prediction accuracy depending on the prediction condition. It is found that reasonable prediction accuracy would be obtained when the detectors are placed at the vicinity of radiation sources of interest.

DOI： 10.1016/j.anucene.2018.09.022

Flux Region Assignment Method Using Ray Trace Information for the Method of Characteristics to Improve Cache Efficiency Reviewed International journal

Akio Yamamoto, Akinori Giho, Tomohiro Endo

Nuclear Science and Engineering Vol. 192 ( 3 ) page： 240 - 253 2018.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A flux region assignment algorithm to increase cache efficiency for the method of characteristics (MOC) is proposed. In order to minimize the stride of memory access, flux region identifications are assigned based on the ray trace sequence during the MOC calculation. The present method is implemented in the three-dimensional transport code GENESIS and its performance is confirmed through verification calculations ranging from single pressurized water reactor (PWR) fuel assembly to PWR full-core benchmark problems. Quantitative comparison of cache efficiency is carried out and the present method shows improved cache efficiency, which results in a reduction in computation time. The present method can reduce computational time by improving cache efficiency while suppressing memory requirement.

DOI： 10.1080/00295639.2018.1501978

Underestimation of statistical uncertainty of local tallies in Monte Carlo eigenvalue calculation for simple and LWR lattice geometries Reviewed International journal

Koji Hayashi, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 55 ( 12 ) page： 1434 - 1458 2018.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A prediction method of the true variance of local tally in a Monte Carlo (MC) critical calculation is developed. In the MC calculation, the effective multiplication factor (keff) and the fission rate distribution are estimated by simulating fission chain reactions. The statistical uncertainty of calculation result is commonly estimated by the standard error based on the central limit theorem. However, the evaluated statistical uncertainty would be underestimated when the inter-cycle correlation is not appropriately taken into account. In this study, a theoretical formula of the underestimation ratio (UR) of the statistical uncertainty for a local tally is derived using the eigenfunction expansion and the Autoregressive model. Note that the UR is defined by the ratio of uncertainty estimated by a MC calculation to the true statistical uncertainty. The proposed method is applied to one-dimensional slab and multi-assembly geometries with reflective boundary conditions. In the one-dimensional slab geometry, the prediction results of UR show reasonable agreement with the reference. In the multi-assembly geometry, on the other hand, the prediction results of UR are agreement with the reference regarding the relative spatial shape but there are considerable differences in the absolute values of UR.

DOI： 10.1080/00223131.2018.1513875

Estimation of Sensitivity Coefficient based on Lasso-type Penalized Linear Regression Reviewed International journal

Ryota Katano, Tomohiro Endo, Akio Yamamoto, Kazufumi Tsujimoto

Journal of Nuclear Science and Technology Vol. 55 ( 10 ) page： 1099 - 1109 2018.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

We proposed the penalized regression 'adaptive smooth-lasso' for the estimation of sensitivity coefficients of the neutronics parameters. The proposed method utilizes the variation of the microscopic cross-sections and the neutronics parameters obtained by random sampling. The weighted penalty term of the proposed method is more appropriate for the estimation of the sensitivity of neutronics parameters to the microscopic cross-section than that of the conventional methods. In a numerical verification calculation, sensitivity coefficients of keff of an accelerator-driven system are estimated using the proposed method, the conventional penalized regression, and the direct method. Comparison of these results indicates that the proposed method is superior to the conventional penalized linear regression from the viewpoint of reproduction of the reference sensitivity coefficients obtained by the direct method. Through the verification calculations, the proposed method can be a candidate for a practical method to estimate the sensitivity coefficients with low calculation cost.

DOI： 10.1080/00223131.2018.1479988

Uncertainty quantification of criticality in solid-moderated and -reflected cores at Kyoto University Critical Assembly Reviewed International journal

Cheol Ho Pyeon, Masao Yamanaka, Makoto Ito, Go Chiba, Tomohiro Endo, Song Hyun Kim, Willem Fredrik G. van Rooijen

Journal of Nuclear Science and Technology Vol. 55 ( 7 ) page： 812 - 821 2018.7

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Uncertainty quantification is conducted for the criticality of excess reactivity and control rod worth obtained at the Kyoto University Critical Assembly (KUCA). By combining SRAC2006 and MARBLE code systems, the sensitivity coefficients of the cross sections for aluminum-27 (27Al) comprising mainly of core components are large in the solid-moderated and -reflected cores (A cores) at KUCA. Also, the uncertainty is dominant in the uranium-235 isotope by the covariance data of JENDL-4.0, and a quantitative value is about 150 pcm induced by the JENDL-4.0 data library in the KUCA A cores, whereas the covariance data of 27Al are not prepared in JENDL-4.0. Moreover, the effect of decreasing uncertainty is obtained by applying the cross-sectional adjustment method to the uncertainty analyses. From the results, a series of uncertainty quantifications is expected to clarify the uncertainty of sub-criticality in accelerator-driven system experiments with spallation neutrons in the KUCA A cores.

DOI： 10.1080/00223131.2018.1432426

Experimental analysis and uncertainty quantification using random sampling technique for ADS experiments at KUCA Reviewed International journal

Tomohiro Endo, Go Chiba, Willem Frederik Geert van Rooijen, Masao Yamanaka, Cheol Ho Pyeon

Journal of Nuclear Science and Technology Vol. 55 ( 4 ) page： 450 - 459 2018.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Nuclear data-induced uncertainties of neutronics parameters (neutron multiplication factor keff, one-point kinetics parameters and prompt neutron decay constant α) are quantified for lead-bismuth zoned accelerator-driven system experiments at the Kyoto University Critical Assembly, in order to contribute validation for subcritical core analysis. The random sampling technique using SCALE6.2.1/Sampler/NEWT/PARTISN is utilized for the validation and the uncertainty quantification, because the random sampling technique is applicable for a problem which is not easy to apply the perturbation theory. Consequently, it is confirmed that the numerical results of α reasonably agree with the experimental ones, compared with the nuclear data-induced uncertainties. In addition, it is clarified that the nuclear data-induced correlations between α and keff and between α and neutron generation time Λ are strongly negative and positive, respectively. This fact implies that the numerical predictions of keff and Λ can be improved by the data assimilation technique using subcritical experimental results of α, which can be directly measured even for a deep subcritical system.

DOI： 10.1080/00223131.2017.1403387

Analysis of the KUCA ADS benchmarks with diffusion theory Reviewed International journal

W.F.G. van Rooijen, T. Endo, G. Chiba, C. H. Pyeon

Progress in Nuclear Energy Vol. 101 page： 243 - 250 2017.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

This manuscript discusses the analysis of the KUCA-A ADS with deterministic theory, specifically diffusion theory. The KUCA-A ADS is a small, thermal-spectrum ADS. For the series of experiments in this manuscript, a DT fusion neutron source was used (14 MeV neutrons). Several sets of KUCA ADS experiments are available as international benchmarks. In our analysis, we calculated the multiplication factor, prompt neutron decay constant (α-eigenvalue), and used time-dependent diffusion theory to analyze pulsed neutron operation of the KUCA-A ADS. The results are that the multiplication factor is generally well predicted as long as the void regions in the core remain of a limited extent. The time-eigenvalue (α-eigenvalue) is also well predicted, and knowledge of the α-mode can be effectively used in the selection of measurement data for curve fitting methods.

DOI： 10.1016/j.pnucene.2017.08.007

Benchmarks of subcriticality in accelerator-driven system at Kyoto University Critical Assembly Invited Reviewed International journal

Cheol Ho Pyeon, Masao Yamanaka, Song-Hyun Kim, Thanh-Mai Vu, Tomohiro Endo, Willem Fredrik G. Van Rooijen, Go Chiba

Nuclear Engineering and Technology Vol. 49 ( 6 ) page： 1234 - 1239 2017.9

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

Basic research on the accelerator-driven system is conducted by combining 235U-fueled and 232Th-loaded cores in the Kyoto University Critical Assembly with the pulsed neutron generator (14 MeV neutrons) and the proton beam accelerator (100 MeV protons with a heavy metal target). The results of experimental subcriticality are presented with a wide range of subcriticality level between near critical and 10,000 pcm, as obtained by the pulsed neutron source method, the Feynman-α method, and the neutron source multiplication method.

DOI： 10.1016/j.net.2017.06.012

Recent developments in the GENESIS code based on the Legendre polynomial expansion of angular flux method Invited Reviewed International journal

Akio Yamamoto, Akinori Giho, Tomohiro Endo

Nuclear Engineering and Technology Vol. 49 ( 6 ) page： 1143 - 1156 2017.9

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

This paper describes recent development activities of the GENESIS code, which is a transport code for heterogeneous three-dimensional geometry, focusing on applications to reactor core analysis. For the treatment of anisotropic scattering, the concept of the simplified Pn method is introduced in order to reduce storage of flux moments. The accuracy of the present method is verified through a benchmark problem. Next, the iteration stability of the GENESIS code for the highly voided condition, which would appear in a severe accident (e.g., design extension) conditions, is discussed. The efficiencies of the coarse mesh finite difference and generalized coarse mesh rebalance acceleration methods are verified with various stabilization techniques. Use of the effective diffusion coefficient and the artificial grid diffusion coefficients are found to be effective to stabilize the acceleration calculation in highly voided conditions.

DOI： 10.1016/j.net.2017.06.016

Experimental benchmarks on kinetic parameters in accelerator-driven system with 100 MeV protons at Kyoto University Critical Assembly Reviewed International journal

Cheol Ho Pyeon, Masao Yamanaka, Tomohiro Endo, Willem Fredrik G. van Rooijen, Go Chiba

Annals of Nuclear Energy Vol. 105 page： 346 - 354 2017.7

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

Accelerator-driven system experiments with spallation neutrons (100 MeV protons and Pb-Bi target) are carried out in the 235U-fueled and Pb-Bi-zoned core at the Kyoto University Critical Assembly, under a subcritical state ranging between 1160 and 11,556 pcm. In these experiments, measurement of the prompt neutron decay constant and the subcriticality is conducted by the pulsed neutron source (PNS) method and the Feynman-α method with the use of optical fiber detectors. The experimental results successfully validate the prompt neutron decay constant and the subcriticality through the deduction of kinetic parameters by both the PNS and the α-fitting methods. The detector position dependency, neutron spectrum and subcriticality measurement methods still remain, however, in these experiments. For onward studies, the experimental benchmarks obtained from these experiments are expected to be involved in the numerical verification of subcriticality on-line monitoring, in the analysis of subcriticality uncertainty and in the deterministic approach to kinetic parameters.

DOI： 10.1016/j.anucene.2017.03.030

Estimation of sensitivity coefficients of core characteristics based on reduced-order modeling using sensitivity matrix of assembly characteristics Reviewed International coauthorship International journal

Ryota Katano, Tomohiro Endo, Akio Yamamoto, Mohammad Abdo, Hany Abdel-Khalik

Journal of Nuclear Science and Technology Vol. 54 ( 6 ) page： 637 - 647 2017.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

We propose an estimation method of sensitivity coefficients of core neutronics parameters based on a multi-level reduced-order modeling approach. The idea is to use lower-level models to identify the dominant input parameter variations, constrained to the so-called active subspace, which are employed to determine the sensitivity coefficients of the core neutronic parameters. In our implementation, the lower-level model is represented by two-dimensional assembly calculations, which are employed in the preparation of the few-group cross-sections for core-wide calculations. The active subspace basis is estimated using the singular value decomposition of sensitivity matrices of assembly neutronics parameters. In numerical verification calculation, sensitivity coefficients of core characteristics for a typical three-loop PWR equilibrium-cycle are estimated using the proposed method and the direct method. Comparison of these two results shows that the proposed method well reproduces the results obtained by the direct method with lower calculation costs. Through the verification calculations, applicability of the proposed method to practical light water reactor analysis is confirmed.

DOI： 10.1080/00223131.2017.1299052

Estimation of modeling approximation errors using data assimilation with the minimum variance approach Reviewed International journal

Akio Yamamoto, Kuniharu Kinoshita, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. 54 ( 4 ) page： 459 - 471 2017.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

In this paper, we estimate prediction errors owing to approximations in calculation models (modeling approximation error) using the data assimilation method. Correlations between the modeling approximation error and neutronics parameters obtained through calculations are evaluated in test configurations and then the evaluated correlations are used to predict the modeling approximation errors in design configuration. Formulae to estimate the modeling approximation error using the correlations are derived based on the minimum variance approach and the physical interpretation of the formulae is discussed through simple cases. The proposed method is applied in 2 × 2 and 3 × 3 fuel assembly geometries using specifications of the KAIST benchmark problem. The correlation between the modeling approximation error and parameters (neutron leakage in each fuel assembly) is estimated in 2 × 2 fuel assemblies and then the modeling approximation error in 3 × 3 fuel assemblies is predicted using the correlation. The calculation results not only indicate feasibility of the present method, but also suggest a need for further investigation on the assumptions used in the present study, i.e. applicability and robustness of the correlation among different geometries.

DOI： 10.1080/00223131.2017.1286271

GENESIS: A three-dimensional heterogeneous transport solver based on the legendre polynomial expansion of angular flux method Reviewed International journal

Akio Yamamoto, Akinori Giho, Yuki Kato, Tomohiro Endo

Nuclear Science and Engineering Vol. 186 ( 1 ) page： 1 - 22 2017.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A heterogeneous transport solver in three-dimensional (3-D) geometry, GENESIS, is developed incorporating recent developments in the method of characteristics (MOC) in 3-D geometry. The Legendre Polynomial Expansion of Angular Flux (LEAF) method is implemented in the GENESIS code, in which neutron transport is calculated in two-dimensional (2-D) characteristics planes rather than in one-dimensional characteristics lines adopted in the conventional approach of 3-D MOC. Unlike the planar MOC method that combines 2-D MOC calculations through axial leakages, the GENESIS code explicitly considers angular and spatial dependence of outgoing and incoming angular fluxes between axial planes. Thus, the GENESIS code eliminates a crucial approximation used in the planarMOC method: No approximation is used for axial leakage treatment. The GENESIS code can handle flexible shapes of objects in rectangular or hexagonal geometry. A two-level, multigroup generalized coarse mesh rebalance acceleration method is adopted for efficient convergence of neutron transport calculation. Performance of the GENESIS code is verified through various benchmark calculations. The calculation results indicate the fidelity of the GENESIS code based on the LEAF method.

DOI： 10.1080/00295639.2016.1273002

Automated generation of burnup chain for reactor analysis applications Reviewed International coauthorship International journal

Viet-Phu Tran, Hoai-Nam Tran, Akio Yamamoto, Tomohiro Endo

Kerntechnik Vol. 82 ( 2 ) page： 196 - 205 2017.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Carl Hanser Verlag

This paper presents the development of an automated generation of burnup chain for reactor analysis applications. Algorithms are proposed to reevaluate decay modes, branching ratios and effective fission product (FP) cumulative yields of a given list of important FPs taking into account intermediate reactions. A new burnup chain is generated using the updated data sources taken from the JENDL FP decay data file 2011 and Fission yields data file 2011. The new burnup chain is output according to the format for the SRAC code system. Verification has been performed to evaluate the accuracy of the new burnup chain. The results show that the new burnup chain reproduces well the results of a reference one with 193 fission products used in SRAC. Burnup calculations using the new burnup chain have also been performed based on UO2 and MOX fuel pin cells and compared with a reference chain th2cm6fp193bp6T.

DOI： 10.3139/124.110671

An efficient execution of Monte Carlo simulation based on delta-tracking method using GPUs Reviewed International journal

Takuya Okubo, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 54 ( 1 ) page： 30 - 38 2017.1

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

An efficient execution method for Monte Carlo simulation using graphic processing unit (GPU) is proposed. The delta-tracking method is used since the delta-tracking method can reduce conditional branches and complexity of code implementation, which degrade computational performance on GPUs. In order to improve parallel efficiency in the eigenvalue calculation, generated fission neutrons are recorded using the atomic operation which avoids the data race in GPUs. We also propose a method to efficiently tally neutron flux in a region. The present method is based on the atomic operation and use of fixed-point type number instead of common floating-point type number. The verification calculations using the C5G7 benchmark problem show effectiveness of the proposed numerical algorithms on GPUs through comparison with calculations using central processing units.

DOI： 10.1080/00223131.2016.1202793

Reduction of MOC Discretization Errors through a Minimization of Source Ratio Variances Reviewed International journal

M. Tabuchi, A. Yamamoto, T. Endo, M. Tatsumi

Journal of Nuclear Science and Technology Vol. 53 ( 11 ) page： 1858 - 1869 2016.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A new technique to reduce discretization errors for ray tracing in the method of characteristics (MOC) is proposed focusing on depletion calculations of single and multi-assembly geometries. In order to efficiently carry out depletion calculations, a calculation scheme using the superhomogenization (SPH) method can be used. However, the discretization errors are caused by changes of neutron sources and total cross sections according to a depletion. This fact means that improvement of accuracy cannot be expected by the calculation scheme with the SPH method when changes of the above parameters are significant. In order to mitigate this problem, a new approach is developed. In the new approach, the discretization errors are reduced by minimizing a variance of a certain parameter which is composed of a ratio of neutron source to total cross section. The verification results suggest that accuracy is degraded by the SPH method as expected especially in a geometry where neutron sources and total cross sections are drastically changing through a depletion. On the other hand, the new approach gives more accurate results compared to the conventional MOC in all calculation cases. Consequently, improvement of calculation efficiency by the new approach is confirmed.

DOI： 10.1080/00223131.2016.1171172

Nuclear data-induced uncertainty quantification of neutronics parameters of accelerator-driven system Reviewed International journal

Go Chiba, Cheol Ho Pyeon, Wilfred van Rooijen, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. 53 ( 10 ) page： 1653 - 1661 2016.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Nuclear data-induced uncertainties of neutronics parameters of one accelerator-driven system concept designed by the Japan Atomic Energy Agency are quantified. The variance-covariance data provided in the JENDL-4.0 library are used. Uncertainties are quantified for effective neutron multiplication factor, subcritical neutron multiplication rate, a family of delayed neutron fractions, power peaking and coolant void reactivity at several operational states. Inter-cycle and inter-parameter correlation matrices and detailed information such as nuclide-wise and nuclear data-wise uncertainties are also provided.

DOI： 10.1080/00223131.2015.1127185

A CMFD acceleration method for SP3 advanced nodal method Reviewed International journal

Akio Yamamoto, Tatsuya Sakamoto, Tomohiro Endo

Nuclear Science and Engineering Vol. 184 ( 2 ) page： 168 - 173 2016.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Flux-level-fixup (FF) coarse-mesh finite difference (CMFD) (FF-CMFD), which increases numerical stability during nonlinear iterations for the SP3 advanced nodal method, is proposed as an improved CMFD implementation. In contrast to the scalar flux that appeared in the advanced nodal method with diffusion theory, the second flux moment φ2 in the SP3 method could take a very small value since it can take both positive and negative values in a node. This is a root cause of inefficiency of the SP3 advanced nodal method when conventional CMFD acceleration is directly applied. In the proposed FF-CMFD method, a constant value is added to the second flux moment φ2 to fix up its value to a sufficiently large positive value for stable numerical calculations. The efficiency of the FF-CMFD method is verified through benchmark calculations.

DOI： 10.13182/NSE16-53

Statistical error estimation of the Feynman-α method using the bootstrap method Reviewed International journal

Tomohiro Endo, Akio Yamamoto, Takahiro Yagi, Cheol Ho Pyeon

Journal of Nuclear Science and Technology Vol. 53 ( 9 ) page： 1447 - 1453 2016.9

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Applicability of the bootstrap method is investigated to estimate the statistical error of the Feynman-α method, which is one of the subcritical measurement techniques on the basis of reactor noise analysis. In the Feynman-α method, the statistical error can be simply estimated from multiple measurements of reactor noise, however it requires additional measurement time to repeat the multiple times of measurements. Using a resampling technique called “bootstrap method,” standard deviation and confidence interval of measurement results obtained by the Feynman-α method can be estimated as the statistical error, using only a single measurement of reactor noise. In order to validate our proposed technique, we carried out a passive measurement of reactor noise without any external source, i.e. with only inherent neutron source by spontaneous fission and (α,n) reactions in nuclear fuels at the Kyoto University Criticality Assembly. Through the actual measurement, it is confirmed that the bootstrap method is applicable to approximately estimate the statistical error of measurement results obtained by the Feynman-α method.

DOI： 10.1080/00223131.2015.1113898

Discontinuity factors for simplified P3 theory Reviewed International journal

Akio Yamamoto, Tatsuya Sakamoto, Tomohiro Endo

Nuclear Science and Engineering Vol. 183 ( 1 ) page： 39 - 51 2016.5

Language：English Publishing type：Research paper (scientific journal) Publisher：American Nuclear Society

New discontinuity factors (DFs), i.e., individual and common DFs, for the simplified P3 (SP3) theory are proposed. In the individual DFs, two DFs are used for zeroth- and second-order angular moments in order to preserve first- and third-order angular moments of SP3 at a surface of the homogenized region. Contrarily, the same value of DF is used for zeroth- and second-order angular moments, and the first-order angular moment is preserved in the common DF. Theoretical derivation for these DFs are described, and then, actual numerical calculation procedures for these DFs are explained. Verification results in color-set geometries loaded with UO2 and mixed oxide fuel assemblies indicate the validity of the present method for cell-homogenized pin-by-pin SP3 calculations. Homogenization errors on keff and pin-power distribution are significantly reduced by the present DFs. The proposed DFs can be used for practical pin-by-pin core analyses using the SP3 theory.

DOI： 10.13182/NSE15-102

Uncertainty Quantification of LWR Core Characteristics Using Random Sampling Method Reviewed International journal

Akio Yamamoto, Kuniharu Kinoshita, Tomoaki Watanabe, Tomohiro Endo, Yasuhiro Kodama, Yasunori Ohoka, Tadashi Ushio, Hiroaki Nagano

Nuclear Science and Engineering Vol. 181 ( 2 ) page： 160 - 174 2015.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Uncertainties of various neutronics characteristics in commercial boiling water reactor (BWR) and pressurized water reactor (PWR) cores due to cross-section covariance are evaluated by the Latin Hypercube Sampling (LHS) method, which is an efficient random sampling algorithm. Thermal-hydraulic feedback and burnup effects are fully and explicitly taken into account using a licensing-grade core simulator. Uncertainties for various core characteristics are evaluated by the statistical processing of core calculation results based on the LHS method. The calculation results indicate that uncertainty of critical eigenvalue (i.e., core reactivity) in the BWR core is comparable to that of a typical PWR core. On the other hand, uncertainties of assembly relative power distribution and maximum assembly burnup in the present BWR core are much smaller than those of the present PWR core. The strong thermal-hydraulic feedback effect in the BWR core significantly contributes to the difference of uncertainties in BWR and PWR cores.

DOI： 10.13182/NSE14-152

Application of correction technique using leakage index combined with SPH or discontinuity factors for energy collapsing on pin-by-pin BWR core analysis Reviewed International journal

Tatsuya Fujita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 52 ( 3 ) page： 355 - 370 2015.3

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A correction technique to capture the spectral interference effect on collapsed cross sections is combined with the superhomogenization (SPH) factor or the discontinuity factor (DF) and is applied to the pin-by-pin core analysis for boiling water reactors (BWRs). The spectral interference effect has relationship with variations of neutron leakage in each pin-cell from the viewpoint of neutron balance. In order to correct collapsed cross sections, a new correction technique, in which the neutron leakage in each pin-cell is used as a correction index, was proposed in the previous study. By this correction technique, the reference coarse group cross sections are well reproduced and the calculation accuracies are improved. However, the reference fine group calculation results could not be reproduced since the correction technique cannot reduce energy collapsing errors. Thus, we combine the correction technique with the SPH factor or the DF to reduce energy collapsing errors. In order to verify and discuss the applicability of the correction technique with the SPH factor or the DF, two-dimensional benchmark calculations considering typical characteristics of BWR cores are carried out. The correction technique with the DF more accurately reproduces the reference fine group calculation results than that with the SPH factor.

DOI： 10.1080/00223131.2014.948520

Applicability of angular flux discontinuity factor preserving region-wise leakage for integro-differential transport equation Reviewed International journal

Tatsuya Sakamoto, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 51 ( 10 ) page： 1264 - 1273 2014.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

In the current core analysis, spatial homogenization is utilized to reduce the computational time. The discontinuity factor (DF) is one of the effective correction factors to reduce spatial homogenization error. The DF in diffusion equation is widely used on the other hand the DF in transport equation has not been put to practical use although several efforts have been carried out. In this paper, the angular flux discontinuity factor (AFDF) as the DF for the integro-differential transport equation (e.g., the discrete-ordinate method, the method of characteristics) is theoretically described and its applicability is discussed. The AFDF is used to preserve the region-wise neutron leakage at each spatial mesh and defined as a ratio of heterogeneous and homogeneous angular fluxes at the homogenized region surface. In a homogeneous calculation with the AFDF, the angular flux is discontinuous at the region surface. In this paper the applicability of the AFDF to fuel pin cell homogenization is verified for one-dimensional slab geometry. As a result of this verification, it is confirmed that the AFDF has the capability to reduce the spatial homogenization error of fuel pin cell homogenization.

DOI： 10.1080/00223131.2014.919882

A new technique for spectral interference correction on pin-by-pin BWR core analysis Reviewed International journal

Tatsuya Fujita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 51 ( 6 ) page： 783 - 797 2014.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A new correction technique to capture the spectral interference effect on collapsed cross sections, which focuses on application to the pin-by-pin boiling water reactor (BWR) core analysis, is proposed. The spectral interference effect, which is caused by adjacent loadings of different types of fuel assemblies, has relationship with variations of neutron leakage in each pin-cell from the viewpoint of neutron balance. Variation of neutron leakage affects neutron spectrum and thus the neutron leakage is considered to be important to correct coarse-group cross sections used in core calculations. We focus on the neutron leakage in each pin-cell and use it as a correction index (i.e., a leakage index (LI)), which is defined as the volume-averaged neutron leakage in a pin-cell. By utilizing the leakage index, we represent the variations of coarse-group cross sections as the linear combination of LIs. In order to verify and discuss the applicability of the present correction technique, two-dimensional benchmark calculations considering typical characteristics of BWR cores are carried out. From the calculation results, the present correction technique well reproduces the reference coarse-group cross sections and improves the calculation accuracies.

DOI： 10.1080/00223131.2014.903212

Cross section adjustment method based on random sampling technique Reviewed International journal

Tomoaki Watanabe, Tomohiro Endo, Akio Yamamoto, Yasuhiro Kodama, Yasunori Ohoka, Tadashi Ushio

Journal of Nuclear Science and Technology Vol. 51 ( 5 ) page： 590 - 599 2014.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A cross section adjustment method based on the random sampling technique is proposed. In the proposed method, correlations among cross sections and core parameters are used instead of sensitivity coefficients of cross sections, which are necessary in the conventional method. The correlations are statistically estimated by the random sampling technique. The proposed method is theoretically consistent with the conventional method and provides comparable adjusted cross sections when sufficient number of random sampling is taken into account. The proposed method would be suitable for practical light water reactor (LWR) core analysis since estimation of sensitivity coefficients, which requires considerable computational cost in typical LWR problems, is not necessary. Through a benchmark problem in simple pin-cell geometry, adjusted cross sections by the present and the conventional cross section adjustment method are compared. The adjusted cross sections by the present method well reproduce the conventional ones, thus the feasibility of the present method is confirmed.

DOI： 10.1080/00223131.2014.882801

A macroscopic cross-section model for BWR pin-by-pin core analysis Reviewed International journal

Tatsuya Fujita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 51 ( 3 ) page： 282 - 304 2014.3

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A macroscopic cross-section model used in boiling water reactor (BWR) pin-by-pin core analysis is studied. In the pin-by-pin core calculation method, pin-cell averaged cross sections are calculated for many combinations of core state and depletion history variables and are tabulated prior to core calculations. Variations of cross sections in a core simulator are caused by two different phenomena (i.e. instantaneous and history effects). We treat them through the core state variables and the exposure-averaged core state variables, respectively. Furthermore, the cross-term effect among the core state and the depletion history variables is considered. In order to confirm the calculation accuracy and discuss the treatment of the cross-term effect, the k-infinity and the pin-by-pin fission rate distributions in a single fuel assembly geometry are compared. Some cross-term effects could be negligible since the impacts of them are sufficiently small. However, the cross-term effects among the control rod history (or the void history) and other variables have large impacts
thus, the consideration of them is crucial. The present macroscopic cross-section model, which considers such dominant cross-term effects, well reproduces the reference results and can be a candidate in practical applications for BWR pin-by-pin core analysis on the normal operations.

DOI： 10.1080/00223131.2014.864248

Application of augmented reality to nuclear reactor core simulation for fundamental nuclear engineering education Reviewed International journal

Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Nuclear Technology Vol. 185 ( 1 ) page： 71 - 84 2014.1

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A nuclear reactor core simulation system using augmented reality (AR) has been developed. Augmented reality is a technology that can provide additional information by overlaying computer graphics onto the image of actual world. In the past, AR has been applied to operation assistance in various fields. In the field of nuclear engineering, AR has been applied to support the decommissioning of nuclear power plants. Using AR, workers can simultaneously see the image of the actual world and helpful information
thus, they can intuitively imagine their works. This advantage of AR can be applied not only to operation assistance but also to other purposes. Therefore in this study we have tried to apply AR to a nuclear core simulator. The major purpose of the present AR core simulator is education of novice students who are not very familiar with nuclear reactor core behavior by enabling direct "hand manipulation" of a reactor model in the real world. For example users can directly insertlwithdraw a control rod and can directly see the power variation of the reactor through the AR technology.

DOI： 10.13182/NT13-7

Uncertainty estimation of core safety parameters using cross-correlations of covariance matrix Reviewed International journal

Akio Yamamoto, Yoshihiro Yasue, Tomohiro Endo, Yasuhiro Kodama, Yasunori Ohoka, Masahiro Tatsumi

Journal of Nuclear Science and Technology Vol. 50 ( 10 ) page： 966 - 978 2013.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

An uncertainty reduction method for core safety parameters, for which measurement values are not obtained, is proposed. We empirically recognize that there exist some correlations among the prediction errors of core safety parameters, e.g., a correlation between the control rod worth and the assembly relative power at corresponding position. Correlations of errors among core safety parameters are theoretically estimated using the covariance of cross sections and sensitivity coefficients of core parameters. The estimated correlations of errors among core safety parameters are verified through the direct Monte Carlo sampling method. Once the correlation of errors among core safety parameters is known, we can estimate the uncertainty of a safety parameter for which measurement value is not obtained.

DOI： 10.1080/00223131.2013.820155

Preservation of transmission probabilities in the method of characteristics Reviewed International journal

Masato Tabuchi, Akio Yamamoto, Tomohiro Endo, Naoki Sugimura

Journal of Nuclear Science and Technology Vol. 50 ( 8 ) page： 837 - 843 2013.8

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

An efficient calculation scheme for the method of characteristics, which allows coarser ray separation width, is newly proposed. Effective lengths of characteristics lines are evaluated from the viewpoint of preservation of transmission probability in the present method. The effective lengths to preserve transmission probabilities can be rigorously estimated through detailed numerical integrations. However, calculation and storage of all effective lengths is inefficient since the transmission probabilities depend on many parameters such as azimuthal angle, polar angle, position of characteristics line, and total cross section. To resolve this issue, in this paper, the analytical equations for the effective lengths are derived from an assumption that distribution function of actual characteristics lengths can be expressed by a linear function. The new approach introduced in this paper is named as transmission probability preservation through linear approximation (TPPL). Verification results indicate that accurate results can be obtained by the TPPL even if ray separation width becomes coarse.

DOI： 10.1080/00223131.2013.807753

Convergence analysis of MOC inner iterations with large negative self-scattering cross-section Reviewed International journal

Masato Tabuchi, Akio Yamamoto, Tomohiro Endo, Naoki Sugimura

Journal of Nuclear Science and Technology Vol. 50 ( 5 ) page： 493 - 502 2013.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

When the transport correction is applied to the total cross-section, the self-scattering cross-section could have a negative value in order to preserve the balance of partial cross-sections. The negative self-scattering cross-section may lead to a negative impact on the convergence behavior for the method of characteristics (MOC), especially in a problem with large moderator regions containing hydrogen. In order to address this issue, the spectral radius of the inner iteration of MOC is theoretically estimated for various self-scattering cross-sections. It is found that the spectral radius of the inner iteration of MOC could exceed unity for a large negative self-scattering cross-section, which results in numerical divergence. A countermeasure for the divergence using the successive over relaxation method is also discussed in this paper.

DOI： 10.1080/00223131.2013.785271

Analysis of integral experiment on erbia-loaded thermal spectrum cores using Kyoto University Critical Assembly by MCNP code with various cross section libraries Reviewed International journal

Yevgeniy Tur, Tomohiro Endo, Akio Yamamoto, Hironobu Unesaki, Masatoshi Yamasaki

Journal of Nuclear Science and Technology Vol. 49 ( 10 ) page： 1028 - 1041 2012.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Under the project on high burnup nuclear fuel development using erbium as a burnable poison, a series of experiments were performed at the Kyoto University Critical Assembly. The experimental results have formed the basis for this study which aims to analyze the suitability of various evaluated nuclear data libraries for using them in neutronic calculations under the project. The MCNP code was used for the analysis. Calculation model geometry was fully detailed, and ENDF, JENDL, JEFF, and TENDL libraries were used during calculation. For the cross sections of erbium nuclides, the analysis revealed that calculated results upon all the libraries corresponded with experimental data within the errors. However, in some libraries, significant differences were found in case of carbon and uranium nuclides under certain conditions.

DOI： 10.1080/00223131.2012.723174

An optimization approach to establish an appropriate energy group structure for BWR pin-by-pin core analysis Reviewed International journal

Tatsuya Fujita, Kenichi Tada, Tomohiro Endo, Akio Yamamoto, Shinya Kosaka, Go Hirano, Kenichiro Nozaki

Journal of Nuclear Science and Technology Vol. 49 ( 7 ) page： 689 - 707 2012.7

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

An optimization approach to establish an appropriate multi-group energy structure for boiling water reactor (BWR) pin-by-pin finemesh core analysis is proposed. In the present approach, the number of energy groups of cross sections is successively reduced or increased. In order to select an energy group boundary that is removed or added, performances of all possible candidates of energy group structures are tested in multi-assembly geometries. Then, the energy group boundary, which provides theminimumdifference of the k-infinity or the pin-by-pin fission rate distribution, is finally removed or added. This procedure is repeated until the number of energy groups reaches to the target value. In order to confirm the applicability of the present approach, the accuracies of the k-infinity and the pin-by-pin fission rate distribution are investigated in various 2 × 2 multi-assembly geometries with the established energy group structure. From the verification results, the differences of the k-infinity and the pin-by-pin fission rate distribution between the reference (fine) and the established (coarse) energy group structure are small in the various 2 × 2 multiassembly geometries. Therefore, we can conclude that the present approach is efficient to establish an appropriate energy group structure for BWR pin-by-pin fine mesh core analysis.

DOI： 10.1080/00223131.2012.693890

A unified approach for numerical calculation of space-dependent kinetic equation Reviewed International journal

Yuichiro Ban, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 49 ( 5 ) page： 496 - 515 2012.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A unified numerical method based on the factorization approach is developed to solve the spacedependent neutron kinetic equation. Various numerical methods for solving the space-dependent kinetic equation have been developed so far. These methods can be classified into two categories, i.e., the direct and the factorization methods. The factorization method is known as an effective numerical method. In the present study, a new factorization method named the multigrid amplitude function (MAF) method is developed. Unlike the improved quasi-static (IQS) method, an independent amplitude function is assigned for each spatial region and energy group in the MAF method. The MAF method is a generalization of conventional methods, e.g., the frequency transform, IQS, and Theta methods. To evaluate the amplitude function in the MAF method, the time-dependent coarse-mesh finite difference (TCMFD) method is developed. The MAF method is implemented into a space-dependent kinetic code on the basis of the analytical polynomial nodal method. In order to verify the effectiveness of the MAF method, the TWIGL, Langenbuch, Maurer, and Werner (LMW), and Laboratorium fü r Reaktorregelung and Anlagensicherung (LRA) benchmark problems are analyzed. The calculation results show the effectiveness of the present method.

DOI： 10.1080/00223131.2012.677126

Application of quick subchannel analysis method for three-dimensional pin-by-pin BWR core calculations Reviewed International journal

Kenichi Tada, Tatsuya Fujita, Tomohiro Endo, Akio Yamamoto, Shinya Kosaka, Go Hirano, Kenichiro Nozaki

Journal of Nuclear Science and Technology Vol. 48 ( 12 ) page： 1437 - 1452 2011.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Three-dimensional pin-by-pin core analysis is considered to be a candidate for the next-generation BWR core calculation method. In our previous study, the applicability of the transport and burnup calculations for a three-dimensional pin-by-pin BWR core analysis was investigated. However, the thermal-hydraulics calculation has not yet been studied in this framework. In the conventional core analysis code, the bundlewise thermal-hydraulics calculation is adopted. In the actual core analysis, the power distribution inside a fuel assembly is tilted at the region adjacent to a control blade or the core peripheral region. In these regions, the consideration of the subchannel-wise void distribution has an impact on the fission rate distribution. Therefore, an evaluation of the detailed void distribution inside an assembly, i.e., the incorporation of the subchannel wise void distribution, is desirable for the pin-by-pin BWR core analysis. Although several subchannel analysis codes have been developed, these subchannel analysis codes generally require a large computational effort to estimate the subchannel-wise void distribution in a whole BWR core. Therefore, to analyze a whole BWR core within a reasonable computation time, it was necessary to apply a fast subchannel analysis code. In this paper, a quick subchannel analysis code dedicated to pin-by-pin BWR core analysis is newly developed, and the void distribution of the present subchannel analysis code is compared with the prevailing subchannel analysis code NASCA using three-dimensional single-assembly geometries. Since the present subchannel analysis code is used for a coupled neutronics/thermal-hydraulics analysis, the results of the coupling calculation are also compared with those of NASCA. The calculation result indicates that the void distribution difference between NASCA and the present subchannel analysis code is slightly less than 10%. This result indicates that the prediction accuracy of the present subchannel analysis code will be reasonably appropriate for a pin-by-pin BWR core analysis. Furthermore, the results show that the calculation time of the present subchannel analysis code is only 10 min for a hypothetical three-dimensional ABWR quarter-core geometry using a single CPU. This calculation time is sufficient for a pin-by-pin BWR core analysis.

DOI： 10.1080/18811248.2011.9711837

Application of the robust design concept for fuel loading pattern Reviewed International journal

Tomohiro Endo, Kazuma Ohori, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 48 ( 7 ) page： 1077 - 1086 2011.7

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Application of the robust design concept for fuel loading pattern design is proposed as a new approach to improve the prediction accuracy of core characteristics. The robust design is a design concept that establishes a resistant (robust) system for perturbations or noises, by properly setting design variables. In order to apply the concept of robust design to fuel loading pattern design, we focus on a theoretical approach based on the higher order perturbation method. This approach indicates that the eigenvalue separation is one of the effective indices to measure the robustness of a designed fuel loading pattern. In order to verify the effectiveness of the eigenvalue separation as an index of robustness, numerical analysis is carried out for typical 3-loop PWR cores, and we evaluated the correlation between the eigenvalue separation and the variation of relative assembly power due to the perturbation of the cross section. The numerical results show that the variation of relative power decreases as the eigenvalue separation increases
thus, it is confirmed that the eigenvalue separation is an effective index of robustness. Based on the eigenvalue separation of a fuel loading pattern, we discuss design guidelines of a fuel loading pattern to improve the robustness. For example, if each fuel assembly has independent uncertainty on its cross section, the robustness of the core can be enhanced by increasing the relative power at the center of the core. The proposed guidelines will be useful to design a loading pattern that has robustness for uncertainties due to cross section, calculation method, and so on.

DOI： 10.1080/18811248.2011.9711792

Improved derivation of multigroup effective cross section for heterogeneous system by equivalence theory Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Hiroki Koike

Nuclear Science and Engineering Vol. 168 ( 2 ) page： 75 - 92 2011.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The validity of effective cross section obtained by the conventional equivalence theory is discussed from the viewpoint of reaction rate preservation in a heterogeneous system. It is shown that the reaction rate is not preserved when the escape probability is expressed by a multiterm rational approximation, which is commonly used in light water reactor (LWR) analyses. A new derivation method for obtaining a multigroup effective cross section, which accurately reproduces the result of reference ultrafine group calculation, is proposed. The validity of the proposed method is confirmed through test calculations in various heterogeneous geometries, which represent typical LWR configurations. Because the implementation of the proposed method is very simple, it is useful for existing lattice physics codes that utilize the equivalence theory on the basis of two-term (or multiterm) rational approximation.

DOI： 10.13182/NSE10-50

Resonance calculation for large and complicated geometry using Tone's method by incorporating the method of characteristics Reviewed International journal

Hao Yu, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 48 ( 3 ) page： 330 - 336 2011.3

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A new efficient approach for evaluating the background cross section, which is based on Tone's method, is presented. Though the collision probability method is used in the conventional Tone's method, the method of characteristics (MOC) is used in the present method. Since the computation time of MOC is shorter than that of the collision probability method in a large and complicated geometry, the present method will be useful not only for lattice physics calculation, but also for analyses of advanced reactors with complicated geometry. Verification calculations are carried out in two configurations, i.e., a PWR fuel assembly geometry and a multiassembly geometry adjacent to the baffle-reflector region. The validity of the present method has been confirmed through the results of verification calculations.

DOI： 10.1080/18811248.2011.9711707

Overview of Core Simulation Methodologies for Light Water Reactor Analysis Reviewed International journal

A. Yamamoto, T. Endo

International Electronic Journal of Nuclear Safety and Simulation Vol. 2 ( 1 ) page： 12 - 21 2011.3

Language：English Publishing type：Research paper (scientific journal)

The current in-core fuel management calculation methods provide a very efficient route to predict neutronics behavior of light water reactor (LWR) cores and their prediction accuracy for current generation LWRs is generally sufficient. However, since neutronics calculations for LWRs are based on various assumptions and simplifications, we should also recognize many implicit limitations that are "embedded" in current neutronics calculation methodologies. Continuous effort for improvement of core simulation methodologies is also discussed.

Explicit Time Integration Scheme Using Krylov Subspace Method for Reactor Kinetics Equation Reviewed International journal

Yuichiro Ban, Tomohiro Endo, Akio Yamamoto, Yoshihiro Yamane

Journal of Nuclear Science and Technology Vol. 48 ( 2 ) page： 243 - 255 2011.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The spatial discretization form of the space-dependent reactor kinetics equation is a first-order simultaneous ordinary differential equation in time. Conventional numerical methods of the space-dependent kinetics equation, i.e., the generalized Runge-Kutta method, the implicit method (backward Euler method), and the Theta method, are based on the time difference approximation. However, the present study adopts the analytical solution of the space-dependent kinetics equation expressed by the matrix exponential and no time difference approximation is used. In this context, our present approach is classified as an explicit method in which no iteration calculation on space and energy is necessary. The Krylov subspace method is used to evaluate the matrix exponential observed in the solution of the spatially discretized space-dependent kinetics equation. The Krylov subspace method is implemented into a space-dependent kinetics solver. In order to examine the effectiveness of the Krylov subspace method, the TWIGL benchmark problem is analyzed as a verification calculation. The calculation results show the effectiveness of the present method especially in the step reactivity perturbation.

DOI： 10.1080/18811248.2011.9711698

Improvement of Tone's method with two-term rational approximation Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Go Chiba

Journal of Nuclear Science and Technology Vol. 48 ( 2 ) page： 263 - 271 2011.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also discussed. The validity of improved Tone's method is confirmed through a verification calculation in an irregular lattice geometry, which represents part of an LWR fuel assembly. The calculation result clarifies the validity of the present method.

DOI： 10.1080/18811248.2011.9711700

AEGIS: An Advanced Lattice Physics Code for Light Water Reactor Analyses Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Masato Tabuchi, Naoki Sugimura, Tadashi Ushio, Masaaki Mori, Masahiro Tatsumi, Yasunori Ohoka

Nuclear Engineering and Technology Vol. 42 ( 5 ) page： 500 - 519 2010.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Korean Nuclear Society

AEGIS is a lattice physics code incorporating the latest advances in lattice physics computation, innovative calculation models and efficient numerical algorithms and is mainly used for light water reactor analyses. Though the primary objective of the AEGIS code is the preparation of a cross section set for SCOPE2 that is a three-dimensional pin-by-pin core analysis code, the AEGIS code can handle not only a fuel assembly but also multi-assemblies and a whole core geometry in two-dimensional geometry. The present paper summarizes the major calculation models and part of the verification/validation efforts related to the AEGIS code.

DOI： 10.5516/NET.2010.42.5.500

Other Link： https://doi.org/10.5516/NET.2010.42.5.500

Development of deterministic code based on the discrete ordinates method for the third-order neutron correlation technique Reviewed International journal

Tomohiro Endo, Akio Yamamoto, Yoshihiro Yamane

Annals of Nuclear Energy Vol. 35 ( 5 ) page： 927 - 936 2008.5

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

The third-order neutron correlation technique is one of the subcriticality measurement techniques. The significant feature of this technique is that an absolute value of subcriticality can be evaluated from the measured neutron correlation factors, namely Y-infinity and X-infinity In order to extend the applicability of the third-order neutron correlation technique to actual complicated subcritical systems, we previously derived the spatial and neutron energy dependent theoretical formulas of Y-infinity and X-infinity by using the first-, second-, and third-order importance functions. These theoretical formulas depend on the locations of both an external neutron source and a neutron detector. The numerical solutions of these formulas are very useful to design the arrangements of the external neutron source and the neutron detector and to investigate the contamination of the spatial effect in the measured neutron correlation factors, Y-infinity and X-infinity Therefore, we developed a novel deterministic code that can calculate both Y-infinity and X-infinity based on the SN method. In this paper, we focus on the description of the numerical procedure of this code and its verification by comparing it with the results of Monte Carlo simulations.

DOI： 10.1016/j.anucene.2007.09.014

Neutron Transport Models of AEGIS: An Advanced Next-Generation Neutronics Design System Reviewed International journal

Naoki Sugimura, Akio Yamamoto, Tadashi Ushio, Masaaki Mori, Masato Tabuchi, Tomohiro Endo

Nuclear Science and Engineering Vol. 155 ( 2 ) page： 276 - 289 2007.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A very rigorous and advanced next-generation neutronics design system, AEGIS (Anisotropic, Extended Geometry, Integrated Neutronics Solver), which is based on the deterministic method, is being developed using advanced computer science technology. The method of characteristics, which has the merit of treating heterogeneous geometry explicitly, is utilized in AEGIS as a neutron transport solver. So, the AEGIS code can explicitly model many types of fuel lattices in both commercial light water reactors (LWRs) and advanced reactors such as Generation IV reactors. The AEGIS code can also treat higher-order anisotropic scattering accurately based on spherical harmonics expansion. To compute a large-scale problem, a nonuniform ray-tracing method is implemented in AEGIS. It utilizes the Gauss-Legendre quadrature weight and the macroband method to decide position and width of ray traces to reduce spatial discretization error efficiently. The transport solution of AEGIS has been verified through various benchmark problems. It was found that the AEGIS code can explicitly treat complicated geometry and can efficiently solve a large-scale problem. These results show that flexibility in handling geometry and the very rigorous neutronics calculation models of AEGIS will contribute to predicting neutronics characteristics accurately, not only for commercial LWRs but also for advanced reactors.

DOI： 10.13182/NSE155-276

Effect of error propagation of nuclide number densities on Monte Carlo burn-up calculations Reviewed International journal

Masayuki Tohjoh, Tomohiro Endo, Masato Watanabe, Akio Yamamoto

Annals of Nuclear Energy Vol. 33 ( 17-18 ) page： 1424 - 1436 2006.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

As a result of improvements in computer technology, the continuous energy Monte Carlo burn-up calculation has received attention as a good candidate for an assembly calculation method. However, the results of Monte Carlo calculations contain the statistical errors. The results of Monte Carlo burn-up calculations, in particular, include propagated statistical errors through the variance of the nuclide number densities. Therefore, if statistical error alone is evaluated, the errors in Monte Carlo burn-up calculations may be underestimated. To make clear this effect of error propagation on Monte Carlo burn-up calculations, we here proposed an equation that can predict the variance of nuclide number densities after burn-up calculations, and we verified this equation using enormous numbers of the Monte Carlo burn-up calculations by changing only the initial random numbers. We also verified the effect of the number of burn-up calculation points on Monte Carlo burn-up calculations. From these verifications, we estimated the errors in Monte Carlo burn-up calculations including both statistical and propagated errors. Finally, we made clear the effects of error propagation on Monte Carlo burn-up calculations by comparing statistical errors alone versus both statistical and propagated errors. The results revealed that the effects of error propagation on the Monte Carlo burn-up calculations of 8 x 8 BWR fuel assembly are low up to 60 GWd/t.

DOI： 10.1016/j.anucene.2006.09.010

Derivation of theoretical formula for the third order neutron correlation technique by using importance function Reviewed International journal

Tomohiro Endo, Yoshihiro Yamane, Akio Yamamoto

Annals of Nuclear Energy Vol. 33 ( 10 ) page： 857 - 868 2006.7

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

The third order neutron correlation technique is one of the subcriticality measurement techniques. This technique was originally proposed by Furuhashi and utilizes the second and third order neutron correlation factors Y(T) and X(T), which are evaluated from the variance and third order central moment of neutron counts detected during a counting gate width T, respectively. We can obtain the absolute value of subcriticality from the Y infinity and X infinity, which are saturation values of Y(T) and X(T) when T goes to infinity. In the previous paper, we derived the generalized theoretical formulas of Y infinity and X infinity that took account of both the spatial and neutron energy effects. Its derivation was based on a heuristic method in which we consider the branching process of neutron family, and we utilized the alpha-eigenfunction expansion technique. Then, the previous formulas are expressed by multiple sums involving both the alpha-eigenfunctions and their adjoint functions. In this paper, we derive the new compact expressions of Y infinity and X infinity by using the importance functions related to the neutron detection process. Present derivation is based on the stochastic equation of neutron transport. New expressions have two advantages. We can clarify the physical meanings of Y infinity and X infinity. And, without alpha-eigenfunction expansion, we can calculate Y infinity and X infinity directly by calculating the importance functions which satisfy the adjoint neutron transport equations. Moreover, we prove that new expressions of Y infinity and X infinity are identical with the previous ones, so that we can conclude that our previous derivation based on a heuristic method is correct.

DOI： 10.1016/j.anucene.2006.05.005

Space and energy dependent theoretical formula for the third order neutron correlation technique Reviewed International journal

Tomohiro Endo, Yoshihiro Yamane, Akio Yamamoto

Annals of Nuclear Energy Vol. 33 ( 6 ) page： 521 - 537 2006.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

We have studied measurement techniques of subcriticality by using the neutron correlation techniques. Among various techniques, we have paid attention to the third order neutron correlation technique, which was proposed by Furuhashi originally and utilizes the third order fluctuations of neutron counts. By using this technique, we can obtain the absolute value of subcriticality with the aid of factorial moments of fission neutron v and external source neutron q, without prior knowledge of the prompt neutron decay constant at a reference state. However, in order to apply the third order neutron correlation technique to actual experiments, we must consider the spatial and neutron energy effects in this technique. For this purpose, we derived more generalized theoretical formulas of the third order neutron correlation technique that took account of the spatial and neutron energy effects by virtue of the alpha-eigenfunction expansion. Making use of the newly derived formulas, we propose the practical formulas and the experimental procedures based on the fundamental mode approximation.

DOI： 10.1016/j.anucene.2006.02.002