Faculty Profiles - ENDO Tomohiro

MISC - ENDO Tomohiro

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Subcriticality: from basics to applications; (3) The ABC's of Subcriticality Measurements Reviewed

T. Endo, S. Atsushi

ATOMOΣ: Journal of the Atomic Energy Society of Japan Vol. 61 ( 12 ) page： 857 - 862 2019.12

Subcriticality Estimation without Point Kinetics Parameters Based on Autocovariance of Reactor Noise Using Delayed Neutron Components Reviewed International journal

Tomohiro Endo, Ryoga Hirota, Akio Yamamoto, Kenichi Watanabe, Genichiro Wakabayashi, Kengo Oda, Junichi H. Kaneko

Proc. M&C2025 page： 2028 - 2037 2025.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The reactor noise analysis method is useful as a passive measurement technique for a steady-state target subcritical system. When detailed information is not available in the target system, there are large uncertainties in the point kinetics parameters, such as the effective delayed neutron fraction and the neutron generation time. In this case, if the subcriticality measurement techniques using the point kinetics parameters (e.g., indirect conversion method from the measured prompt neutron decay constant to the subcriticality) are applied, the measured subcriticality will inevitably have a large uncertainty. To address this problem, the present study aims to investigate the absolute measurement of subcriticality without the point kinetics parameters by focusing on the delayed neutron components in the zero-power reactor noise. For this purpose, an analytical formula for the lag-1 autocovariance of the reactor noise is derived via the pair detection probability based on the fundamental mode approximation using the forward and adjoint eff-eigenfunctions. The proposed method utilizes the nonlinear least squares fitting method for the measured autocovariance to determine the following three fitting parameters: the subcriticality in the dollar units; the ratio of eff ⁄Λ; and a proportional factor related to the Diven factor, the detection efficiency, and so on. Preliminary experimental analysis using the proposed method is demonstrated through the reactor noise measurement at UTR-KINKI (University Teaching and Research Reactor of Kindai University) under a shutdown state.

DOI： 10.13182/MC25-46579

A Simple Resonance Calculation Method for Flexible Geometry Using Equivalence Relation and Point-wise Cross Sections (ERPX) Reviewed International journal

A. Yamamoto, T. Endo

Proc. M&C2025 page： 544 - 553 2025.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

ERPX, a simple resonance calculation method that can incorporate space-dependent shelf-shielding is proposed. ERPX calculates space-dependent escape cross sections using the ultra-fine group (UFG) calculation in heterogeneous and homogeneous geometries with the narrow resonance (NR) approximation. Then the space-dependent escape cross sections and the explicit slowing down calculation in homogeneous geometry are then used to estimate the space-dependent effective cross section to mitigate the error caused by the NR approximation. The reduce-order model is developed and used in the UFG calculation in heterogeneous geometry to achieve short computation time. Verification calculation is carried out in 3x3 pin-cell geometry containing a large water region. The fuel pellet in focus is azimuthally and annularly divided. The calculation results indicated that the ERPX method can provide reasonable accuracy with practical computation time that can be used for the design calculations.

DOI： 10.13182/MC25-47330

Correction Method of Few-Group Cross Sections for Core Analysis of High-Temperature Gas-Cooled Reactors Reviewed International journal

Amane Haga, Tomohiro Endo, Akio Yamamoto, Go Chiba

Proc. M&C2025 page： 472 - 481 2025.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

To reduce the discretization error associated with the energy group collapsing, a correction method for few-group cross sections used in a core calculation of High-Temperature Gas-cooled Reactors (HTGRs) was investigated. It was confirmed that the correction of the removal scattering cross section as a function of the spectral index, which is the ratio of the fast and thermal group neutron fluxes, improves the calculation accuracy of the k-effective and the fuel compact-wise relative power distribution in the two-dimensional heterogeneous full core model of the High Temperature engineering Test Reactor (HTTR). The method of correcting the total scattering cross section, including the self-group scattering cross section, did not improve the accuracy. The method using the removal scattering cross section may be a candidate for a core design method of HTGRs.

DOI： 10.13182/MC25-47343

Reactivity Estimation in Dollar Units Based on Bayesian Monte Carlo Using Autocovariance of Reactor Noise Measurement Reviewed International journal

Ryoga Hirota, Tomohiro Endo, Akio Yamamoto, Kenichi Watanabe, Genichiro Wakabayash, Kengo Oda, Junichi H. Kaneko

Proc. M&C2025 page： 2038 - 2047 2025.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The reactor noise analysis method can measure the prompt neutron decay constant using only time series data of neutron counts measured in a steady-state subcritical system. However, the point kinetics parameters such as the neutron generation time Λ and the effective delayed neutron fraction eff are needed to estimate the reactivity in dollar units by conversion from the measured value. To address the above-mentioned problem, this study aims to develop the estimation technique of the reactivity in dollar units eff , by utilizing the delayed neutron component of reactor noise. To extract the delayed neutron components, this study focused on the lag-1 autocovariance for reactor noise. In addition, the Bayesian Monte Carlo (BMC) with merging particle filter (MPF) was applied as the data assimilation technique to estimate eff from the measured variation of the autocovariance with respect to the counting gate width. As a result, the proposed method was validated through the reactor noise measurement at UTR-KINKI (University Teaching and Research Reactor of Kindai University).

2D Cylindrical SP3 Transport Calculation Using Finite Volume Method with Cross-Diffusion Treatment for Unstructured Meshes Reviewed International journal

Tomohiro Endo, Akio Yamamoto

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 1053 - 1056 2024.11

Authorship：Lead author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

This study presents a prototype of an in-house code to numerically solve the simplified P3 (SP3) neutron transport equation for a 2D cylindrical (r-z) geometry using unstructured meshes for spatial discretization. In the developed SP3 calculation code, the cross-diffusion effect due to the unstructured meshes can be treated by a variant of the Green-Gauss reconstruction technique.

DOI： 10.13182/T131-46095

Study on Fusion Safety Concept Based on Nuclear Safety (2) Defense in Depth in Fusion Safety Reviewed International journal

Yoshiki Yamashita, Tomohiro Endo, Akio Yamamoto, Takashi Ino

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 299 - 302 2024.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The concept of fusion safety is studied with reference to nuclear safety. Risk profiles of fusion reactor facilities are reviewed and organized and implementation of defense in
depth (DID) in fusion safety is developed based on the risk profiles.

DOI： 10.13182/T131-46140

Study on Fusion Safety Concept Based on Nuclear Safety (1) Fusion Safety Objective and Principles Reviewed International journal

Yoshiki Yamashita, Tomohiro Endo, Akio Yamamoto, Takashi Ino

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 292 - 295 2024.11

A Simple Resonance Calculation Approach for Space-Dependent Self-Shielding Reviewed International journal

Akio Yamamoto, Tomohiro Endo

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 1038 - 1041 2024.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A simple resonance calculation method for space-dependent self-shielding treatment is proposed. The present method is based on three calculations: 1) ultra-fine group (UFG) calculation with the narrow resonance (NR) approximation in a homogeneous medium, 2) UFG calculation with explicit slowing down (SLD) calculation in a homogeneous medium, and 3) UFG calculation with the NR approximation in a heterogeneous system. The space-dependent effective cross sections are generated by the synthesis of these three calculations.

DOI： 10.13182/T131-45885

Implementation of track length estimator for flux distribution tallies using proper orthogonal decomposition in one-dimensional geometry Reviewed International journal

Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto

EPJ Web of Conferences Vol. 302 page： 04002 2024.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

In a recent study, we have developed an efficient flux distribution tallying method in the Monte Carlo calculation toward the high-fidelity, large scale multi-physics simulation. In this method, the proper orthogonal decomposition is applied to the flux distribution tallies. While the tallying method was implemented with the collision estimator in the previous study, the track length estimator is implemented in the present study to obtain the tally with lower statistical error. The implementation of the flux distribution tally with the track length estimator is compared with that of the collision estimator and the normal track length estimator in a one-dimensional problem. The numerical results reveal that the distribution tally using the proper orthogonal decomposition with the track length estimator can obtain a more precise solution compared with that with the collision estimator. Therefore, in terms of the statistical error, the relationship between the distribution tally with track length and collision estimators is similar to that between the conventional track length and collision estimators.

DOI： 10.1051/epjconf/202430204002

Data Assimilation Using Deterministic Sampling Method to Selectively Reduce Uncertainty due to Thermal Neutron Scattering Law for Light Water Reviewed International journal

Yoshinari Harada, Hibiki Yamaguchi, Tomohiro Endo, Akio Yamamoto, Kenichi Tada

Transactions of the American Nuclear Society Vol. 130 ( 1 ) page： 758 - 762 2024.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

This study presents data assimilation using the prompt neutron decay constant α of the water tank system to selectively reduce the uncertainties due to the thermal neutron scattering law of light water. For efficient uncertainty quantification and data assimilation, the deterministic sampling method was applied in this study. Furthermore, in the data assimilation, the α measurement of the water tank system was utilized to improve the prediction accuracy of keff calculations in a critical experiment involving light water.

DOI： 10.13182/T130-44516

Loading Pattern Optimization with Deep Learning and Monte-Carlo Tree Search Reviewed International journal

Rikuto Kasama, Akio Yamamoto, Tomohiro Endo

Transactions of the American Nuclear Society Vol. 130 ( 1 ) page： 1044 - 1047 2024.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

We have developed a new optimization method based on Deep Learning (DL) and Monte-Carlo Tree Search (MCTS) for fuel loading pattern optimization. The fuel loading pattern optimization is redefined as a sequence of fuel loadings to an empty core, and the sequence is optimized by the DL and MCTS approach, which is used in AI for board games such as Go, Chess, and Shogi (Japanese Chess).

DOI： 10.13182/T130-44319

Statistical Error Estimation of Autocorrelation Method Using Circular Block Bootstrap Method Reviewed International journal

Ryoga Hirota, Tomohiro Endo, Akio Yamamoto, Kenichi Watanabe, Junichi H. Kaneko

Proc. PHYSOR2024 page： 78 - 86 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The autocorrelation method is a subcriticality measurement technique based on the reactor noise analysis method. In this method, the prompt neutron decay constant can be obtained from the exponential decay of the autocorrelation of successively detected neutron counts in a target subcritical system. To simply estimate the statistical error of the prompt neutron decay constant, several measurements of the reactor noise are required, although the total measurement time is inevitably long for typical systems where the reactor noise analysis method is applied. Therefore, the purpose of this study is to investigate the applicability of the circular block bootstrap method in order to estimate the statistical error of the prompt neutron decay constant obtained by the autocorrelation method using a single reactor noise measurement. The bootstrap-based statistical error estimation method is validated using the time series data of reactor noise measurements at UTR-KINKI in a shutdown state with the inherent neutron source in the uranium-aluminum fuel. Consequently, this study demonstrates that the circular block bootstrap method can be also utilized for the autocorrelation method, to estimate the confidence interval of the prompt neutron decay constant as the statistical error. Namely, a single reactor noise measurement can be effectively reused for error estimation instead of multiple measurements.

Other Link： https://www.ans.org/meetings/physor2024/sessions/attachment/paper-9424/

Investigation of Subcriticality Monitoring Method Using Improved Simplest Reactivity Estimator with Bilateral Filter Reviewed International journal

Taiyo Moribe, Tomohiro Endo, Akio Yamamoto, Junichi H. Kaneko

Proc. PHYSOR2024 page： 97 - 106 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

In the retrieval of fuel debris from the Fukushima Daiichi nuclear power plant, there are the following issues: lack of information needed to inversely estimate the subcriticality; and the limitation of neutron detector size. In order to address these issues, we propose a reactivity estimation method that combines the improved simplest reactivity estimator (SRE) and the least squares inverse kinetics method. This study aims to estimate the reactivity in dollar units in a data driven manner only from the measured neutron count rate without point kinetics parameters. Furthermore, the usefulness of the bilateral filter in combination with the median for the count rate is also investigated to mitigate statistical errors in the reactivity estimation results due to the statistical fluctuation and outlier in the measured count rate data. To verify our proposed method, point kinetics calculation is performed to simulate the time series data of the neutron count rate during a stepwise transient from a deep subcritical state to the shallower state. Here, the magnitude of the count rate at the initial state is parametrically varied to investigate the effect of the statistical count rate fluctuation on the estimated reactivity. As a result, it is observed that the estimated reactivity tends to be overestimated (i.e., closer to critical) as lower count rate data are used in our proposed method. Thus, our proposed method is considered practical from the perspective of criticality control. Moreover, it is clarified that the combinational use of the bilateral filter and the median can effectively reduce the error of the estimated reactivity due to the statistical fluctuation of the count rate. Consequently, this feasibility study demonstrates our proposed method for monitoring the reactivity change even under the low neutron count rate condition.

DOI： 10.13182/PHYSOR24-43487

Loading Pattern Optimization for LWRs Using Monte Carlo Tree Search Reviewed International journal

Rikuto Kasama, Akio Yamamoto, Tomohiro Endo

Proc. PHYSOR2024 page： 2490 - 2499 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Inspired by recent breakthroughs in AI for games, we transform the fuel loading pattern
optimization problem into a game tree search problem and adopt Monte Carlo Tree Search (MCTS) to solve it. The performance of MCTS is compared with the conventional optimization methods, such as the random search and simulated annealing (SA), for the loading pattern optimization of a typical pressurized water reactor. The results demonstrate the superior efficiency of MCTS over the conventional methods. MCTS consistently produces high-quality patterns and effectively avoids the common problem of falling into local minima. By using techniques rooted in AI, we are
opening up a new way of solving complex problems in nuclear engineering, offering the prospect of more reliable and efficient core designs. This innovative approach will not only benefit the nuclear field, but also serve as a bridge between optimization and artificial intelligence.

DOI： 10.13182/PHYSOR24-43466

Preliminary Study on Two-Dimensional SP3 Calculation Based on POD-Local/Global Iterations Reviewed International journal

Masato Ito, Akio Yamamoto, Tomohiro Endo, Yasuhiro Kodama, Taichi Takeishi, Hiroaki Nagano

Proc. PHYSOR2024 page： 1612 - 1621 2024.4

Authorship：Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

As a preliminary study 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 SP3 calculation with the global/local 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 scale of the simultaneous 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 p-CMFD calculation is applied to the coarse mesh calculation (global calculation). These local and global calculations are iterated until convergence. Through the two-dimensional small and large UO2-MOX core calculations, our proposed method is verified by comparing with the reference result by the conventional fine mesh SP3 calculation.

DOI： 10.13182/PHYSOR24-43629

Real-Time 3D Fine Spatial Mesh Kinetics Simulator Using POD for Coupled Core Reviewed International journal

Kaito Ito, Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Proc. PHYSOR2024 page： 6986 2024.4

Authorship：Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Toward the development of the digital triplets to effectively educate the reactor physics experiment, the present study develops a real-time 3D fine spatial mesh kinetics simulator based on the proper orthogonal decomposition (POD). Our developed simulator, called Ikaros3D, was specifically designed for a coupled core to promote students’ better understanding of the complicated behavior of the spatial variation of the dynamic reactivity depending on the neutron detector position. Through a verification test, we confirmed that the reduced order model (ROM) using POD was able to accurately and quickly simulate the variation in the total core power due to the operation of two different control rods, thanks to the pre-tabulated compressed coefficient matrices for the POD based kinetics calculation.

DOI： 10.13182/PHYSOR24-43834

Reconstruction of In-Core Power Distribution Based on POD Using Ex-Core Detector Signals Reviewed International journal

Yuki Urase, Tomohiro Endo, Akio Yamamoto

Proc. PHYSOR2024 page： 1642 - 1651 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A reconstruction method of in-core power distribution using the proper orthogonal decomposition (POD) and the signal from ex-core detectors is developed. In the present method, the neutron flux distribution is expanded in a small number of POD bases and expansion coefficients. Neutron transport calculations were performed with several calculation conditions to perturb the neutron flux distributions in the reactor core and the POD bases were obtained using the multiple neutron flux distributions as the snapshot data. The neutron counts of ex-core detectors were evaluated from the in-core neutron flux distributions and the detector response coefficients. Considering the neutron counts of ex-core detectors as measured signals, the expansion coefficients of POD that represent the in-core neutron flux distributions were determined. Assuming a simple two-dimensional core with nine regions, the reconstruction accuracy of in-core neutron flux distribution was verified for several conditions. The results indicate that the in-core neutron flux distributions can be reconstructed by the ex-core detector signals when the distance between the detectors and the core is appropriately chosen.

DOI： 10.13182/PHYSOR24-43478

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

Proc. PHYSOR2024 page： 1036 - 1047 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

An improved sampling method for flight distance is proposed for Monte Carlo analysis of TRISO fuel particles using the statistical geometry method. The statistically uniform distribution of fuel particles, which is usually assumed as a default sampling method of flight distance of a neutron in graphite matrix, shows considerable bias on neutronics property when coating layers of a TRISO fuel particle are homogenized with graphite matrix. The proposed new sampling method almost resolves the difference between the homogenized coating model and the reference model that explicitly considers coating layers. By adopting the present method, the homogenized coating model can be used without significant loss of accuracy in the statistical geometry method. Computation time for a typical HTTR fuel compact cell with a continuous energy Monte Carlo code is reduced to 1/7 when the homogenized coating model is used.

DOI： 10.13182/PHYSOR24-43318

α-eigenvalue Calculation using the Sn Method with GPU Diffusion Acceleration Reviewed International journal

H. Yamaguchi, T. Endo, A. Yamamoto

Proceedings of the Reactor Physics Asia 2023 (RPHA2023) Conference 2023.10

2D Neutron Diffusion Calculation Based on Local/Global Iterations Using Proper Orthogonal Decomposition Reviewed International journal

M. Ito, T. Endo, A. Yamamoto, T. Takeishi, Y. Kodama, H. Nagano

Proceedings of the Reactor Physics Asia 2023 (RPHA2023) Conference 2023.10

Feasibility Study on Subcritical Rod Worth Measurement for UTR-KINKI Reviewed International journal

T. Endo, G. Chiba, K. Watanabe, C. H. Pyeon, G. Wakabayashi

Proceedings of the Reactor Physics Asia 2023 (RPHA2023) Conference 2023.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

In this study, we investigate the feasibility of the subcritical rod worth measurement (SRWM) to UTRKINKI (University Training Reactor, Kindai University) through a virtual numerical experiment.

Comparison of Neutronic Characteristics of BWR Burnup Fuel between JENDL-4.0 and JENDL-5 Reviewed International journal

Tomoaki Watanabe, Kenichi Tada, Tomohiro Endo, Akio Yamamoto

Proc. ICNC2023 2023.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

The present study investigated the effect of the nuclear data modification from JENDL-4.0 to JENDL-5 on the criticality characteristics of a typical 9×9 BWR burnup fuel. In JENDL-5, many nuclear data essential to characterize burnup fuels, such as the cross sections of Gd-155 and Gd-157, were modified. The depletion calculations showed that kinf of JENDL-5 was smaller than that of JENDL-4.0 at almost all burnup steps for 0–50 GWd/t. Significant burnup dependencies of the kinf difference between JENDL-4.0 and JENDL-5 were also found. For example, the kinf difference significantly increased around 12 GWd/t, and the kinf difference gradually increased as the burnup value increased. The direct sensitivity calculations were carried out to specify which nuclear data impacts the kinf difference. The specific nuclear data of interest was replaced from JENDL-4.0 to JENDL-5. The sensitivity calculation results showed that the kinf difference around 12 GWd/t was mainly caused by the modification of the cross sections of U-235, Gd-155, Gd-157, and TSL data of H in H2O. These modifications affected the composition of Gd-155 and Gd-157. The sensitivity calculation results also clarified that modifying the U-235 and Pu-239 cross sections and TSL data of H in H2O affected the increase in the kinf difference as the burnup value increased. The modifications of the TSL data for H in H2O also affected the composition of U-235.

Program of Reactor Physics Experiment to Measure Subcriticality for an Unknown System Reviewed International journal

Shunya Teratani, Yoshinari Harada, Kaito Mori, Yoshiki Yamashita, Tomohiro Endo, Go Chiba

Proc. ICNC2023 2023.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

In order to train human resources for the future nuclear field, we have been developing an advanced educational program for the reactor physics experiments by utilizing a Japanese educational reactor (University Training Reactor, Kindai University, UTR-KINKI) with recent measurement techniques. This paper summarizes the advanced reactor physics experiment program for training graduate students to tackle unknown problems. As a problem-based learning program (PBL) of reactor physics experiments, we focused on the subcriticality measurement for an unknown system without prior knowledge of the external neutron source intensity and the point kinetics parameters. In order to solve this challenging problem, the basic lectures and the interactive exercise were prepared to help graduate students better understand (1) the criticality approach based on the inverse multiplication and (2) the measurement of the prompt neutron decay constant by the Feynman-α method. Through the series of lectures, the instructors hope that graduate students will get an idea of how to determine the subcriticality for a target unknown system, e.g., by combining the inverse multiplication and the Feynman-α methods through the Simmons-King method. The combined method was demonstrated by the actual reactor physics experiment at UTR-KINKI.

Nuclear Data Sensitivity Analysis of a Sodium Shielding Experiment Based on Generalized Perturbation Theory for Data Assimilation Reviewed International journal

Shuhei Maruyama, Tomohiro Endo, Akio Yamamoto

Proc. ICNC2023 2023.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

This paper investigates the feasibility of uncertainty reduction by sharing the experimental database between different fields (e.g., reactor physics and radiation shielding) and using data assimilation techniques. To perform this study, we have developed a sensitivity analysis tool based on a transport generalized perturbation theory, which can be applied not only to the analysis of reactor physics experiments, but also to the analysis of shielding experiments. As the first step in this study, we focus on the ORNL sodium shielding experiments with Bonner Ball neutron detectors and perform a sensitivity analysis of these experiments. Using the sensitivity coefficients evaluated here and those of the fast reactor core characteristics evaluated to date by JAEA, we have shown that the sodium shielding experimental data can contribute to the uncertainty reduction of sodium void reactivity by adopting a data assimilation technique. Based on this preliminary study, the uncertainty reduction effect is expected to be significant, especially for sodium void reactivity dominated by the neutron leakage phenomena. Although new reactor physics experimental data on sodium void reactivity may be difficult to obtain, the results of this study suggest that the data from sodium shielding experiments can partially substitute for this role. This study demonstrates the value of the mutual use of integral experimental data in fast reactor design.

Efficient Uncertainty Quantification Using Deterministic Sampling Method with Simplex Ensemble and Scaling Method Reviewed International journal

Tomohiro Endo, Akio Yamamoto

Proc. ICNC2023 2023.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

In the field of criticality safety, the uncertainty quantification (UQ) of the neutron multiplication factor is important to investigate the appropriate safety margin for a target system. The random sampling method is a practical and useful method for the UQ. Note that, when using the random sampling method, the statistical error of the estimated uncertainty is inevitably caused. Therefore, a longer calculation time is required because of the larger sample size to reduce the statistical error. 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, this study proposes an improved deterministic sampling method using the simplex ensemble and the scaling method for efficient UQ. The features of the proposed method are summarized as follows: 1) the sample size is equal to (r+2), where r corresponds to the effective rank of the covariance matrix between the input variables; 2) the scaling method enables us to arbitrarily give a perturbation amount of the input parameters in the deterministic sampling method, thereby the weighted mean and covariance for the target output parameters are deterministically estimated depending on the weight by the scaling factor; 3) the scaling factor can be updated to prevent the negative values in the perturbed input variables. The effectiveness of the proposed method is demonstrated through the UQ due to fuel manufacturing uncertainties for a typical PWR pin-cell burnup calculation.

Data Assimilation Using Prompt Neutron Decay Constant for Water to Reduce Uncertainties due to Thermal Neutron Scattering Law Reviewed International journal

Yoshinari Harada, Hibiki Yamaguchi, Tomohiro Endo, Akio Yamamoto

Proc. ICNC2023 2023.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

In the neutronics analysis for a water-containing system, the thermal neutron scattering law (TSL) of water affects the calculated values of the neutronics parameters. In our previous study, we quantified the TSL data-induced uncertainty of the prompt neutron decay constant measured for water tank systems and evaluated the correlations between the different-sized water tank systems. Our previous study clarified that there were strong TSL data-induced correlations of ~0.9 in between the smallest and other water tank systems. Based on these strong correlations, it was suggested that the TSL data-induced uncertainties in the numerical predictions of for other water tank systems can be improved by the data assimilation using the experimental result of α for the smallest water tank. To demonstrate the uncertainty reduction using the experimental result of , this study aims to perform the data assimilation by the Bayesian Monte Carlo (BMC). To address the degeneracy problem in the conventional BMC, the merging particle filter was applied in this study. Consequently, the relative standard deviation of the TSL data-induced uncertainty of was reduced to 1/3. While the experimental results of existed within the 2σ-uncertainty range of the calculated values before the data assimilation, the calculated values of after the data assimilation were improved so that the experimental results were located within the posterior 1σ-uncertainty range.

Application of the RSE Method for the Resonance Treatment of HTGR Fuel with Double Heterogeneity Reviewed International journal

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

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

The resonance calculation using energy spectrum expansion (RSE) method is applied to realistic HTGR fuel elements containing the double heterogeneity. The pointwise disadvantage factor is used to spatially homogenize fuel particles in a fuel compact. The pointwise disadvantage factor is calculated using the method of characteristics coupled with the statistical geometry method. Verification calculations are carried out for a typical fuel compact cell of HTGR fuel. The ultra-fine group spectra, multi-group effective microscopic cross sections, and multi-group microscopic reaction rates are compared with the reference solution obtained by ultra-fine group (UFG) spectrum calculation. Differences between the RSE and UFG calculations are small and the difference in k-infinity due to the present resonance treatment is estimated to be 0.025% Δk.

Uncertainty Quantification of Prompt Neutron Decay Constant α due to Thermal Neutron Scattering Law of Water Reviewed International journal

Yoshinari Harada, Hibiki Yamaguchi, Tomohiro Endo, Akio Yamamoto

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

Thermal neutron scattering law (TSL) data for 1 H in H2O causes uncertainties of neutronics calculations for systems containing light water. As a preliminary study to improve the TSL data by the data assimilation using experimental data of prompt neutron decay constant for simple water tank systems, this study quantifies the TSL data-induced uncertainty of prompt neutron decay constant based on the random sampling method. In this study, 200 LEAPR formatted TSL data from TENDL-2021 is utilized as the randomly sampled TSL data for 1 H in H2O. For each TSL data, the numerical result of is calculated using an in-house deterministic code of eigenvalue calculation. As a result, this study clarifies that experimental results of exist within the 2 uncertainty range of the calculated values for four different sized water tank systems. Furthermore, TSL data-induced correlations of between different water tank sizes are also estimated. Consequently, there are strong positive correlations between them, i.e., correlation coefficients are greater than 0.9. This result implies that the TSL data for 1 H in H2O can be updated by the data assimilation using the measurement to reduce the TSL data-induced uncertainties of neutronics calculations for other systems that have the strong correlation due to the TSL data.

Study on a Data-Driven Neutron Transport Calculation Method Using Proper Orthogonal Decomposition Reviewed International journal

Shunya Teratani, Masato Ito, Tomohiro Endo, Akio Yamamoto

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

The proper orthogonal decomposition (POD) can reduce the dimension of the neutron flux distribution using a small number of POD bases and their expansion coefficients. POD can be directly applied to neutron diffusion calculations because the neutron diffusion equations can be discretized in a matrix form for the total neutron flux. However, application of POD to neutron transport calculations that rigorously treat the angular dependency of the neutron flux is difficult, because the transport calculation cannot be directly expressed by a matrix form equation for the total neutron flux. To address this problem, we propose a new POD transport calculation method based on a data-driven approach that utilizes multiple input and output data in transport calculations. As a feasibility study, the data-driven POD transport calculation method was implemented in a one-dimensional homogeneous slab geometry to verify the proposed method. Then, using a non-parametric way based on the Wilks' method, the upper tolerance limit (UTL) of the calculation error was statistically evaluated with the probability of 95% and the confidence level of 95%. Through this study, we demonstrate the proposed method can accurately calculate the total neutron flux, if "the number of input or output data used in the data-driven POD, " is larger than or equal to "the number of POD bases, " and is sufficiently large. In addition, we investigated the relationship between the contribution ratio of singular values for snapshot or data matrices and the UTL of relative root mean square error. Consequently, we observed the relationship of "(1−contribution ratio) ≈ UTL of rRMSE." Therefore, we expect that the number of POD bases can be determined based on the contribution ratio according to a target calculation accuracy.

Optimization of Nuclear Fuel Management for Multi-Module SMRs Reviewed International journal

Yoshiki Yamashita, Tomohiro Endo, Akio Yamamoto

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

A fuel management strategy for light water type Small Modular Reactors (SMRs) was studied assuming that multiple cores share nuclear fuels. Fuel management for two and three cores for the cases with and without fuel sharing and was considered. The optimization of power sharing of fuel batches was used for the optimization of fuel management instead of direct optimization of fuel loading patterns. The average discharge burnups and cycle lengths for various operating patterns were compared by changing the cycle length (the number of fresh fuel assemblies) of each core. As a result, it was found that the fuel cycle cost could be improved by sharing the nuclear fuels among multiple cores when their cycle lengths are different.

Evaluation of Neutron Flux Expansion Error by POD Bases Based on Wilks' Method Reviewed International journal

Masato Ito, Tomohiro Endo, Akio Yamamoto, Yasuhiro Kodama, Hiroaki Nagano

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

Proper orthogonal decomposition (POD) is a numerical analysis method to reduce the core analysis cost. In POD, orthonormal bases (POD bases) can be obtained by the data-driven approach to efficiently expand the spatial distribution of neutron flux. To ensure high accuracy of core analysis using POD, statistical evaluation of the upper tolerance limit (UTL) of neutron flux expansion error by POD bases is necessary. In the present study, the statistical evaluation for the expansion error is investigated using the non-parametric method based on the one-sided Wilks' formula. Using the first-order Wilks' method, the desired UTL with the target probability and confidence level can be estimated as the maximum value among the wilks random sampling results. In the verification for a pin-by-pin single UO2 fuel assembly without control rods, we investigate whether the UTL of the POD expansion error can be appropriately estimated using the Wilks' method. First, many estimated UTLs of the expansion error are estimated by randomly changing the calculation conditions. Next, each of the UTLs is tested whether it can be successfully estimated by checking the calculating probability using the estimated UTL is larger than or equal to the target probability. Finally, the confidence level is calculated as the ratio of the "successfully estimated UTLs" to the total UTLs. Consequently, the calculated confidence level calc includes the reference level ref within the range of statistical uncertainty. Therefore, this study demonstrates that the UTL of the expansion error can be appropriately estimated using the first-order Wilks' method.

Development of Real-Time 3D Fine Mesh Kinetics Calculation Method Based on POD Reviewed International journal

Kaito Ito, Akio Yamamoto, Tomohiro Endo, Kosuke Tsujita

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

A reduced order model using the proper orthogonal decomposition to reproduce 3D fine mesh kinetics calculations in real time is proposed and its applicability is verified through a benchmark calculation. The orthogonal basis is generated with the results of the 3D fine mesh calculation and a reduced order model is developed using the orthogonal basis. The results obtained by the 3D fine mesh kinetics model and the reduced order model are compared for a benchmark problem considering a control rod operation in the LMW benchmark problem. The relative root mean square error of the integrated core power is within 0.1%. The computation time per time step of the reduced order model is approximately 0.1 s, which confirms that the model is available for real-time application including on-line monitoring.

Deep Penetration Calculations Combining Proper Orthogonal Decomposition and Monte Carlo Methods Reviewed International journal

Kaito Mori, Akio Yamamoto, Tomohiro Endo

Proc. M&C2023 2023.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：Canadian Nuclear Society

A deep penetration calculation method that combines a POD basis obtained by deterministic calculations and the expansion coefficients for the POD basis obtained by the continuous energy Monte Carlo method is proposed. The present method is applied to a simple deep penetration calculation of a slab geometry. By comparing the results obtained by the present method, the continuous energy Monte Carlo method, and the multigroup deterministic transport method, the statistical error of the continuous energy Monte Carlo method in deep penetration calculations and the systematic error of the multigroup deterministic transport method can be reduced by the present method.

Application of Equivalent Dancoff Factor Method for Resonance Calculation of Double Heterogeneous Fuel Reviewed International journal

Akio Yamamoto, Tomohiro Endo

Transactions of the American Nuclear Society Vol. 128 ( 1 ) page： 690 - 693 2023.6

Statistical Uncertainty Quantification of Probability Tables for Unresolved Resonance Cross Sections Reviewed International journal

Kenichi Tada, Tomohiro Endo

EPJ Web of Conferences Vol. 284 page： 14013 - 14013 2023.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

The probability table method is an important method to treat the self-shielding effect in the unresolved resonance region. A probability table is generated by using many “ladders” that represent pseudo resonance structures. This study developed a quantification method of the statistical uncertainty of a probability table. The product of the probability table and average cross section in each probability bin was considered as the target of the statistical uncertainty of the probability table. The central limit theorem (CLT), bootstrap method, and jackknife method were adopted to calculate the statistical uncertainty. The statistical uncertainties calculated using these methods were compared with the reference results. The calculation results showed that the statistical uncertainties obtained by CLT were similar to those of the other methods. Because the CLT calculation time was faster than that of the other methods, CLT was deemed as the best method for calculating the statistical uncertainty of the probability table. The statistical uncertainty quantification of the probability table developed in this study was implemented in nuclear data processing code FRENDY version 2. FRENDY version 2 can generate a probability table using the tolerance of the statistical uncertainty of the probability table.

DOI： 10.1051/epjconf/202328414013

Applicability evaluation of Akaike’s Bayesian information criterion to covariance modeling in the cross-section adjustment method Reviewed International journal

Shuhei Maruyama, Tomohiro Endo, Akio Yamamoto

EPJ Web of Conferences Vol. 281 page： 00008 2023.3

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

The applicability of Akaike’s Bayesian Information Criterion (ABIC) to the covariance modeling in the cross-section adjustment method has been investigated. In the conventional cross-section adjustment method, the covariance matrices are assumed to be true. However, this assumption is not always appropriate. To improve the reliability of the cross-section adjustment method, the estimation of the covariance model using the metric ABIC has been introduced, and the performance of ABIC has been investigated through simple numerical experiments. This paper derives the formula to efficiently evaluate ABIC which is represented by a lower rank matrix to enable numerical experiments with large samples in a realistic computation time. From the results of the numerical experiments, it has been confirmed that ABIC tends to select a covariance model with fewer hyperparameters and a smaller variance for the estimation error. However, it has also been found that this desirable property of ABIC will be lost when the structure of the covariance model is far from the true one.

DOI： 10.1051/epjconf/202328100008

Development of a robust nuclear data adjustment method to outliers Reviewed International journal

Yuhei Fukui, Tomohiro Endo, Akio Yamamoto, Shuhei Maruyama

EPJ Web of Conferences Vol. 281 page： 00006 2023.3

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

We developed a new nuclear data adjustment method for experimental data containing outliers. This method mitigates the effect of outliers by applying M-estimation, a type of robust estimation, to the conventional nuclear data adjustment method using sensitivity coefficients. Based on the M-estimation, we derived a weighted nuclear data adjustment formula and developed a weight calculation method. The weighted nuclear data adjustment formula was derived by weighting the function to take the extremum of the conventional nuclear data adjustment. The weighting of each nuclear characteristic is calculated from the difference between the measured and calculated values of the nuclear characteristic. This weight calculation method can evaluate the validity of each nuclear characteristic by considering correlations between nuclear characteristics using singular value decomposition. The proposed method and the conventional method were compared and verified by twin experiments. In the twin experiments, the nuclear data were adjusted using experimental data that intentionally included outliers. As a result of twin experiments, it was confirmed that the nuclear data were adjusted robustly and appropriately even with the experimental data containing outliers.

DOI： 10.1051/epjconf/202328100006

A New Approach for Resonance Treatment of Doubly Heterogeneous Fuel Using the RSE Method Reviewed International journal

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

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) page： 2042 - 2051 2022.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A new resonance calculation method for the doubly-heterogeneous (DH) fuels such as high temperature gas-cooled reactor fuel is proposed based on the Resonance calculation based on Spectral Expansion (RSE) method. The concept of pointwise disadvantage factor for fuel grain is taken into account to treat the DH fuels. The verification calculation is carried out for simplified single fuel cell and fuel compact consisting of five fuel cells and graphite moderator. The calculation results indicate that the present method can appropriately handle the space dependent self-shielding effect for DH fuels.

DOI： 10.13182/PHYSOR22-37251

Proposal and Application of ROM-Lasso Method for Sensitivity Coefficient Evaluation Reviewed International journal

Ryota Katano, Akio Yamamoto, Tomohiro Endo

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) page： 2032 - 2041 2022.5

Authorship：Last author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

We propose a novel method for evaluating sensitivity coefficients of neutronics parameters to cross sections, so-called the ROM-Lasso. In this method, cross sections of interest are randomly sampled, and corresponding perturbed core analyses are performed. Then, the sensitivity coefficient vector of the higher-level model is expanded via the active subspace bases obtained with the lower-level model whose dimensional complexity is smaller than that of the higher-level model, and the expansion coefficients are estimated by the lasso regression. A unique feature of the ROM-Lasso method allows the use of different bases optimized for each neutronics parameter. We conducted a verification calculation for an accelerator-driven system and demonstrated that the ROM-Lasso method can reproduce the sensitivity coefficients with a much smaller number of forward calculations than the direct method. The proposed method can be used to practically evaluate the sensitivity coefficients.

DOI： 10.13182/PHYSOR22-37557

Neutron Diffusion Calculation in Heterogeneous Geometry Based on Local/Global Iteration Using Proper Orthogonal Decomposition Reviewed International journal

Masato Ito, Tomohiro Endo, Akio Yamamoto, Yoshitada Masaoka, Yasuhiro Kodama, Hiroaki Nagano

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) page： 503 - 512 2022.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

This study newly proposes a heterogeneous core calculation method based on local/global iteration using proper orthogonal decomposition (POD). By using the singular value decomposition (SVD) and the low-rank approximation, appropriate POD bases for expanding the neutron flux can be obtained from snapshot data of the neutron flux obtained by fine mesh calculations. By projection using the POD bases, the dimension of the target equation (e.g., discretized neutron diffusion equation) can be dramatically reduced. In the proposed method, POD is effectively applied to each single assembly calculation (local calculation). Furthermore, using the local/global iteration, the effective neutron multiplication factor and the neutron flux distribution in the whole core geometry can be obtained by combining the numerical results of the local calculation for each fuel assembly and the global calculation for the whole core. As a feasibility study, the proposed method is applied to a one-dimensional heterogeneous core analysis, and the accuracy is investigated by changing the total number of POD bases.

DOI： 10.13182/PHYSOR22-37693

Development of Nuclear Data Processing CodeFRENDY Version 2 Reviewed International journal

Kenichi Tada, Akio Yamamoto, Tomohiro Endo, Go Chiba, Michitaka Ono, Masayuki Tojo

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) page： 107 - 116 2022.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Nuclear data processing is an important interface between an evaluated nuclear data library and neutronics calculation codes. JAEA has been developed the new nuclear data processing code FRENDY from 2013. FRENDY version 1 generates the ACE files used for the continuous-energy Monte Carlo codes including PHITS, Solomon, Serpent, and MCNP and it was released as the open-source software under the 2-clause BSD license in 2019.After we released FRENDY version 1, many functions, e.g., the multi-group neutron cross-section library generation, the statistical uncertainty quantification of the probability tables for unresolved resonance cross-section, the perturbation of the ACE file, and the modification of the ENDF-6 formatted nuclear data file, are developed. We released FRENDY version 2including these functions. The present paper explains the overview of FRENDY and features of new functions implemented in FRENDY version 2.

DOI： 10.13182/PHYSOR22-37299

Area Ratio Method Using Dynamic Mode Decomposition Reviewed International journal

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

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) page： 3366 - 3375 2022.5

Authorship：Lead author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

To reduce the higher mode effects on the subcriticality estimation using the pulsed neutron source without the aid of a high-fidelity neutron transport calculation, we propose a new area ratio method based on a data-driven approach using the dynamic mode decomposition (DMD) with the neutron count data measured by multiple neutron detectors. Thanks to eigenvalues and eigenvectors based on DMD, the fundamental mode of the prompt neutrons and the background component due to delayed neutrons are extracted from the measured neutron count data matrix. The effectiveness of the proposed method is demonstrated via experimental analysis for a pulsed neutron source measurement performed at Kyoto University Critical Assembly.

DOI： 10.13182/PHYSOR22-37184

Dimension-reduced Nuclear Data Adjustment Method based on the Bayesian Monte-Carlo Method Reviewed International journal

Yuhei Fukui, Tomohiro Endo, Akio Yamamoto

Transactions of the American Nuclear Society Vol. 125 ( 1 ) page： 900 - 903 2021.11

Application of Regionwise Even-Parity Discontinuity Factor to the Multigroup Analog Monte-Carlo Method Reviewed International journal

Yoshiki Oshima, Tomohiro Endo, Akio Yamamoto, Naoto Aizawa

Transactions of the American Nuclear Society Vol. 125 ( 1 ) page： 904 - 907 2021.11

Sensitivity Analysis in Dynamic Multi-unit PRA Evaluation Using Correlated Sampling Method Reviewed International journal

Yuki Morishita, Akio Yamamoto, Tomohiro Endo

Proc. Asian Symposium on Risk Assessment and Management (ASRAM2021) page： ASRAM2021-034 2021.10

Language：English Publishing type：Research paper, summary (international conference)

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 failure rate of safety components. In the correlated sampling method, original and perturbed samples are assumed to trace the identical accident sequence, but the weight of the perturbed sample is adjusted to incorporate the variation of input data. The correlated sampling method is applied to the sensitivity analysis of a simple system to prove the principle. The result indicates that the sensitivity analysis for the CMMC coupling method is possible by the correlated sampling method.

Development of estimation method for prompt neutron decay constant using dynamic mode decomposition Reviewed International journal

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

Proc. M&C 2021 page： 1719 - 1728 2021.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

To estimate the prompt neutron decay constant α corresponding to the fundamental mode in a subcritical system, we try applying the Dynamic Mode Decomposition (DMD) to time-series data of neutron counts obtained by the pulsed-neutron source (PNS) method. In this study, we newly develop an estimation method of α with the statistical uncertainty by the DMD and the random sampling method. The applicability of the proposed method is demonstrated by analyzing a PNS experiment carried out at the Kyoto University Critical Assembly (KUCA).

DOI： 10.13182/M&C21-33631

Theoretical derivation of unique combination-number for higher order neutron correlation factors based on Pál-Bell equation Invited Reviewed International journal

Tomohiro Endo, Akio Yamamoto

Proc. M&C 2021 page： 1568 - 1576 2021.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The Pál-Bell equation is a master equation to describe the probability generating function (PGF) of neutron counts in the 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. Thereby, the unique combination numbers for the higher-order neutron-correlation factors for a near-critical state can be theoretically clarified. This knowledge is useful to judge whether a target system is a near-critical state or not using only a histogram (or factorial moments) of neutron counts.

DOI： 10.13182/M&C21-33627

S2 Consistent Analytic CMFD Acceleration for Method of Characteristics Reviewed International journal

Yoshiki Oshima, Akio Yamamoto, Tomohiro Endo

Proc. M&C 2021 page： 1840 - 1849 2021.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A coarse mesh finite-difference (CMFD) acceleration consistent with the S2 discrete ordinate method using the step-characteristics is proposed. The analytically derived finite-difference formulation for diffusion theory (ACMFD), which is theoretically consistent with the discrete ordinate method in one-dimensional slab geometry with the S2 Gauss-Legendre quadrature, is used for the acceleration of a transport calculation. Our numerical calculations in simple geometry revealed that the consistent treatment of scattering source distribution in the ACMFD acceleration has a significant impact on the convergence property. Further, the linearized Fourier analysis of ACMFD acceleration shows the same convergence property as numerical calculations. These numerical and theoretical analyses show that the S2-consistent ACMFD acceleration is unconditionally stable without any correction to the diffusion coefficient.

DOI： 10.13182/M&C21-33737

Fuel assembly analyses with resonance calculation using energy spectrum expansion method Reviewed International journal

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

Proc. M&C 2021 page： 2219 - 2230 2021.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Efficient numerical algorithms for a Resonance calculation using energy Spectrum Expansion (RSE) method were proposed for a large and complicated geometry such as a fuel assembly. The RSE method can treat complicated heterogeneous geometry considering resonance interference effect among different regions. Calculation procedure of the RSE method is composed of (1)generation of ultra-fine group spectra from ultra-fine group calculations in homogeneous geometry, (2)expansion of the spectra by orthogonal basis on energy based on singular value decomposition, (3)transport calculation for expansion coefficients and (4)reconstruction of ultra-fine group spectra in target heterogeneous regions by the expansion coefficients and the orthogonal basis. In this study, the efficient numerical algorithms for the RSE method were developed and applied. The algorithms are composed of (i)scattering source calculation by the combination of conventional slowing down and moment-to-moment transfer calculations, and (ii)matrix exponential generation in transport calculation of the RSE method with method of characteristics by diagonalization using eigenvalue decomposition. Through numerical verification, it was confirmed that effective multi-group cross sections by the RSE method with the new algorithms are well agreed with those by direct ultra-fine group calculation in the fuel assembly geometry. The RSE method with the new algorithms is applicable to the fuel assembly analysis.

DOI： 10.13182/M&C21-33621

FRENDY/MG: a multi-group cross section generation module using ace pointwise cross sections Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Basma Foad, Go Chiba, Kenichi Tada

Proc. M&C 2021 page： 710 - 720 2021.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A generation capability of neutron multi-group cross sections is being implemented to the FRENDY nuclear data processing code, as FRENDY/MG. FRENDY/MG generates neutron multi-group cross sections for deterministic core analysis codes considering an arbitrary energy group structure. Distinguished features of FRENDY/MG are 1) use of ACE pointwise cross sections as the source of nuclear data (no evaluated nuclear data file is directly used), 2) treatment of a compound material consisting of multiple nuclides to explicitly consider the resonance interference effect. Various verifications are being carried out through the comparison with the multi-group cross sections generated by NJOY.

DOI： 10.13182/M&C21-33679

Multi-Group Cross Section Library Generation by FRENDY for Fast Reactor Neutronics Calculations Reviewed International journal

Go Chiba, Akio Yamamoto, Kenichi Tada, Tomohiro Endo

Transactions of the American Nuclear Society Vol. 124 page： 556 - 558 2021.6

Verification of the Multi-Group Generation Capability of FRENDY Nuclear Data Processing Code for Recent Nuclear Data through Comparison of One-group Reaction Rates Reviewed International journal

Akio Yamamoto, Kenichi Tada, Go Chiba, Tomohiro Endo

Transactions of the American Nuclear Society Vol. 124 page： 544 - 547 2021.6

Perturbation-Theory-Based Sensitivity Analysis of Prompt Neutron Decay Constant for Water-Only System Reviewed International journal

Tomohiro Endo, Akihiro Noguchi, Akio Yamamoto, Kenichi Tada

Transactions of the American Nuclear Society Vol. 124 page： 184 - 187 2021.6

A Resonance Calculation Method using Energy Expansion based on a Reduced Order Model: Use of Ultra-Fine Group Spectrum Calculation and Application to Heterogeneous Geometry Reviewed International journal

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

EPJ Web of Conferences Vol. 247 page： 02006 - 02006 2021.2

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

A Resonance calculation using energy Spectral Expansion (RSE) method has been recently proposed in order to efficiently treat complicated heterogeneous geometry and resonance interference effect. In the RSE method, ultra-fine group spectra are generated from ultra-fine group calculations in homogeneous geometry, and the spectra are expanded by the orthogonal basis on energy based on the singular value decomposition. Then the transport calculation for expansion coefficients is numerically performed, and the ultra-fine group spectra in the target heterogeneous regions are reconstructed by the expansion coefficients and the orthogonal basis. In this study, the RSE method is applied to multi-cell geometries including UO2, MOX and water cells, in which the resonance interference effect between UO2 and MOX fuel cells appears. The validity of the RSE method is confirmed through comparison with the reference effective multi-group cross sections obtained from the direct ultra-fine group calculation in the target heterogeneous geometry.

DOI： 10.1051/epjconf/202124702006

Experiment of Unique Combination Number due to the Third-Order Neutron-Correlation Reviewed International journal

Tomohiro Endo, Sho Imai, Kenichi Watanabe, Akio Yamamoto, Atsushi Sakon, Kengo Hashimoto, Masao Yamanaka, Cheol Ho Pyeon

EPJ Web of Conferences Vol. 247 page： 09004 - 09004 2021.2

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

From zero-power reactor noise measurement, the second- and third-order neutron correlation factors <italic>Y</italic> and <italic>y</italic>3 can be evaluated by analyzing mean, variance, the third-order central moment of neutron count data. Theoretically, it is expected that the neutron-correlation ratio <italic>y</italic>3/<italic>Y</italic>2 converges to the unique combination number “3” at a near-critical state in an arbitrary system without depending on the fissile material and the neutron-energy spectrum of core, as the neutron counting gate width <italic>T</italic> increases sufficiently. Thus, the information about the difference between <italic>y</italic>3/<italic>Y</italic>2 and “3” has the potential to judge whether a target unknown system is critical or not and to roughly guess the absolute value of subcriticality. In this study, the detector dead-time effect on <italic>y</italic>3/<italic>Y</italic>2 is theoretically investigated based on the heuristic method using the single-, pair-, and trio-detection probabilities with the fundamental mode approximation. As a result, it is clarified that the saturation value of <italic>y</italic>3/<italic>Y</italic>2 converges to “3” independent of the dead time, when a target system is a critical state. For validation, actual experimental results are presented for a non-multiplication system driven by 252Cf spontaneous source, and shallow and deep subcritical systems at Japanese experimental facilities (UTR-KINKI and KUCA) under the shutdown state. Consequently, it is demonstrated that <italic>y</italic>3/<italic>Y</italic>2 shows a significant difference from “3” in the non-multiplication system. In the case of subcritical systems driven by inherent neutron sources, it is confirmed that the ratios <italic>y</italic>3/<italic>Y</italic>2 are close to the unique combination number “3,” and the slight difference from “3” is measurable by the long-time reactor noise measurement for the deep subcritical system.

DOI： 10.1051/epjconf/202124709004

Estimated Criticality Lower-Limit Multiplication Factor of Low-Enriched Uranium Dioxide-Concrete System Using the Bootstrap Method Reviewed International journal

Takuto Hayashi, Fuga Nishioka, Tomohiro Endo, Akio Yamamoto

EPJ Web of Conferences Vol. 247 page： 17001 - 17001 2021.2

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

The present paper aims to evaluate the estimated criticality lower-limit multiplication factor of fuel debris in a form of uranium dioxide-concrete mixture for a study of criticality control on the fuel debris generated through the molten core concrete interaction in a severe accident of a light water reactor. The estimated criticality lower-limit multiplication factor is evaluated using the bootstrap method where the assumption of the normal distribution is not necessary. In addition, it is calculated taking into account correlation coefficients that represent the degrees of neutronic similarity between the target system and benchmark critical experiment systems, experimental uncertainties of benchmark data, and statistical uncertainties of calculated effective multiplication factor by a continuous energy Monte Carlo code. This paper shows that the estimated criticality lower-limit multiplication factor using the bootstrap method can be comparable with a baseline upper-subcritical-limit which is evaluated by Whisper-1.1 without margins of subcriticality for uncertainties from nuclear covariance data and undetected errors in software.

DOI： 10.1051/epjconf/202124717001

Basic Study on a Pseudo Trend Phenomenon of The Feynman-α Analysis with Bunching Method Reviewed International journal

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

EPJ Web of Conferences Vol. 247 page： 09008 - 09008 2021.2

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

In these years, reactor noise analysis methods have been studied to apply for the Debris’ criticality management at the Fukushima Daiichi NPP, Japan. The Feynman-α analysis with bunching method is one of the candidate techniques, however the bunching method itself has never been validated in detail. This synthesis technique is useful to reduce a time required for the experiment, however it is known that a non-physical trend unrelated to the state of a nuclear reactor is generated by the multiple use of time series data, and this phenomenon (we call “pseudo trend phenomenon”) has never been systematically studied in detail. In this study, Poisson events, whose statistical characteristics were clarified, were employed to investigate the pseudo trend phenomenon of the bunching method. The time-sequence count data for various statistical parameters were generated by the Monte Carlo time series simulator. Comparing the two results obtained by applying the conventional bunching method and the moving-bunching method for the same Poisson event time series, and it was found that the same pseudo trend component appears in both results of the bunching method and the moving bunching method. In addition, it was also found that the fluctuation width of the pseudo trend component is smaller than the statistical fluctuation range.

DOI： 10.1051/epjconf/202124709008

Study on Multi-unit PRA Considering Correlation between Multiple Safety Systems Using the Continuous Markov chain Monte Carlo Method Reviewed International journal

Kento Sawada, Tomohiro Endo, Akio Yamamoto, Sunghyon Jang, Daisuke Fujiwara, Chikahiro Sato

Proc. ASRAM2020 page： 1027 2020.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：Atomic Energy Society of Japan

After the accident in Fukushima Dai-ichi Nuclear Power Plants, the necessity for the safety assessment considering multiple nuclear power units is increasing. However, the conventional event tree (ET) method, which is widely used in probabilistic risk assessment (PRA), cannot consider the interdependency among safety systems or events in multiple units as well as time dependency of the accident progressions. Recently, a new approach that couples the Continuous Markov chain Monte Carlo (CMMC) method with a plant safety analysis or a severe accident analysis code is suggested to address these issues. However, applications of the CMMC coupling method to safety assessment for multiple units are still limited. In the present study, the CMMC coupling method is applied to multiple units analysis in order to get practical insights and to clarify the issues of this method. Since the CMMC coupling method requires a large number of executions of an accident analysis code, a meta-model that simplifies the systems and the physical phenomena in accidents is used in this study to avoid the high computational cost of the existing accident analysis codes. In the present study, the numerical investigation of a BWR accident under station blackout (SBO) with loss of RCIC is carried out. The preliminary results suggested that the CMMC coupling method can appropriately treat the interdependency and time dependency among events in multiple units.

Subcriticality Estimation using Unscented Kalman Filter for Reactivity- and Source-Transients Reviewed International journal

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

Transactions of the American Nuclear Society Vol. 123 page： 841 - 844 2020.11

Fast Reproduction of Time-dependent MOC Calculations using the Reduced Order Model based on the Proper Orthogonal and Singular Value Decompositions Reviewed International journal

Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Transactions of the American Nuclear Society Vol. 123 page： 1349 - 1353 2020.11

Development of FRENDY Nuclear Data Processing Code: Generation Capability of Multi-group Cross Sections from ACE File Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Kenichi Tada

Transactions of the American Nuclear Society Vol. 122 page： 714 - 717 2020.6

Application of Bootstrap Method to Estimated Criticality Lower-Limit Multiplication Factor Considering Nuclear Data-Induced Uncertainty Reviewed International journal

Takuto Hayashi, Tomohiro Endo, Akio Yamamoto

Transactions of the American Nuclear Society Vol. 122 page： 458 - 461 2020.6

Impact of Diffusion Coefficient and Correction Term on the Convergence of CMFD Acceleration for MOC Reviewed International journal

Y. Oshima, T. Endo, A. Yamamoto

Proceedings of Reactor Physics Asia 2019 page： 62 - 65 2019.12

Application of Singular Value Decomposition and Low Rank Approximation for Compression of Macroscopic and Microscopic Cross Section Table for Core Calculations Reviewed International journal

M. Yamamoto, T. Endo, A. Yamamoto

Proceedings of Reactor Physics Asia 2019 page： 166 - 169 2019.12

Uncertainty Quantification of Neutronics Characteristics in Thermal Systems Using Random Sampling and Continuous Energy Monte-Carlo Methods Reviewed International journal

H. Oike, R. Kondo, T. Endo, A. Yamamoto

Proceedings of Reactor Physics Asia 2019 page： 14 - 17 2019.12

Performance of the RSE (Resonance calculation using energy Spectral Expansion) Method for Heterogeneous Pin-cell Geometry Reviewed International journal

R. Kondo, T. Endo, A. Yamamoto, S. Takeda, H. Koike, K. Yamaji, D. Sato

Proceedings of Reactor Physics Asia 2019 page： 162 - 165 2019.12

Estimated Criticality Lower-Limit Multiplication Factor Considering Neutronic Similarity and Uncertainties of Effective Multiplication Factor Using the Bootstrap Method (2) Application Reviewed International journal

F. Nishioka, T. Hayashi, T. Endo, A. Yamamoto

Proceedings of Reactor Physics Asia 2019 page： 254 - 257 2019.12

T. Hayashi, F. Nishioka, T. Endo, A. Yamamoto

Proceedings of Reactor Physics Asia 2019 page： 250 - 253 2019.12

Effectiveness of Subcritical Measurement at Solid Moderated KUCA Core for Reducing Nuclear Data-Induced Uncertainties in Other Light Water Reactor Analysis Reviewed International journal

T. Endo, A. Yamamoto

Proceedings of Reactor Physics Asia 2019 page： 262 - 265 2019.12

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference)

This paper aims to clarify that the subcritical measurement at the solid moderated KUCA core is useful to reduce nuclide data-induced uncertainties of the effective neutron multiplication factors keff in other light water moderated systems. For this purpose, we pay attention to the prompt neutron decay constant α, which was measured by the Feynman-α method with the moving block bootstrap method for the deep subcritical KUCA core under the shutdown state without any external neutron source. The sensitivity analyses of α for the subcritical KUCA core and of keff for various light water moderated critical cores were carried out based on the first-order perturbation theory. Consequently, it is demonstrated that the nuclear data-induced uncertainties of keff can be reduced by the bias factor method using the measurement value of α, if the target keff value has a strong correlation with the measured α value in the subcritical KUCA core.

Discontinuity Factor; A Discontinuity Condition for Angular Flux? Reviewed International journal

A. Yamamoto, T. Endo

Proceedings of Reactor Physics Asia 2019 page： 155 - 157 2019.12

C5G7-TD Benchmark Analysis using Multigrid Amplitude Function Method Reviewed International journal

K. Tsujita, T. Endo, A. Yamamoto

Proceedings of Reactor Physics Asia 2019 page： 201 - 204 2019.12

Application of Surrogate Modeling with Singular Value Decomposition for Design Basis Accident Aiming Statistical Safety Analysis Reviewed International journal

M. Matsushita, T. Endo, A. Yamamoto

Proceedings of Reactor Physics Asia 2019 page： 282 - 285 2019.12

Development of Efficient Data Sampling Method to Construct Surrogate Model of Severe Accident Analysis Code for SBO Aiming Probabilistic Safety Margin Analysis Reviewed International journal

M. Matsushita, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 121 page： 979 - 982 2019.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

An efficient data sampling method is developed in order to construct a ROM, which accurately reproduces the results of a severe accident code, with the small number of the training data. The proposed sampling method is categorized as the adaptive sampling and this study newly applies the concept of the gravity field to its sampling method in order to make efficient sampling. The proposed sampling method can choose the input training data which have significant new information for ROM construction. The proposed sampling method is applied to PCT obtained by RELAP5/SCDAPSIM calculations for the SBO accident scenario. ROM is improved by adding the new training data to satisfy MPCT=1200°C on the core intact/damage boundary. The core intact/damage boundary predicted by ROM improved as the number of iterations increases. In other words, the input training data are heavily sampled near the core intact/damage boundary. This sampling makes the proposed method more efficient than the conventional random sampling method. As future problems, applications of the present method to calculate CDF considering the uncertainty of the ROM and to the other accident scenarios will be considered.

DOI： 10.13182/T30744

Resonance Calculation Using Energy Spectral Expansion Based on Reduced Order Model: Application to Heterogeneous Geometry Reviewed International journal

A. Yamamoto, R. Kondo, T. Endo, S. Takeda, H. Koike, K. Yamaji, D. Sato

Trans. Am. Nucl. Soc. Vol. 121 page： 1316 - 1320 2019.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The Resonance calculation based on energy Spectral Expansion (RSE) is applied to a pin cell geometry and its accuracy is verified through comparison with the results by the ultra-fine group MOC and the MCNP calculations. Impact of the generation method of the orthogonal bases and the neutron source treatment is quantified through the benchmark calculation. The numerical results are promising; the RSE method accurately reproduces the reference results obtained by the ultra-fine group calculation by MOC or MCNP. There are several issues to be addressed; performance of the present method in more complicated and practical geometries/material arrangements, treatment of scattering source term, numerical solution method, extension of the present concept to the unresolved resonance energy range.

DOI： 10.13182/T30993

Reduction of Macroscopic and Microscopic Cross Section Table Size for Heterogeneous Core Calculation using Dimensionality Reduction Reviewed International journal

M. Yamamoto, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 121 page： 1309 - 1312 2019.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Reduction of cross section table size including macroscopic and microscopic cross sections is tried by applying the dimensionality reduction technique with the singular value decomposition and the low-rank approximation. Among the material-wise cross sections obtained by a lattice physics calculation, those of fuel region are considered in this study. The impact of dimensionality reduction is investigated with a comparison of the assembly calculations using the reconstructed and original cross sections. In this study, approximately 99% reduction in cross section table size is possible while suppressing the error of keff and flux below 0.1%. As a future study, development of the tabulation method using dimensionality reduced cross sections is considered to verify the applicability of the present method for core calculations.

DOI： 10.13182/T30783

Subcriticality: from basics to applications; (1) Revisiting subcriticality Reviewed

T. Endo, K. Tsujimoto, A. Yamamoto

ATOMOΣ: Journal of the Atomic Energy Society of Japan Vol. 61 ( 10 ) page： 734 - 738 2019.10

Conversion from prompt neutron decay constant to subcriticality using point kinetics parameters based on α- and keff-eigenfunctions Reviewed International journal

T. Endo, A. Yamamoto

Proc. ICNC2019 2019.9

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference)

The conversion from the measurement value of prompt neutron decay constant α to the subcriticality –ρ is investigated, using special point kinetics parameters which are defined by mixing forward α- and adjoint keff-eigenfunctions. The mixing α-k weighted point kinetics parameters are very useful to reduce the conversion bias of neutron multiplication factor in a deeper subcritical system. In the same manner as the k-ratio method, the mixing α-k weighted point kinetics parameters can be well approximated by three eigenvalues of α, keff, and prompt keff,p to be simply estimated by the forward eigenvalue calculations without any adjoint calculations.

Measurement of subcriticality in dollar units using time-domain decomposition based integral method Reviewed International journal

A. Nonaka, T. Endo, A. Yamamoto, M. Yamanaka, T. Sano, C.H. Pyeon

Proc. ICNC2019 2019.9

Language：English Publishing type：Research paper, summary (international conference)

This paper presents an estimation method of subcriticality in dollar units developed on the basis of an integral method for arbitrary state changes in a subcritical system. In a general transient in a subcritical system, reactivity, neutron source intensity, and point kinetics parameters (and) can vary simultaneously. To address this problem, the "time-domain decomposition based integral method (TDDI)" has been proposed. The TDDI method can estimate the subcriticality only using the time variation of the neutron count rate. Therefore, the proposed method is useful to estimate the subcriticality in the reactor where the detailed conditions are unknown. To investigate the applicability of the TDDI method to actual subcritical measurement, a transient experiment in a source-driven subcritical system is conducted at the Kyoto University Critical Assembly. As a result, it is concluded that the TDDI method can approximately estimate the order of magnitude for the subcriticality in dollar units. Meanwhile, the estimation is difficult owing to the statistical errors when the neutron count rate is low.

Application of Various Superhomogenization (SPH) methods for the Method of Characteristics Reviewed International journal

K. Sawada, T. Endo, A. Yamamoto

Proc. M&C2019 page： 1534 - 1543 2019.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

To reduce the error due to the difference between the fine and the coarse calculation conditions in a transport calculation using method of characteristics (MOC), the superhomogenization (SPH) method has been widely used. However, the conventional SPH method has a problem with numerical stability in the iterative calculations for the estimation of SPH factors, especially when local strong absorbers exist in a calculation geometry. To address this problem, improvements of the SPH methods were tested to reduce the angular and spatial discretization error of the MOC. The performances of the various SPH methods were confirmed in pressurized water reactor (PWR) 2 × 2 fuel assembly geometries and in a PWR core geometry. The results of verification indicate that in a core geometry the improved SPH methods provide better accuracy than that of the conventional SPH.

Implementation of Random Sampling for ACE-format Cross Sections using FRENDY and Application to Uncertainty Reduction Reviewed International journal

R. Kondo, T. Endo, A. Yamamoto, K. Tada

Proc. M&C2019 page： 1493 - 1502 2019.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

For uncertainty quantification and reduction using the random sampling technique through a continuous energy Monte Carlo method, the perturbation capability of nuclear data libraries for MCNP is developed using a nuclear data processing system FRENDY, which is being developed by JAEA. The implemented capability is applied to uncertainty quantification using the random sampling method and to uncertainty reduction of kinetic parameter based on the bias factor method. Validity of the implemented capability is confirmed through comparison with the results obtained by the conventional sandwich formula using SCALE and MCNP.

Calculation Method of Estimated Criticality Lower-limit Multiplication Factor using the Bootstrap Method Reviewed International journal

T. Hayashi, T. Endo, A. Yamamoto

Proc. M&C2019 page： 1874 - 1885 2019.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The present paper describes a calculation method of the estimated criticality lower-limit multiplication factor (ECLLMF) using the bootstrap method, which is an uncertainty evaluation method. In the conventional method, the normal distribution is assumed for a probability distribution with respect to calculation biases of effective multiplication factors (keff) to evaluate ECLLMF. To propose a methodology without the assumption of the normal distribution, an estimation method of ECLLMF is newly developed using the bootstrap method, where the assumption of the normal distribution is not necessary. From the verification results, it is confirmed that the estimation result using the non-parametric bootstrap method is more reasonable than that using the conventional method, when a probability distribution of keff does not obey the normal distribution.

A Resonance Calculation Method using Energy Expansion Bases based on a Reduced Order Model Reviewed International journal

A. Yamamoto, T. Endo, S. Takeda, H. Koike, K. Yamaji, K. Ieyama, D. Sato

Proc. M&C2019 page： 1081 - 1092 2019.8

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A Resonance calculation using energy Spectral Expansion bases (the RSE method) is newly proposed. In the present method, an ultra-fine group spectrum appeared in a resonance calculation is expanded by expansion bases on energy. The transport equation for the expansion coefficients is derived, which is the simultaneous first order differential equation for the expansion coefficients. The present method is applied to a one-dimensional slab geometry composed of U238. Comparisons of the results obtained by the present and the ultra-fine group (reference) methods show the fundamental validity of this method.

Data Assimilation using Subcritical Measurement of Prompt Neutron Decay Constant Reviewed International journal

T. Endo, A. Yamamoto

Proc. M&C2019 page： 1864 - 1873 2019.8

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

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

Uncertainty Quantification/Reduction of BWR Core Characteristics considering Cross Section and Thermal- hydraulics Uncertainties Reviewed International journal

M. Ito, A. Yamamoto, T. Endo, T. Ama

Trans. Am. Nucl. Soc. Vol. 120 page： 851 - 854 2019.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The uncertainty quantification of the critical eigenvalue of BWR is performed considering uncertainties of cross sections and thermal-hydraulics using the random sampling method. Using the quantified results, the uncertainty reduction of predicted critical eigenvalues is carried out using the bias factor (BF) or the physics-guided coverage mapping (PCM) method. The dominant contributor to the uncertainty for critical eigenvalue is the cross section, followed by the void fraction. Uncertainties of the rated thermal power and the core flow have a smaller impact than those of the cross section and void fraction. By applying the BF or the PCM method, bias of the predicted critical eigenvalue can be reduced. However, reduced uncertainty seems to be too small, suggesting there are still missing uncertainties that should be taken into account. The measurement error and the modeling approximation error would be the candidates for additional uncertainties.

Development of assembly bowing model for pin-by-pin core calculations International journal

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

The Proceedings of the International Conference on Nuclear Engineering (ICONE) Vol. 2019.27 page： 1022 - 0 2019.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Society of Mechanical Engineers (ASME)

Calculation capability of the pin-power distribution considering the variation of the assembly gap size due to assembly bowing was implemented in the pin-by-pin core calculation code SCOPE2. The previous studies show that the perturbation of geometry can be treated by the perturbation of macroscopic cross-section or atomic number density of the region instead of explicit consideration of geometry deformation. This methodology was applied to the assembly gap region: the variation of the gap size was treated by the correction on the macroscopic cross-section of the gap water. The correction model for the cross-section of gap water was implemented in SCOPE2 since it treats pin-by-pin cross-sections in a transport calculation. The correction was made according to the variation in the gap size. This implemented model has an advantage that the modification of the cross-section tables used in the core calculation is not necessary to consider the variation of gap size. For single assembly and multi-assemblies geometries, the assembly bowing model implemented in SCOPE2 was verified by comparing with the reference results using the assembly calculation code AEGIS, where the gap size perturbation was explicitly considered by varying the geometry of the gap region. It was confirmed that the variation of pin-power distribution due to the assembly bowing can be appropriately treated by SCOPE2 with the assembly bowing model.

DOI： 10.1299/jsmeicone.2019.27.1022

Scopus

A Simple Treatment of Bowed Assembly Gap Through Correction of Cross Section Reviewed International journal

A. Yamamoto, T. Endo, H. Nagano, Y. Ohoka, K. Yamamoto

Trans. Am. Nucl. Soc. Vol. 119 page： 1199 - 1202 2018.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A simplified treatment for offset fuel assemblies due to bowing is proposed. In the present method, nominal (nonoffset) geometry is used while cross section of the gap region is corrected to incorporate the variation of gap size. Verification results in the single assembly geometries and the 5x5 assembly geometry indicate that the present method accurately reproduces the reference results obtained by explicit consideration of the deformed geometry. Since the present method does not require geometry change, it will be a convenient candidate for high-fidelity core simulators that explicitly consider the heterogeneous geometry. In the present summary, validity of the proposed method is verified by a typical situation. Verification in other conditions (e.g., use of different energy group structures, transport or diffusion method) will be a future task.

Transport Consistent Diffusion Coefficient for CMFD Acceleration Reviewed International journal

A. Yamamoto, T. Endo, A. Giho

Trans. Am. Nucl. Soc. Vol. 119 page： 1179 - 1181 2018.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The transport consistent diffusion (TCD) coefficient is derived using the even-parity transport equation and the twonode problem in one-dimensional geometry. TCD depends on the optical mesh size and shows similar behavior with the effective diffusion (EffD) and the artificial grid diffusion (AGD) coefficients. Since EffD and AGD coefficients can contribute to the stabilization of the CMFD/GCMR acceleration for MOC calculation, TCD coefficient will be also useful for the CMFD acceleration.

Surrogate Model of Severe Accident Analysis Code for SBO Aiming Probabilistic Safety Margin Analysis Reviewed International journal

M. Matsushita, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 119 page： 900 - 903 2018.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A surrogate model (ROM) for severe accident analysis (SBO) is developed using the low-rank approximation with SVD in order to reduce the calculation costs of a severe accident code for safety margin analysis. ROM can rapidly reconstruct many accident progression results using 25 samples obtained by the RELAP5/SCDAPSIM. Only 9 bases out of 25 bases are used to construct the surrogate model. The boundary between the core damage and core intact regions estimated by ROM reproduces that obtained by the RELAP5/SCDAPSIM within the accuracy of approximately 300 s. In order to improve the accuracy, two issues will be addressed. The first one is the improvement on interpolation of expansion coefficients. The second one is the optimum number of samples and sampling methods to reach sufficient reproduction accuracy.

Reduction of Cross Section Table Size for Core Analysis Using Dimensionality Reduction Technique Reviewed International journal

M. Yamamoto, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 119 page： 1226 - 1228 2018.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Reduction of cross section table size is tried by applying the dimensionality reduction technique with the singular value decomposition. The pin-by-pin multi-group cross sections obtained by a single assembly calculation are considered in this study. The accuracy of the reconstructed cross section is verified by comparison with the original cross section. In the present study, approximately 78% reduction in cross section table size is possible while keeping the accuracy of k-infinity higher than 1e−4. As the future study, the impact of the reconstructed cross section on the spatial distribution of neutron flux should be investigated. For example, assembly or core calculation using the reconstructed and original cross sections are carried out and their results will be compared. Finally, the validity of the present method should be verified in an actual core analysis.

Estimation of Subcriticality in Dollar Units Based on Integral Method for Arbitrary State-Change in Subcritical System Reviewed International journal

A. Nonaka, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 119 page： 1112 - 1115 2018.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

In this paper, the estimation method of subcriticality in dollar units based on the integral method for arbitrary state changes in a subcritical system is newly proposed. To confirm the applicability of the proposed method in a three dimension geometry, verification calculations of the virtual numerical experiments were carried out for the modified LMW benchmark problem. As a result, it was confirmed that the proposed method can roughly estimate the subcriticality in dollar units after the step-wise transient of state-change and the accuracy depends on the measuring region of neutrons. Therefore, in order to accurately estimate the subcriticality of a whole core, the spatial correction will be necessary. In the future study, the subcritical experiments using the proposed method at actual nuclear experimental facilities will be carried out. Treatment of measurement signals by a plurality of neutron detectors located at different positions will be an issue to be resolved.

Estimation of Subcriticality using Particle Filter Method Reviewed International journal

T. Ikeda, T. Kimura, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 118 page： 851 - 854 2018.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

In this summary, the applicability of the Particle Filter (PF) method to estimate the subcriticality was investigated. Through the experimental result at the Kindai University reactor (UTR-KINKI), the estimated reactivity using the PF method is almost the same as that using the conventional inverse kinetics method (IKM) within the range of ±2σ. In case of the retrieval of fuel debris at Fukushima Daiichi Nuclear Power Station (1F-NPS), it is supposed that the temporal variations of (-ρ, Λ, βeff) could be occurred at the same time by changing H/U ratio due to the submersing and the drilling operations. As one of the future studies, the applicability of the PF method for the simultaneous estimation not only (-ρ) but also (Λ, βeff) will be investigated.

Quantification of Modeling Approximation Error of Pin-Cell Calculation Using Kriging and Principal Component Analysis Reviewed International journal

T. Hanai, A. Yamamoto, T. Endo, K. Yamamoto, Y. Ohoka, H. Nagano

Trans. Am. Nucl. Soc. Vol. 118 page： 875 - 878 2018.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

In the present study, an estimation method of modeling approximation error using the Kriging and the the principal component analysis (PCA) is developed and verified. The difference between the results obtained by a deterministic lattice physics code and a continuous-energy Monte Carlo code can be estimated by the proposed surrogate model. In the present study, the accuracy of the surrogate model is verified in a simple geometry. Verifications with more complicated and practical conditions are the future tasks.

Cache Efficient Flux Region Assignment for the Method of Characteristics Reviewed International journal

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2018 page： 788 - 799 2018.4

Language：English Publishing type：Research paper, summary (international conference)

A flux region assignment algorithm to increase cache efficiency for the method of characteristics is proposed. In order to minimize the stride of memory access, flux region IDs are assigned based on the ray trace sequence during the method of characteristics calculation. The present method is implemented in the three-dimensional transport code GENESIS and its performance is confirmed through verification calculations ranging from single PWR fuel assembly to PWR full core benchmark problems. The present method can reduce computational time by improving cache efficiency while suppressing memory requirement.

Sensitivity Coefficient Analysis of Omega-Eigenvalue based on First-Order Perturbation Theory Reviewed International journal

T. Endo, A. Yamamoto

Proc. PHYSOR2018 page： 1240 - 1253 2018.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference)

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 ω eigenvalue. For this purpose the numerical calculation method using the standard first order perturbation theory is investigated. A specific theoretical formula is derived to evaluate the sensitivity coefficient of ω to nuclear data. The derived formula utilizes forward and adjoint eigenfunctions which consist of neutron flux and delayed neutron precursor densities. Through a feasibility study based on the multi group diffusion calculation the derived formula is verified by comparing with the reference results using the direct method. In addition it is confirmed that the prompt approximation is applicable to the evaluation of sensitivity coefficient of α for a subcritical state where α is sufficiently larger than decay constants of delayed neutron precursors.

Inverse Estimation Methods of Unknown Radioactive Source for Fuel Debris Search Reviewed International journal

S. Sugaya, T. Endo, A. Yamamoto

Proc. PHYSOR2018 page： 2632 - 2643 2018.4

Language：English Publishing type：Research paper, summary (international conference)

To identify 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 measured values of radiation counts. The Maximum Likelihood-Expectation Maximization (ML-EM) method and the Moore-Penrose Matrix Inverse (MPMI) method are examined. The ML-EM method has been used for image reconstruction of computed tomography, and the MPMI method is one of the solution methods for simultaneous linear equations. A simple calculation model simulating the containment vessel were constructed including detectors and radiation sources. In actual situation, 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) are smaller than positions of radiation source. 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 a radiation count at a detector and a radioactive source. 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 radiation count measurement positions. The ML-EM and the MPMI methods show different prediction accuracy depending on the calculation condition. It is found that the detectors should be placed at vicinity of radiation sources of interest and that the applicability of the inverse estimation does not strongly depend on the radioactivity distribution.

Estimation of Subcriticality in Dollar Units using Integral Method for Subcritical System Reviewed International journal

A. Nonaka, T. Endo, A. Yamamoto

Proc. PHYSOR2018 page： 3271 - 3282 2018.4

Language：English Publishing type：Research paper, summary (international conference)

A subcriticality measurement method using the integral method is developed for any step-wise transient. The integral method usually applied to a negative reactivity insertion using the rod-drop and the source-jerk methods. In this study, it is clarified that the integral method can be applied to measure positive reactivity insertion. During refueling of a reactor, not only reactivity but also neutron source intensity and neutron generation time simultaneously change. In order to accurately monitor the subcriticality under these conditions, variations of these parameters must be taken into consideration. Therefore, a subcriticality measurement method is developed, which is applicable to not only variation of reactivity but also simultaneous variations of neutron source intensity and neutron generation time. Furthermore, the present method utilizes only measurement value of neutron count rate, thus the proposed method is practical. Verification calculations are carried out for a step-wise change of reactivity, neutron source intensity, and neutron generation time. The results indicate that reactivity is accurately predicted for the change of the neutron source intensity, which is difficult to achieve by the neutron source multiplication method. On the other hand, although the change of the neutron generation time has considerable impacts on the estimated result of subcriticality, the predicted error is less than 10% for very large variation of neutron generation time.

Estimation of Region-Wise Even-Parity Discontinuity Factor for MOC Through Iterative Procedure Reviewed International journal

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2018 page： 1892 - 1903 2018.4

Language：English Publishing type：Research paper, summary (international conference)

To reduce angular and spatial discretization error of MOC with a coarse calculation condition, region-wise even-parity discontinuity factor (EPDF) for transport calculations is evaluated through an iterative procedure using only region-wise scalar flux, i.e., without odd parity angular flux, partial-, or net-current at region boundary. Region-wise EPDF is evaluated in a single assembly geometry with reflective boundary condition. The evaluated EPDFs are applied to a 2x2 colorset assembly configuration and its performance is compared to the conventional superhomogenization (SPH) method. The calculation results indicate that 1) no convergence issue is observed during the iteration process to estimate EPDF, 2) performance of the region-wise EPDF is better than that of the conventional SPH method.

Development of the Uncertainty Quantification Method of Activation in Reactor Structures using Reduced-Order Modeling Reviewed International journal

K. Yokoi, T. Endo, A. Yamamoto, K. Hayashi, R. Mizuno, Y. Kimura

Proc. PHYSOR2018 page： 1793 - 1804 2018.4

Language：English Publishing type：Research paper, summary (international conference)

Uncertainty quantification of activation in structure materials around a nuclear reactor is important for efficient planning of decommissioning. In order to quantify the uncertainty of activation in reactor structures, neutron shielding calculations are necessary. Since the neutron shielding calculation is performed for spatially large regions around a reactor, it requires a lot of computation time especially in the case of multi-dimensional geometry. In this study, the reduced-order modeling (ROM) is applied to the sensitivity and uncertainty analysis of activation in reactor structures to reduce computation time. The ROM can reduce calculation cost for evaluation of sensitivity coefficients by identifying important or sensitive subspace (active subspace, AS) in input data. In this study, an AS is constructed by the several sensitivity coefficients in reactor structures which are evaluated by the perturbation theory (PT). Sensitivity coefficients of activation throughout reactor structures are estimated using the AS and the uncertainty of activation is evaluated by the "sandwich formula." The calculation results indicate that the uncertainty of the activation in reactor structures can be reproduced with low calculation cost (approximately 30 neutron transport calculations) using the ROM in one-dimensional geometry of a 500 MWe class BWR.

Development of Reduced Order Model of Severe Accident Analysis Code for Probabilistic Safety Margin Analysis Reviewed International journal

M. Matsushita, T. Endo, A. Yamamoto, T. Kitao

Proc. PHYSOR2018 page： 3042 - 3053 2018.4

Language：English Publishing type：Research paper, summary (international conference)

For probabilistic safety margin analysis, we developed a reduced order model (ROM) that reconstruct calculation results of typical severe accident progressions obtained by the severe accident analysis code, MAAP. The ROM is applied for fast reconstruction of time series plant parameters (e.g., pressure and temperature) obtained by the MAAP code. The ROM is applied to two severe accident scenarios, i.e., the station black out (SBO) with loss of all feed water capabilities and the large break loss of coolant accident (large break LOCA) without the emergency core cooling system (ECCS) capability. Verification results indicate that the ROM reasonably reproduces temporal variation of plant parameters with a few bases obtained by the ROM, which enables very fast reconstruction of complicated accident progression of a severe accident.

Application of the GENESIS Code to the Kobayashi 3D Benchmark Problem Reviewed International journal

A. Yamamoto, A. Giho, T. Endo

Trans. Am. Nucl. Soc. Vol. 117 page： 1403 - 1406 2017.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The GENESIS code, which is a transport code based on the LEAF method for a three-dimensional heterogeneous geometry, is applied to the Kobayashi 3D benchmark problem that is characterized by deep penetration and streaming through a void region.

Estimation of Modeling Approximation Error of Core Analysis using the Surrogate Model with Kriging Reviewed International journal

T. Hanai, T. Endo, Y. Kodama, Y. Ohoka, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 117 page： 1269 - 1272 2017.10

Application of the Bias Factor Method using the Random Sampling Technique for Prediction Accuracy Improvement of Neutronics Parameters of BWR Reviewed International journal

M. Ito, T. Endo, A. Yamamoto, Y. Kuroda, T. Yoshii

Trans. Am. Nucl. Soc. Vol. 117 page： 804 - 807 2017.10

On prediction accuracy of neutronics parameters of accelerator-driven system Reviewed International journal

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

EPJ Web of Conferences Vol. 146 page： 09005 2017.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

Nuclear data-induced uncertainty of neutronics parameters of one specific ADS design is quantified. The nuclear data adjustment method with available integral data is employed to reduce the uncertainties, and usefulness of these integral data is investigated. Numerical results reveal that the uncertainty reduction by the present nuclear data adjustment is insignificant and restrictive. Future perspecitives are also provided.

DOI： 10.1051/epjconf/201714609005

Scopus

Estimation of Reactivity, Neutron Generation Time, and Effective Delayed Neutron Fraction using Extended Kalman Filter Reviewed International journal

T. Ikeda, T. Endo, A. Yamamoto

Proc. Reactor Physics Asia 2017 Vol. CD-ROM page： CD-ROM 2017.8

Uncertainty Quantification due to Modeling Approximation Error of Core Analysis using the Kriging Method Reviewed International journal

T. Hanai, T. Endo, Y. Kodama, Y. Ohoka, A. Yamamoto

Proc. Reactor Physics Asia 2017 Vol. CD-ROM 2017.8

Application of Bias Factor Method using Random Sampling Technique for Prediction Accuracy Improvement of Critical Eigenvalue of BWR Reviewed International journal

M. Ito, T. Endo, A. Yamamoto, Y. Kuroda, T. Yoshii

Proc. ICAPP2017 page： 1709 - 1716 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Atomic Energy Society of Japan

The bias factor method based on the random sampling technique is applied to the benchmark problem of Peach Bottom Unit 2. Validity and availability of the present method, i.e. correction of calculation results and reduction of uncertainty, are confirmed in addition to features and performance of the present method. In the present study, core characteristics in cycle 3 are corrected with the proposed method using predicted and "measured" critical eigenvalues in cycles 1 and 2. As the source of uncertainty, variance-covariance of cross sections is considered. The calculation results indicate that bias between predicted and measured results, and uncertainty owing to cross section can be reduced. Extension to other uncertainties such as thermal hydraulics properties will be a future task.

Uncertainty Quantification of Activation Due to Cross Section Data in Neutron Shielding Calculation Reviewed International journal

K. Yokoi, T. Endo, A. Yamamoto, R. Mizuno, Y. Kimura

Proc. ICAPP2017 page： 2152 - 2156 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Atomic Energy Society of Japan

Quantification of activation in structure materials around a nuclear reactor using results of neutron shielding calculations is necessary for efficient planning of decommissioning. In this study, the random sampling method is applied to the neutron shielding calculation in order to estimate uncertainties of neutron flux and activation of Co59 in structure materials due to cross section covariance. The calculation results indicate that the magnitude of uncertainty of activation of Co59 due to cross section data is approximately 15~30% inside structure materials.

Evaluation of the n/γ Discrimination Performance of the Neutron Detector with Eu Doped TRUST-LiCaAlF6 Reviewed International journal

M. Maeno, T. Endo, A. Yamamoto

Proc. ICAPP2017 page： 1510 - 1516 2017.4

Authorship：Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Atomic Energy Society of Japan

The n/γ discrimination performance of the prototype neutron detector using Eu doped TRUST-LiCaAlF6 is quantitatively investigated, in order to confirm its applicability to the subcriticality monitoring in the decommissioning works at Fukushima Daiichi Nuclear Power Plant units 1-3, especially focusing on removal of fuel debris. In this paper, the experimental results of pulse-height distribution measurement using Cf252 at the Nagoya University Cobalt 60 irradiation facility are shown. Additionally, in order to investigate the applicability to the reactor noise analysis, preliminary experimental results of the Feynman-α method are also shown.

Effective Use of Engineering Reactor Simulator for Education of Nuclear Safety Reviewed International journal

A. Yamamoto, T. Endo

Proc. ICAPP2017 page： 2065 - 2069 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Atomic Energy Society of Japan

Effective use of a reactor simulator to lecture nuclear safety for undergraduate/master's course students majoring nuclear engineering is discussed. Various scenarios from normal operating to severe accident conditions are used for an exercise of a few days' course. Through discussions on plant behaviors of various scenarios within a small group and among class members, participants can understand physics behind responses of a nuclear power plant.

Development of Dynamic Probabilistic Risk Assessment Model for PWR using Simplified Plant Simulation Method Reviewed International journal

S. Otsuki, T. Endo, A. Yamamoto

Proc. ICAPP2017 page： 1737 - 1742 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Atomic Energy Society of Japan

The CMMC (Continuous Markov Monte Carlo) coupling method is proposed for quantifying accident scenarios that have time-dependence in accident progression and inter-dependence of individual events. In order to analyze large number of samples within realistic computing time, we developed a simplified accident progression analysis model and coupled the simplified model to the CMMC method. Large number of samples for station black out in PWR were analyzed using the random sampling method based on the CMMC method considering uncertainty of decay heat from a core. As a result, uncertainties of event initiation time and FPs release ratio to the atmosphere are estimated.

Implementation of Fuel Burnup Sensitivity Calculation Capability into a Deterministic Reactor Physics Code System CBZ for Accelerator-Driven System Multi-Cycle Burnup Calculations Reviewed International journal

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

Proc. M&C 2017 page： P233 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

A new capability of calculating fuel burnup sensitivity with the generalized perturbation theory is implemented into a deterministic reactor physics code system CBZ, which is under development at Hokkaido University. This capability is well verified through comparisons with reference sensitivities obtained by numerical differentiation. Nuclear data-induced uncertainties of two neutronics parameters, keff and coolant void reactivity, of an accelerator-driven system designed by the Japan Atomic Energy Agency are quantified using sensitivities calculated with the new version of CBZ, and effect of burnup term in the sensitivities is also quantified. On both keff and coolant void reactivity, cancellation between static and burnup components in nuclear data-induced uncertainties is observed; uncertainties become small if the burnup component is taken into account.

Inverse Estimation of Unknown Radioactive Source using Detection Probability by Adjoint Calculation Reviewed International journal

S. Sugaya, T. Endo, A. Yamamoto

Proc. M&C 2017 page： P411 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

In order to investigate distribution of fuel debris remaining in the reactor containment vessel of Fukushima Daiichi NPS, we focused on the estimations based on the measured value of neutron counts. Maximum Likelihood-Expectation Maximization (ML-EM) method and Moore-Penrose Matrix Inverse (MPMI) method were examined. The ML-EM method is used for image reconstruction of Computed Tomography, and the MPMI method is one of the solution of the simultaneous linear equations. Concrete shielding were set between detectors and neutron sources in the calculation system, since where detector position in actual applications would be outside of the shielding such as the pedestal. Since sufficient number of count measurement positions would not be secured owing to the complexity of structures inside containment vessel, the number of measurement points were set to be smaller than that of neutron sources. Since the detection probability is used as the coupling coefficient between the radiation count and the radioactivity, the adjoint transport calculation is performed to obtain the detection probability. The detection probability calculated by adjoint neutron flux reproduced the physical trend expected from detector and neutron source positions. Result of estimation using this detection probability indicates that two methods gave reasonable neutron emission rate distribution that is close to the true value.

Benchmarks of Subcriticality in Accelerator-Driven System at Kyoto University Critical Assembly Reviewed International journal

C.H. Pyeon, M. Yamanaka, S.H. Kim, T.M. Vu, T. Endo, W.F.G. van Rooijen, G. Chiba

Proc. M&C 2017 page： P211 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

Basic research on the accelerator-driven system is conducted with the combined use of U235-loaded core (the Kyoto University Critical Assembly) and the accelerators (100 MeV protons and 14 MeV neutrons). The results of experimental subcriticality are presented with a wide range of subcriticality level between near critical and 10000 pcm, as obtained by the measurement methods.

Uncertainty Quantification of Bell Factor for Sjöstrand Method using Random Sampling Method Reviewed International journal

T. Kimura, T. Endo, A. Yamamoto

Proc. M&C 2017 page： P206 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

Sjöstrand Method is one of the subcriticality measurement techniques for the accelerator driven system (ADS). In this study, we investigated the uncertainty quantification of a spatial correction factor, Bell factor, due to cross-section data, using the random sampling method. As a result, the uncertainty of the Bell factor due to cross-section uncertainty is smaller than that of the subcriticality in dollar units, because the sensitivities of the Bell factor to cross-sections are cancelled between the area ratio and subcriticality.

Theoretical Discussion of Statistical Error for Variance-to-Mean Ratio Reviewed International journal

T. Endo, A. Yamamoto

Proc. M&C 2017 page： P305 2017.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

In the present paper, statistical error of variance-to mean ratio, or Y value in the Feynman-α method, is theoretically investigated to discuss the relationship among the statistical error of Y value, external neutron source strength, and measurement time. Practical theoretical formulae are derived to estimate the statistical error of Y value from a single measurement of reactor noise. The derived formulae clarify that the statistical error of Y value can be reduced by the total number of counting gate, or total measurement time, rather than the strength of external neutron source. Through an actual reactor noise experiment at the Kyoto University Criticality Assembly, the derived estimation formulae are validated.

Nuclear Data-Induced-Uncertainty Quantification of Neutron Multiplication Factor and Prompt Neutron Decay Constant for Pb-Bi loaded ADS Benchmark Problems at KUCA Reviewed International journal

T. Endo, A. Yamamoto

Proc. M&C 2017 page： P210 2017.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

By the sensitivity analysis using the SCALE6.2.1/TSUNAMI-3D and the random sampling method using the SCALE6.2.1/Sampler/NEWT/PARTISN, nuclear data-induced uncertainties of neutron multiplication factor keff and prompt neutron decay constant α are evaluated for Pb-Bi loaded Accelerator Driven System benchmark problems at Kyoto University Critical Assembly. As a result, the nuclear data-induced correlation between α and keff is strongly negative. It is supposed that the nuclear data-induced uncertainty of subcriticality is major contribution to the uncertainty of prompt neutron decay constant.

Development of GENESIS, a Three-dimensional Heterogeneous Transport Code based on the LEAF Method Reviewed International journal

A. Yamamoto, A. Giho, T. Endo

Proc. M&C 2017 page： P057 2017.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

The present 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, concept of the simplified Pn method is introduced in order to reduce storage of flux moments. Accuracy of the present method is verified through a benchmark problem. Next, iteration stability of the GENESIS code for highly voided condition, which would appear in the severe accident conditions, is discussed. Efficiency of the CMFD and GCMR acceleration methods are verified with various stabilization techniques. Use of the effective diffusion coefficient and the artificial grid diffusion (AGD) coefficients are effective to stabilize the acceleration calculation in highly voided conditions.

Comparison of Fuel Loading Pattern Optimization Results using Exhaustive Search for Fresh Fuels and Local Search for Burned Fuels Reviewed International journal

S. Ishiguro, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 115 page： 1265 - 1267 2016.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Optimization performances by combination of the exhaustive search for fresh fuel location and the MSLS are investigated. In the present study, the exhaustive binary swap with the exhaustive search for gadolinia fresh fuel location provides better result. Also, it is suggested that the current subspace divided by gadolinia fresh fuel location still shows multi-modality, thus the present local search method cannot find out an optimum solution in many cases. As a future task, more sophisticated method for subspace division, e.g., utilization of multi-stage divisions, would be necessary.

Uncertainty Quantification of Spatial Correction Factor for Sjöstrand Method due to Cross-section Data Reviewed International journal

T. Kimura, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 115 page： 1081 - 1084 2016.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

We investigated the uncertainty quantification of the Bell factor, which is the spatial correction factor in subcriticality measurement using the Sjöstrand method, due to the uncertainty in cross-section data. As one of the feasibility studies, the uncertainty of the Bell factor is evaluated using the diffusion calculations for the simple one-dimensional slab geometry. As a result, the uncertainty of the Bell factor due to cross section is smaller than that of the subcriticality measurement in dollar units. In addition, as the difference in the calculation results between the area ratio and subcriticality in dollar units is smaller, the uncertainty of the Bell factor tends to become smaller. In future tasks, we will further investigate the same kind of uncertainty quantification for a practical ADS design with MA fuel, and the uncertainty quantification due to other factors, such as the delayed neutron fraction and the calculation method.

Uncertainty Quantification of Activation Due to Cross Section Data in Neutron Shielding Calculation Reviewed International journal

K. Yokoi, T. Endo, A. Yamamoto, R. Mizuno, Y. Kimura

Trans. Am. Nucl. Soc. Vol. 115 page： 1085 - 1087 2016.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The random sampling method is applied to neutron shielding calculation using ANISN/TRANSX in order to estimate uncertainties of neutron flux and activation in a structure material (iron). The calculation results indicate that the magnitude of uncertainty of activation of Co59 due to cross section is approximately 10% inside structural material, which is not very large when attenuation of neutron flux is taken into account.

Prediction on Underestimation of Statistical Uncertainty in Monte Carlo Eigenvalue Calculation for Two-dimensional Heterogeneous Color Set Geometry Reviewed International journal

K. Hayashi, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 115 page： 1213 - 1216 2016.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Theoretical formula for behavior of noise term is derived, which is necessary for prediction of underestimation ratio of statistical uncertainty in Monte Carlo eigenvalue calculation. By using the proposal theoretical formula, underestimation ratio of flux of each fuel cell in 2×2 UO2-MOX assembly geometry is predicted and compared with the reference results obtained by 1000 GMVP runs. The prediction results show reasonable agreement with the reference regarding to relative spatial shape, which suggest the validity of the theoretical formula of the underestimation ratio and the noise term. However, there is considerable difference on the absolute values of the underestimation ratio and investigation of the causes of the difference would be a future task.

Analysis and Interpretation of the KUCA ADS Benchmarks with Deterministic Analysis Codes Reviewed International journal

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

Proc. PHYSOR2016 page： 4200 - 4216 2016.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

This manuscript discusses the analysis of the KUCA-A ADS with deterministic codes (specifically diffusion theory). The KUCA-A ADS is a small, thermal-spectrum ADS driven by 100MeV protons. Several sets of experiments are available as an international benchmark. In our analysis, we calculated the multiplication factor, prompt neutron decay constant (α-eigenvalue), performed the analysis of an irradiation experiment, and used time-dependent diffusion theory to analyze pulsed neutron operation of the KUCA-A ADS in 3D. 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.

Variance Reduction Factor Calculations for Neutronics Parameters of Accelerator-Driven System Reviewed International journal

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

Proc. PHYSOR2016 page： 1661 - 1668 2016.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

In order to identify nuclear data on which further improvement is effective to reduce nuclear data-induced uncertainties of accelerator-driven system (ADS) neutronics parameters, variance reduction factors (VRFs) for keff, beff and coolant void reactivity are calculated. Obtained VRFs suggest that improvement of plutonium-238 nuclear data is quite effective to reduce the uncertainties of keff and beff during the operation of ADS, and that improvement of lead-206 elastic and inelastic scattering cross sections is also important to reduce the uncertainties of coolant void reactivity. Important energy ranges of these nuclear data are also specified by VRFs.

GENESIS - A Transport Solver in Three-Dimensional Heterogeneous Geometry Based on the LEAF Method Reviewed International journal

A. Yamamoto, A. Giho, T. Endo

Proc. PHYSOR2016 page： 4080 - 4106 2016.5

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A heterogeneous transport solver in three dimensional geometry, GENESIS, is being developed incorporating recent developments of the method of characteristics (MOC) in three dimensional geometry. The Legendre Expansion of Angular Flux (LEAF) method is implemented in the GENESIS code, in which neutron transport is calculated in two-dimensional "characteristics planes" rather than in one-dimensional characteristics lines adopted in the conventional approach of 3D MOC. Unlike the planner MOC method that combines 2D 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 planner MOC method. The GENESIS code can handle flexible shape of objects in rectangular or hexagonal geometry. Two-level, multi-group generalized coarse mesh rebalance (GCMR) 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.

Theoretical Expression of Area Ratio Method using Detected-Neutron Multiplication Factor Reviewed International journal

T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 113 page： 1208 - 1211 2015.11

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

In the present paper, the area ratio method is expressed by the detected-neutron multiplication factor kdet. In addition, an appropriate detector position is discussed by investigating the difference between kdet and the effective neutron multiplication factor keff.

Application of Data Assimilation based on Bayesian Theory to Subcriticality Measurements using Area Ratio Method Reviewed International journal

K. Maeno, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 113 page： 1282 - 1286 2015.11

Underestimation of Statistical Uncertainty of Monte Carlo Method with Non-Analog of Fission Source Sampling Reviewed International journal

K. Hayashi, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 113 page： 1153 - 1157 2015.11

Uncertainty Estimation of Analysis Model using the Data Assimilation Method Reviewed International journal

K. Kinoshita, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 113 page： 1141 - 1143 2015.11

Development of a Simplified Estimation Method on Severe Accident Progression in PWR for Education Reviewed International journal

S. Otsuki, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 113 page： 855 - 858 2015.11

Application of Partially-Converged Solution of Assembly Calculation for Core Sensitivity Analysis based on Reduced Order Modeling Reviewed International journal

R. Katano, A. Yamamoto, T. Endo

Trans. Am. Nucl. Soc. Vol. 113 page： 1161 - 1164 2015.11

Discontinuity Factors for Simplified P3 Theory Reviewed

A. Yamamoto, T. Endo

Proc. of Reactor Physics Asia 2015 Vol. CD-ROM 2015.9

Reactor Physics Activities in Nagoya University Reviewed

A. Yamamoto, T. Endo

Proc. of Reactor Physics Asia 2015 Vol. CD-ROM 2015.9

Development of New Statistical Geometry Model using the Delta-tracking Method Reviewed

T. Koide, T. Endo, A. Yamamoto

Proc. of Reactor Physics Asia 2015 Vol. CD-ROM 2015.9

Development of Core Sensitivity Analysis Based on Reduced-Order Modeling using Assembly Calculations Reviewed International journal

R. Katano, A. Yamamoto, T. Endo

Trans. Am. Nucl. Soc. Vol. 112 page： 715 - 718 2015.6

Efficient Execution of Monte Carlo Simulation Based on Pseudo-Scattering using GPU Reviewed International journal

T. Okubo, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 112 page： 648 - 651 2015.6

Comparison of Spatial Source Expansion Methods in the Three Dimensional Transport Method LEAF Reviewed International journal

Y. Kato, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 111 page： 1405 - 1408 2014.11

Statistical Error Estimation using Bootstrap Method for the Feynman-α Method Reviewed International journal

T. Endo, T. Shiozawa, A. Yamamoto, C.H. Pyeon, T. Yagi

Trans. Am. Nucl. Soc. Vol. 111 page： 1204 - 1207 2014.11

Estimation of Sensitivity Coefficient using Random Sampling and L1-norm Minimization Reviewed International journal

T. Watanabe, T. Endo, A. Yamamoto, Y. Kodama, Y. Ohoka, T. Ushio

Trans. Am. Nucl. Soc. Vol. 111 page： 1391 - 1394 2014.11

Confidence Interval Estimation by Bootstrap Method for Uncertainty Quantification using Random Sampling Method Reviewed International journal

T. Endo, T. Watanabe, A. Yamamoto

Proc. PHYSOR2014 Vol. CD-ROM page： 1084668 2014.9

Improvement of a Convergence Technique for MOC Calculation with Large Negative Self-Scattering Cross Section Reviewed International journal

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

Proc. PHYSOR2014 Vol. CD-ROM page： 1105664 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

In the method of characteristics, convergence behavior of inner iteration would be degraded by the transport correction. A previous study revealed that large negative self-scattering cross section due to the transport correction worsens convergence of inner iteration. In order to resolve this issue, a technique to improve the convergence behavior based on the successive over relaxation (SOR) method was proposed in the previous study. However, considerable calculation time is necessary to estimate the optimum acceleration factor for the SOR method especially in large scale geometries. In order to address this drawback, a fast estimation scheme of the acceleration factors is proposed in this study. The present approach can provide acceleration factors which ensure convergence of iterative calculation. In the present approach, the equation to obtain the appropriate acceleration factor is derived by using Gerschgorin’s theorem. Based on the equation, the acceleration factors can be easily obtained in each energy group with negligible calculation time. Verification calculations are performed in various critical experiments, in which degradation of convergence by the transport correction is significant. When the transport correction is used without the SOR method, all iterative calculations diverged. On the other hand, when the SOR method with the acceleration factors based on the present approach is applied, convergent solutions are successfully obtained in all cases. From these results, validity of the present approach is confirmed.

DOI： 10.11484/jaea-conf-2014-003

A Multi-Level Parallel Computation of Reactor Cores using GPU for Loading Pattern Optimization Reviewed International journal

T. Okubo, T. Endo, A. Yamamoto

Proc. PHYSOR2014 Vol. CD-ROM page： 1101184 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

Efficient and rapid computation of multiple loading patterns using GPU is studied aiming application to loading pattern optimization of LWR. The loading pattern has significant impacts on safety and economy of a reactor. However, design of loading pattern is a combinatorial optimization problem, thus it is computationally intensive task. In order to address this issue, efficient and rapid computation method of loading patterns using massively parallel computing capability of GPU is studied in the present paper. Though GPU has higher computational performance than CPU, but different computational algorithm and coding approach are necessary to maximize the performance of GPU, due to different architecture of GPU. In the present study, a multi-level parallel computing approach is examined considering hardware architecture of GPU, i.e., parallel computing is carried out not only in spatial mesh-wise, but also in loading pattern-wise. In other words, multiple loading patterns are simultaneously computed and domain (mesh-wise) decomposition is applied to each loading pattern. With the present approach, computational efficiency using GPU is approximately four times higher than that of CPU. The present core analysis algorithm can be used for screening of poor loading patterns in optimization process.

DOI： 10.11484/jaea-conf-2014-003

Development of Legendre Expansion of Angular Flux Method for 3D-MOC Calculation Reviewed International journal

Y. Kato, T. Endo, A. Yamamoto

Proc. PHYSOR2014 Vol. CD-ROM page： 1106157 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

A three-dimensional transport calculation method, Legendre Expansion of Angular Flux Method (LEAF method) has been proposed for practical MOC calculations in three-dimensional geometry. In the LEAF method, transport calculation is carried out on "characteristics planes(CP)" rather than conventional ray traces, whose concept is similar to that of the ASMOC3D method. By utilizing the characteristics plane, required memory and computational load are significantly reduced. Each characteristics plane forms rectangular regions, thus efficient transport calculation scheme based on transmission probability can be adopted. Consequently, the LEAF method can practically perform MOC calculation in three-dimensional geometry. In the LEAF method, spatial distribution of incoming, outgoing and average angular fluxes in a CP are expressed as a series of the Legendre polynomials in order to accurately capture their spatial dependence. Calculation results in a test problem indicate the accuracy and effectiveness of the LEAF method.

DOI： 10.11484/jaea-conf-2014-003

Investigation on Subcriticality Measurement using Inherent Neutron Source in Nuclear Fuel Reviewed International journal

T. Shiozawa, T. Endo, A. Yamamoto, C.H. Pyeon, T. Yagi

Proc. PHYSOR2014 Vol. CD-ROM page： 1086633 2014.9

Authorship：Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

The subcriticality measurement techniques using inherent neutron source are investigated in this study. In facilities where nuclear fuel is treated, it is considered to install a real-time subcriticality monitoring system. However, it is often unfavorable or impractical to bring an external neutron source into a nuclear facility to carry out subcriticality measurement. Thus, we focus on the inherent neutron source in nuclear fuel such as spontaneous fission and (alpha, n) reaction. By utilizing the inherent neutron source, the subcriticality measurement technique, which does not introduce an external neutron source, can be realized. In this study, the Feynman-alpha method and the neutron source multiplication (NSM) method are chosen as techniques which can be carried out only with the inherent neutron source, and have affinities with a real-time monitoring system. In the Kyoto University Critical Assembly (KUCA), subcriticality measurement experiments of these two techniques were carried out. From the experimental result, it is confirmed that both techniques can be carried out only with the inherent neutron source. It is noted that, however, measured values of subcriticality by both methods show different trends. While the subcriticality measured by the Feynman-alpha method is fairly constant among detectors, the measured value does not agree with that obtained by the pulsed neutron source (PNS) method, in deep subcritical systems. On the other hand, the subcriticality measured by the NSM method show significant dependence on detectors. However, the measurement values by the NSM method using detectors at appropriate position agree with values by the PNS method even in deep subcritical systems.

DOI： 10.11484/jaea-conf-2014-003

Impact of Nearest Neighbor Distribution of Fuel Particle on Neutronics Characteristics in Statistical Geometry Model Reviewed International journal

T. Koide, T. Endo, A. Yamamoto, K. Kirimura, K. Yamaji

Proc. PHYSOR2014 Vol. CD-ROM page： 1101295 2014.9

Generation of Simplified Burnup Chain using Contribution Matrix of Nuclide Production Reviewed International journal

R. Katano, A. Yamamoto, T. Endo, Y. Kamiyama, K. Kirimura, S. Kosaka

Proc. PHYSOR2014 Vol. CD-ROM page： 1101303 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

A procedure to automatically generate a simplified burnup chain is proposed, which preserves prediction accuracy of target nuclides number density using calculation results of a detail burnup chain. In the present procedure, the contributions to production of the target nuclides are quantitatively evaluated at first using the off-diagonal elements of a burnup matrix and nuclides number density. Then, by considering the contributions to nuclide production, which is represented as a “contribution matrix”, the nuclides in detail burnup chain are selected according to the importance represented as the contribution matrix. Finally, a simplified burnup chain is generated with the target nuclides and the selected nuclides from the contribution matrix. Since the present method only utilizes the burnup matrix, which is usually used in the common lattice physics computation, its implementation to production codes is easy. In order to examine the effectiveness of the present method, burnup calculation in a PWR fuel pin-cell problem with some simplification on calculation conditions is carried out. The calculation results suggest that the present method will be a good candidate for an automated generation method for a simplified burnup chain.

DOI： 10.11484/jaea-conf-2014-003

Uncertainty Quantification of BWR Core Characteristics using Latin Hypercube Sampling Method Reviewed International journal

K. Kinoshita, A. Yamamoto, T. Endo, Y. Kodama, Y. Ohoka, T. Ushio, H. Nagano

Proc. PHYSOR2014 Vol. CD-ROM page： 1090063 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

Uncertainties of neutronics characteristics in a commercial BWR core due to cross section covariance are evaluated by the Latin Hypercube Sampling (LHS) method, which is a Monte-Carlo based efficient sampling algorithms. The Peach Bottom Unit 2, which is a BWR core, is a target for the uncertainty quantification in the present study. Thermal hydraulics feedback and burnup effects are fully and explicitly taken into account using a licensing-grade core simulator. Uncertainties for various core characteristics and correlations among them 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 typical PWR. 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 typical PWR. The strong thermal hydraulics feedback effect of BWR would significantly contribute the difference of uncertainties in BWR and PWR.

DOI： 10.11484/jaea-conf-2014-003

Uncertainty Quantification of Neutronics Characteristics using Latin Hypercube Sampling Method Reviewed International journal

K. Kinoshita, A. Yamamoto, T. Endo, Y. Kodama, Y. Ohoka, T. Ushio, H. Nagano

Proc. PHYSOR2014 Vol. CD-ROM page： 1101192 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

The Latin Hypercube Sampling (LHS) method is applied to the uncertainty quantification of neutronics characteristics based on the Monte-Carlo based sampling method. The Monte-Carlo based sampling method is one of the uncertainty quantification methods of neutronics characteristics (e.g. neutron multiplication factor) due to uncertainty cross section. The sampling method has the advantage that burnup and thermal-hydraulics feedback effects are easily considered in complicated light water reactor core analysis. Contrary, the sampling method has the disadvantage that statistical errors are involved in estimated uncertainties of neutronics characteristics since the sampling method is a probabilistic approach. Although the statistical errors can be reduced by increasing the number of samples (e.g. number of perturbed cross section libraries), computational cost also increases. Therefore development of an efficient uncertainty quantification method, which provides smaller statistical error of estimated uncertainty while reducing number of samples, is highly desirable. In the present study, adequacy and performance of the LHS method is investigated as an efficient Monte-Carlo based sampling method. Uncertainty quantification of multiplication factor for a BWR fuel assembly is carried out with the LHS method. The results indicate that uncertainty quantification using the LHS method is more efficient than that using the conventional sampling method, which utilizes simple random sampling of cross sections.

DOI： 10.11484/jaea-conf-2014-003

Theoretical Prediction on Underestimation of Statistical Uncertainty for Fission Rate Tally in Monte Carlo Calculation Reviewed International journal

T. Endo, A. Yamamoto, K. Sakata

Proc. PHYSOR2014 Vol. CD-ROM page： 1126624 2014.9

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

A theoretical model to predict underestimation of standard deviation for the mean of fission rate in each tally region is proposed on the basis of the behavior of higher order modes in fission source distribution and the autoregressive (AR) model. The predicted underestimation of standard deviation for the mean of fission rate is compared with that obtained by actual Monte Carlo calculations and they agree well each other. Dependency of underestimation of standard deviation on number of tally regions and spatial position is clarified by the proposed theoretical model. The present theoretical model can be used to quantitatively predict underestimation of standard deviation of local fission rate tally.

DOI： 10.11484/jaea-conf-2014-003

Applicability of the Cross Section Adjustment Method Based on Random Sampling Technique for Burnup Calculation Reviewed International journal

T. Watanabe, T. Endo, A. Yamamoto, Y. Kodama, Y. Ohoka, T. Ushio

Proc. PHYSOR2014 Vol. CD-ROM page： 1098930 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

Applicability of the cross section adjustment method based on random sampling (RS) technique to burnup calculations is investigated. The cross section adjustment method is a technique for reduction of prediction uncertainties in reactor core analysis and has been widely applied to fast reactors. As a practical method, the cross section adjustment method based on RS technique is newly developed for application to light water reactors (LWRs). In this method, covariance among cross sections and neutronics parameters are statistically estimated by the RS technique and cross sections are adjusted without calculation of sensitivity coefficients of neutronics parameters, which are necessary in the conventional cross section adjustment method. Since sensitivity coefficients are not used, the RS-based method is expected to be practically applied to LWR core analysis, in which considerable computational costs are required for estimation of sensitivity coefficients. Through a simple pin-cell burnup calculation, applicability of the present method to burnup calculations is investigated. The calculation results indicate that the present method can adequately adjust cross sections including burnup characteristics.

DOI： 10.11484/jaea-conf-2014-003

Prediction on Underestimation of Variance for Fission Rate Distribution in Monte-Carlo Calculation Reviewed International journal

A. Yamamoto, K. Sakata, T. Endo

Trans. Am. Nucl. Soc. Vol. 110 page： 515 - 518 2014.6

An Improved CMFD Acceleration for SP3 Advanced Nodal Method Reviewed International journal

T. Sakamoto, A. Yamamoto, T. Endo

Trans. Am. Nucl. Soc. Vol. 110 page： 535 - 537 2014.6

Evaluation of Higher Mode Components of Fission Source Distribution in Monte-Carlo Calculation Reviewed International journal

K. Sakata, T. Endo, A. Yamamoto

Proc. SNA-MC 2013 page： 03503 2014.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

In order to accurately estimate uncertainty of fission source distribution in a Monte Carlo calculation, a theoretical model predicting behavior of higher order modes in fission source distribution at each cycle is proposed considering the inter-cycle correlation. In a Monte Carlo calculation, statistical noise stimulates higher order modes in fission source distribution at each cycle thus the fission source distribution may not be fully converged to a fundamental mode even if number of power iterations is sufficiently large. This is especially true for a large geometry with high dominance ratio and is one of the root cause of underestimation of statistical uncertainty. In the present model, a fission source distribution is expanded by a series of higher order modes and their behaviors are estimated by variation of expansion coefficients at each cycle. The expansion coefficients show fluctuation due to statistical noise during a Monte Carlo calculation. By observing decay ratio of higher order modes in PWR single assembly geometry, validity of the present theoretical model is confirmed. Furthermore, behaviors of higher order mode components in PWR single or multi fuel assemblies geometry are investigated.

DOI： 10.1051/snamc/201403503

Estimation of Self-Shielding Effect on Uncertainty of Neutronics Characteristics using Random Sampling Method and Continuous-Energy Slowing-Down Calculation Reviewed International journal

A. Yamamoto, S. Sato, T. Endo

Trans. Am. Nucl. Soc. Vol. 109 page： 1436 - 1438 2013.11

Subcriticality Measurement Technique using Inherent Neutron Source in Uranium Fuel Reviewed International journal

T. Shiozawa, T. Endo, A. Yamamoto, C.H. Pyeon, T. Yagi

Trans. Am. Nucl. Soc. Vol. 109 page： 826 - 829 2013.11

Behavior of Higher Order Fission Source Distribution in Monte-Carlo Calculations Reviewed International journal

A. Yamamoto, K. Sakata, T. Endo

Trans. Am. Nucl. Soc. Vol. 109 page： 1361 - 1364 2013.11

Uncertainty and Correlation Estimation of Reload Safety Parameters of PWR using Random Sampling Method Reviewed International journal

T. Watanabe, T. Endo, A. Yamamoto, Y. Kodama, Y. Ohoka, T. Ushio

Trans. Am. Nucl. Soc. Vol. 109 page： 1365 - 1368 2013.11

Few-Group Macroscopic Cross Section Adjustment for LWRs using Random Sampling Technique Reviewed International journal

A. Yamamoto, S. Kato, T. Endo

Trans. Am. Nucl. Soc. Vol. 108 page： 894 - 897 2013.6

Study on Discontinuity Factor for Angular Flux in Transport Equation Reviewed International journal

T. Sakamoto, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 108 page： 887 - 890 2013.6

Reduction of Discretization Error for Ray Tracing of MOC Through a Correction on Collision Probabilities Reviewed International journal

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

Proc. M&C2013 page： 1853 - 1864 2013.5

Language：English Publishing type：Research paper, summary (international conference)

A new correction model for ray tracing of the method of characteristics is proposed in order to reduce discretization error. As the ray tracing parameters such as azimuthal angle division, polar angle division and ray separation are considered in this study. In the method of characteristics, region average scalar fluxes can be implicitly expressed by collision probabilities, although these collision probabilities are not directly treated in the ordinary calculation scheme. From this viewpoint, difference between a coarse ray tracing condition and a detailed one can be interpreted as the difference in the estimation of collision probabilities. In other words, the discretization error for ray tracing can be recognized as a consequence of inaccurate collision probabilities caused by coarse ray tracing. This discussion suggests that accurate region average scalar flux can be obtained through an appropriate correction on collision probabilities. In this paper, a correction model on collision probabilities is theoretically derived based on the neutron balance equation, and its validity is confirmed through typical single assembly calculations. The effectiveness of the present correction method is also discussed in this paper. It is confirmed that discretization error for ray tracing can be significantly reduced by the present correction method in a multi-assembly calculation, though the correction factor is estimated in single assembly geometry.

Explicit Estimation of Higher Order Modes in Fission Source Distribution of Monte-Carlo Calculation Reviewed International journal

A. Yamamoto, K. Sakata, T. Endo

Proc. M&C2013 page： 2814 - 2827 2013.5

Language：English Publishing type：Research paper, summary (international conference)

Magnitude of higher order modes in fission source distribution of a multi-group Monte-Carlo calculation is estimated using the orthogonal property of forward and adjoint fission source distributions. Calculation capability of the forward and adjoint fission source distributions for fundamental and higher order modes are implemented in the AEGIS code, which is a twodimensional transport code based on the method of characteristics. With the calculation results of the AEGIS code, magnitudes of the first to fifth higher order modes in fission source distribution obtained by the multi-group Monte-Carlo code GMVP are estimated. There are two contributions in the present study - (1) establishment of a surrogate model, which represents convergence of fission source distribution taking into account the inherent statistical "noise" of higher order modes of Monte-Carlo calculations and (2) independent confirmation of the estimated dominance ratio in a Monte-Carlo calculation. The surrogate model would contribute to studies of the intercycle correlation and estimation of sufficient number of inactive/active cycles.

Higher Order Treatment on Temporal Derivative of Angular Flux for Time-Dependent MOC Reviewed International journal

K. Tsujita, T. Endo, A. Yamamoto, Y. Kamiyama, K. Kirimura

Proc. M&C2013 page： 1826 - 1838 2013.5

Language：English Publishing type：Research paper, summary (international conference)

A new kinetic analysis method, whose angular dependence of temporal derivative for angular flux is accurately treated within practical memory requirement, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, the computational resources, i.e., the memory capacity, can be still a crucial problem for rigorous kinetic calculations using MOC. In the straightforward approach for kinetic calculation using MOC, the segment-averaged angular fluxes should be stored on the memory in order to explicitly calculate the temporal derivative of the angular flux, which would require huge memory. Thus, in the conventional kinetic calculation code using MOC, the temporal derivative of the angular flux has been approximated as angularly isotropic in order to reduce the memory requirement (isotropic assumption). However, the approximation error caused by the conventional isotropic assumption has not been thoroughly and quantitatively investigated so far and an accurate kinetic calculation method, which can quantitatively estimate the above approximation error within practical memory storage, has not been developed. The present study tries to address this issue with a newly developed approach. Effect of the approximate treatment for the temporal derivative of angular flux is evaluated through benchmark calculations.

Application of the Multigrid Amplitude Function Method for Time-Dependent Transport Equation using MOC Reviewed International journal

K. Tsujita, T. Endo, A. Yamamoto

Proc. M&C2013 page： 1839 - 1852 2013.5

Language：English Publishing type：Research paper, summary (international conference)

An efficient numerical method for time-dependent transport equation, the mutigrid amplitude function (MAF) method, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, efficient kinetic calculation method for MOC is still desirable since it requires significant computation time. Various efficient numerical methods for solving the space-dependent kinetic equation, e.g., the improved quasi-static (IQS) and the frequency transform methods, have been developed so far mainly for diffusion calculation. These calculation methods are known as effective numerical methods and they offer a way for faster computation. However, they have not been applied to the kinetic calculation method using MOC as the authors’ knowledge. Thus, the MAF method is applied to the kinetic calculation using MOC aiming to reduce computation time. The MAF method is a unified numerical framework of conventional kinetic calculation methods, e.g., the IQS, the frequency transform, and the theta methods. Although the MAF method is originally developed for the space-dependent kinetic calculation based on the diffusion theory, it is extended to transport theory in the present study. The accuracy and computational time are evaluated though the TWIGL benchmark problem. The calculation results show the effectiveness of the MAF method.

Random Sampling-Based Cross-Section Adjustment Technique for LWR Core Analysis Reviewed International journal

S. Kato, T. Endo, A. Yamamoto, H. Yamauchi, Y. Kimura

Proc. Int. Congress on Advances in Nuclear Power Plants (ICAPP2013) page： 877 - 883 2013.4

Authorship：Corresponding author Language：English Publishing type：Research paper, summary (international conference)

In the present study, a random sampling-based cross-section adjustment technique is developed to apply to LWR reactor core analysis procedure. In this technique, random sampling method is utilized for fine energy group microscopic cross-section libraries used in lattice physics code. For few energy group homogenized macroscopic cross-section used in core analysis code, the covariance and sensitivity matrices are numerically evaluated, and then the cross-section table in core analysis are upgrade by cross-section adjustment technique. As a feasibility study, our proposed technique is verified for small core geometries based on the published data of BWR (Peach Bottom-2). Through the verification, it is confirmed that core characteristics (criticality and assembly-averaged relative power) during operation period can be improved by core analysis using adjusted few energy-group cross-sections.

Correction Technique for Coarse Group Cross Sections Considering Spectral Interference Effect on Pin-by-Pin BWR Core Analysis Reviewed International journal

T. Fujita, T. Endo, A. Yamamoto

Proc. Int. Congress on Advances in Nuclear Power Plants (ICAPP2013) page： 936 - 945 2013.4

Correction of Spectral Interference Effect on Pin-by-Pin BWR Core Analysis Reviewed International journal

T. Fujita, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 107 page： 1141 - 1143 2012.11

Subcriticality Measurement by Neutron Source Multiplication Method with Detected-Neutron Multiplication Factor Reviewed International journal

T. Endo, A. Yamamoto, C.H. Pyeon, T. Yagi

Trans. Am. Nucl. Soc. Vol. 107 page： 648 - 651 2012.11

Efficient Calculation Scheme with Preservation of Transmission Probabilities in the Method of Characteristics Reviewed International journal

M. Tabuchi, N. Sugimura, A. Yamamoto, T. Endo

Trans. Am. Nucl. Soc. Vol. 107 page： 1105 - 1107 2012.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

In this study, an efficient calculation scheme for MOC is investigated. The equation for the effective length of a path line is derived based on an assumption that the lengths are linearly distributed in a strip. By using the effective length, the transmission probabilities in each strip can be preserved. Through the verification calculations, the accuracy of the present method can be confirmed, and efficiency of the MOC calculation is expected to be improved by the present method.

Higher Order Treatment on Temporal Derivative of Angular Flux for Time-Dependent MOC Reviewed International journal

K. Tsujita, T. Endo, A. Yamamoto, Y. Kamiyama, K. Kirimura

Trans. Am. Nucl. Soc. Vol. 107 page： 1101 - 1104 2012.11

Kinetic Calculation Method in Space-Time Frame Using Characteristic Line Reviewed International journal

K. Tsujita, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 106 page： 743 - 746 2012.6

Analysis of Erbia-loaded Critical Experiments in KUCA using AEGIS Cross Section Library Reviewed International journal

A. Yamamoto, T. Endo, X. Wu

Trans. Am. Nucl. Soc. Vol. 106 page： 715 - 718 2012.6

Estimation of Average Burnup of Damaged Fuels Loaded in Fukushima Dai-ichi Reactors by using the Cs134/Cs137 Ratio Method Reviewed International journal

T. Endo, S. Sato, A. Yamamoto

Proc. Physor2012 - Advanced in Reactor Physics - Linking research, Industry and Education page： 3246 - 3253 2012.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference)

Cs134/Cs137 ratio method for measured radioactivities of 134Cs and 137Cs in contaminated soils within the range of 100 km from the Fukushima Dai-ichi nuclear power plants. As a result, the measured Cs134/Cs137 ratio from the contaminated soil is 0.996±0.07 as of March 11th, 2011. Based on the Cs134/Cs137 ratio method, the estimated burnup of damaged fuels is approximately 17.2±1.5 [GWd/tHM]. It is noted that the numerical results of various calculation codes (SRAC2006/PIJ, SCALE6.0/TRITON, and MVP-BURN) are almost the same evaluation values of Cs134/Cs137 ratio with same evaluated nuclear data library (ENDF-B/VII.0). The void fraction effect in depletion calculation has a major impact on 134Cs/137Cs ratio compared with the differences between JENDL-4.0 and ENDF-B/VII.0.

Uncertainty Estimation of Core Safety Parameters using Cross-Correlations of Covariance Matrix Reviewed International journal

A. Yamamoto, Y. Yasue, T. Endo, Y. Kodama, Y. Ohoka, M. Tatsumi

Proc. Physor2012 - Advanced in Reactor Physics - Linking research, Industry and Education page： 2880 - 2895 2012.4

Language：English Publishing type：Research paper, summary (international conference)

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

Development of a Lattice Physics Code for Sensitivity Analysis Based on Generalized Perturbation Theory Reviewed International journal

S. Kato, T. Endo, A. Yamamoto, Y. Kimura

Trans. Am. Nucl. Soc. Vol. 105 page： 851 - 854 2011.10

Evaluation of Correlations among Uncertainties of Core Neutronic Parameters in Infinite Slab Geometry Reviewed International journal

Y. Yasue, T. Endo, A. Yamamoto, Y. Kodama, Y. Ohoka, M. Tatsumi

Trans. Am. Nucl. Soc. Vol. 105 page： 486 - 488 2011.10

Assembly Discontinuity Factor for Angular Flux in Transport Calculation Reviewed International journal

A. Yamamoto, T. Endo

Trans. Am. Nucl. Soc. Vol. 105 page： 862 - 864 2011.10

A Unified Numerical Algorithm for Space-Dependent Kinetic Equation Invited Reviewed International journal

T. Endo, Y. Ban, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 104 page： 865 - 867 2011.6

A Derivation of Discontinuity Factor for Angular Flux in Integro-Differential Transport Equation Reviewed International journal

A. Yamamoto, T. Endo, Y. A. Chao

Trans. Am. Nucl. Soc. Vol. 104 page： 815 - 817 2011.6

Search Strategy of Detector Position for Neutron Source Multiplication Method by using Detected-Neutron Multiplication Factor Invited International journal

T. Endo

Transactions of Korean Nuclear Society 2011 Spring Meeting page： 131 - 132 2011.5

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Korean Nuclear Society

In this paper, based on the idea of kdet, it is clear that correlation factors of the NSM method consist of the sourc-flux correction factor fs to fix the difference of non-fission component of neutron count rate, and the conversion factor fc to convert from kdet to the effective multiplication factor keff. Through the numerical analysis of three-dimensional two-group transport calculations for simple geometry, appropriate detector positions where kdet=keff could be find out for only one certain subcritical state, e.g., the reference state. By putting a neutron detector at such a particular position, the target neutron multiplication factors can be well estimated even without any corrections.

Effect of Uncertainty of Planned Cycle Length in Multicycle Fuel Optimization Reviewed International journal

K. Ohori, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 103 page： 707 - 710 2010.11

Incorporation of Two-Term Rational Approximation in Tone Method for Resonance Calculation Reviewed International journal

A. Yamamoto, T. Endo, G. Chiba

Trans. Am. Nucl. Soc. Vol. 103 page： 711 - 713 2010.11

Investigation of Theoretical Approach to Establish Energy Group Structure for BWR Pin-by-Pin Core Analysis Reviewed International journal

T. Fujita, K. Otsuka, K. Tada, T. Endo, A. Yamamoto, S. Kosaka, G. Hirano

Trans. Am. Nucl. Soc. Vol. 103 page： 721 - 723 2010.11

Verification and validation of AEGIS/SCOPE2 the state-of-the-art in-core fuel management system for PWRs Reviewed International journal

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

Proc. 18th International Conference on Nuclear Engineering Vol. 2 page： 9 - 15 2010.5

Language：English Publishing type：Research paper, summary (international conference)

Verification and validation of AEGIS/SCOPE2, a state-of-the-art in-core fuel management system for PWRs, was conducted. Verification of implementations for processes of tabulation and reconstruction of cross sections data in the system was confirmed through benchmark problems to confirm consistency between AEGIS and SCOPE2 in terms of reactivity and pin power distribution with identical computational condition in single- and multi-assembly geometry. In validation study numerical performance of the system was demonstrated in analyses of the B&amp
W's critical experiment and tracking calculations for commercial PWRs in combination of ENDF/B-VII.0 library. It is found the present system gives stability in prediction of critical boron concentration and radial power distribution. Copyright © 2010 by ASME.

DOI： 10.1115/ICONE18-29154

Scopus

Numerical Solution of Reactor Kinetics Equation with Krylov Subspace Method for Matrix Exponential Reviewed International journal

Y. Ban, A. Yamamoto, Y. Yamane, T. Endo

Proc. International Conference on the Physics of Reactors (Physor2010) page： 951 - 962 2010.5

Critical Experiments in Kyoto University Critical Assembly for Development of >5wt% Enrichment Erbia Bearing Super High Burnup Fuel Reviewed International journal

T. Endo, M. Yamasaki, T. Kuroishi

Proc. Nuclear Criticality Safety Division Topical Meeting on Realism, Robustness and the Nuclear Renaissance (NCSD 2009) page： 536 - 545 2009.9

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference)

In order to improve fuel cycle economics with securing critical safety, the development project on Erbia bearing Super High Burnup (Er-SHB) fuel with >5wt% uranium enrichment is in progress. In this project, a series of critical experiments of erbia loaded core have been performed at Kyoto University Critical Assembly (KUCA). In order to accumulate experimental data under various conditions, four erbia loaded critical cores have been constructed by changing averaged enrichment, erbia content, and H/U-235 ratio. Several experimental data such as criticality and erbia sample worth have been measured. In this paper, we will show the numerical analyses by using probabilistic and deterministic methods. As a result, the C/E values are evaluated by the Monte Carlo method can be predicted within 0.998-1.004, thus the prediction accuracy of criticality for erbia loaded core is validated. For the erbia sample worth evaluated by the deterministic code, it could be generally concluded that significant discrepancy between calculation and measurement could not be observed. However, further study such as the treatment of heterogeneous effects in the fuel elements will be necessary to finalize the C/E values.

Study on Kinetic Transport Solvers for Pin-by-Pin Core Calculation Reviewed International journal

T. Endo, M. Tatsumi

Proc. International Conference on the Physics of Reactors (Physor2008) page： 981 - 987 2008.9

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference)

SCOPE2 is an advanced core calculation code to solve the multi-group SP3 transport equations within three-dimensional pin-by-pin geometry. For the purpose of wider range of applicability such as analysis for dynamic rod worth measurements, widely known kinetic solvers have been implemented in SCOPE2. The implemented solvers are the backward Euler, the theta, and the frequency-transform method. In implementing the theta method in SCOPE2, an automatic determination of weighting parameter is adopted in order to obtain stable solutions with as high accuracy as possible. In the frequency-transform method, the space- and energy dependant frequency is estimated to reduce the discretization error of transformed neutron flux. Through an analysis of the 3-D LMW benchmark problem without thermal hydraulic feedback, it was demonstrated that the kinetic solvers are correctly implemented in SCOPE2, and the accuracy of each solver was verified.

Yet Another Optimum Polar Angle Quadrature Set for the Method of Characteristics Reviewed International journal

M. Tabuchi, A. Yamamoto, T. Endo, N. Sugimura, T. Ushio, M. Mori

Trans. Am. Nucl. Soc. Vol. 93 page： 506 - 507 2005.11

Medical Isotope Production Using Pressurized Water Reactor Reviewed

T. Endo;A. Yamamoto

Proc. International Symposium on Isotope Science and Engineering from Basic to Applications Vol. CD-ROM 2005.9

Efficient Calculation of Time-Dependent Neutron Transport Equation using the Constrained Interpolated Profile (CIP) Method Reviewed International journal

S. Kano, T. Endo, A. Yamamoto, Y. Yamane, Y. Kitamura

Proc. International topical Meeting on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications (M&C2005) page： CD-ROM 2005.9

Development of Advanced Neutronics Design System of Next Generation, AEGIS Reviewed International journal

N. Sugimura, T. Ushio, M. Mori, A. Yamamoto, M. Tabuchi, T. Endo

Proc. International topical Meeting on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications (M&C2005) page： CD-ROM 2005.9

Derivation of the Space and Energy Dependent Formula for the Third Order Neutron Correlation Technique Reviewed International journal

T. Endo, Y. Kitamura, A. Yamamoto, Y. Yamane

Proc. PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems: Global Developments page： 1085 - 1095 2004.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference)

We have studied a measurement technique of subcriticality by using the neutron correlation methods. Among various techniques, we have paid attention to the third order neutron correlation technique, which utilizes the third order fluctuations of neutron counts. By using this technique, we can obtain the absolute value of subcriticality without prior knowledge of the prompt neutron decay constant at a reference state. To apply the third order neutron correlation technique to actual experiments, we must consider the effects of the spatial and neutron energy distributions in this technique. For this purpose, we derived the generalized theoretical formulas of the third order neutron correlation technique that took account of the spatial and neutron energy effects.

Absolute Measurement of the Subcriticality Based on the Third Order Neutron Correlation in Consideration of the Finite Nature of Neutron Counts Data Reviewed International journal

T. Endo, Y. Kitamura, Y. Yamane

Proc. the 7th International Conference on Nuclear Criticality Safety ICNC2003; Challenges in the Pursuit of Global Nuclear Criticality Safety page： 215 - 220 2003.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

We have studied a measurement of subcriticality by using the neutron correlation method. Furuhashi proposed an absolute measurement of subcriticality by using the third order neutron correlation factor X in addition to the second order neutron correlation factor Y. In actual experiments, the number of neutron counts data is not infinity so that we take the effect of the finite nature of the neutron counts data into account. We derived new formulas in consideration of the number of data and verified them.

DOI： 10.11484/jaeri-conf-2003-019

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