Faculty Profiles - YAMAMOTO, Akio

Papers - YAMAMOTO, Akio

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Investigation of Thermal Cutoff Energy for Accurate Analysis of High-Temperature Engineering Test Reactor

Takeda S., Kitada T., Yamamoto A., Yamaji K., Koike H., Asano K.

Journal of Nuclear Engineering and Radiation Science Vol. 11 ( 4 ) 2025.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Engineering and Radiation Science

This study investigates the appropriate thermal cutoff energy for neutron transport calculations in the High-Temperature Engineering Test Reactor (HTTR). Using the Monte Carlo calculation code mvp3.0, the impact of changing thermal cutoff energy on the multiplication factor was evaluated for the single fuel element geometry of HTTR, focusing on variations in fuel and moderator temperatures at the beginning of life (BOL) and end of life (EOL). In the default model of mvp3.0, resonance scattering is approximated by the free-monatomic-gas model with constant cross section. Therefore, the impact of using the exact model for resonance scattering was additionally examined. In the free-monatomic-gas model, a thermal cutoff energy of 30 eV is at least required to maintain the multiplication factor error within approximately ±50 pcm for both BOL and EOL. In addition, the results show that the impact of using the exact model instead of the free-monatomic-gas model on the multiplication factor is more than 200 pcm in the 30-40 eV range where U-238 has large resonance at 37 eV, and the impact becomes less than 50 pcm above 40 eV. These results indicate that a thermal cutoff energy of at least 30 eV is necessary without considering the effects of the exact model, and the energy range up to the 37 eV resonance needs to be considered in the case of applying the exact model to obtain the saturated results on multiplication factor for HTTR.

DOI： 10.1115/1.4067755

Ikaros3D: a real-time 3D fine spatial mesh kinetics simulator using POD

Tsujita, K; Ito, K; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2025.8

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

Toward the development of digital triplets for more effective reactor physics education, the present study develops a real-time 3D fine spatial mesh kinetics simulator based on the proper orthogonal decomposition (POD). The present simulator, Ikaros3D, is specifically designed for a simplified coupled core model using the pre-tabulated compressed coefficient matrices for the POD-based kinetics calculation. It enables us to accurately calculate the time variation of flux distribution in real-time as well as actual experiments and promotes students’ better understanding of the spatial dependence of dynamic reactivity considering the positions of the neutron detectors.

DOI： 10.1080/00223131.2025.2545508

Hybrid data assimilation methods for nuclear-data-induced uncertainties

Maruyama, S; Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2025.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

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

DOI： 10.1080/00223131.2025.2500579

Collapsed energy group structure for analysis of prismatic high-temperature gas-cooled reactor with uranium fuel Open Access

Takeda, S; Kitada, T; Yamamoto, A; Yamaji, K; Koike, H; Asano, K

ANNALS OF NUCLEAR ENERGY Vol. 214 2025.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Annals of Nuclear Energy

Considering computational costs, it is practical to use collapsed energy group structures with less than several tens of groups of the core analysis of High-Temperature Gas-cooled Reactors (HTGRs). This study evaluates the performance of several existing energy group structures and newly optimized 15-group and 25-group structures for prismatic HTGRs with uranium fuel. Both multi-element and two-dimensional core geometries were used to account for neutron spectrum interference effects caused by the presence of control rods, differences in graphite temperature, and variations in the amount of surrounding graphite. The optimization calculations were performed using Genetic algorithm and Particle swarm optimization. Among the group structures with around 15 groups, the newly optimized 15-group structure showed relatively good agreement with the reference solution. For the group structures with around 25 groups, while the newly optimized 25-group structure showed slightly better performance under certain conditions, the existing 26-group structure consistently demonstrated stable and good performance.

DOI： 10.1016/j.anucene.2025.111238

Treatment of corner crossing ray-traces in CMFD acceleration of MOC Open Access

Yamamoto, A; Endo, T

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

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

DOI： 10.1080/00223131.2025.2490832

Impact of nuclear data updates from JENDL-4.0 to JENDL-5 on burnup calculations of light-water reactor fuels Open Access

Watanabe, T; Tada, K; Endo, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

This study investigated the impact of nuclear data updates from JENDL-4.0 (J4) to JENDL-5 (J5) on the light-water reactor fuel burnup calculations. Burnup calculations were conducted with J4 and J5 for pressurized water reactor pin-cell and boiling water reactor (BWR) fuel assembly geometries. The calculation results revealed significant burnup-dependent differences in the neutron multiplication factor (k<inf>inf</inf>). Across the burnup range of 0–50 GWd/t, k<inf>inf</inf> values of J5 were consistently smaller than those of J4 and the difference gradually increased as burnup progressed. Direct sensitivity calculations, in which each nuclide data was replaced from J4 to J5, indicated that updates to the cross-sections of U-235, U-238, and Pu-239 and the thermal scattering law data of H in H<inf>2</inf>O notably impacted the k<inf>inf</inf> differences. For the BWR assembly geometry containing Gd fuels, large k<inf>inf</inf> differences were observed in the burnup range of 10–15 GWd/t. This difference was primarily attributed to updates in the cross-sections of U-235, Gd-155, Gd-157, and thermal scattering law data of H in H<inf>2</inf>O. Furthermore, we investigated how the nuclear data updates affected the k<inf>inf</inf> differences by examining nuclide number densities, the energy-dependent sensitivities, and the neutron spectra.

DOI： 10.1080/00223131.2025.2486798

Development of Multigroup Monte Carlo Neutron Transport Method with Regionwise Even-Parity Discontinuity Factor Open Access

Oshima, Y; Endo, T; Yamamoto, A

NUCLEAR SCIENCE AND ENGINEERING Vol. 199 ( 4 ) page： 586 - 598 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Nuclear Science and Engineering

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

DOI： 10.1080/00295639.2024.2383102

Reduced order SP<sub>3</sub> core calculation based on local/global iterations using proper orthogonal decomposition Open Access

Ito, M; Endo, T; Yamamoto, A; Takeishi, T; Kodama, Y; Hyoudou, H

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 62 ( 4 ) page： 366 - 378 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

For an efficient heterogeneous neutron transport calculation, this study newly proposes a reduced order core calculation method by applying proper orthogonal decomposition (POD) to the simplified P<inf>3</inf> (SP<inf>3</inf>) calculation with the local/global iterations. The fine mesh SP<inf>3</inf> calculation (local calculation) for each single assembly can be efficiently solved using POD, thanks to the matrix form-based SP<inf>3</inf> equation and the relatively small system of linear equations. By reconstructing the fine mesh distribution of neutron flux and partial neutron currents from the POD bases and the expansion coefficients estimated by the local calculation, the partial current-based coarse mesh finite difference (p-CMFD) calculation is applied to the coarse mesh calculation (global calculation). Using the global calculation results, each local boundary condition can be updated. These local and global calculations are iterated until convergence. Through a two-dimensional UO<inf>2</inf>-MOX whole core calculation with different fuel loading patterns, the proposed method is verified in comparison with the reference result by the conventional fine mesh SP<inf>3</inf> calculation. The calculation results show that the proposed method accurately reconstructs the fine mesh distribution of neutron flux.

DOI： 10.1080/00223131.2024.2436958

Verification of direct coupling code system using FRENDY version 2 and GENESIS for light water reactor lattices Open Access

Fujita, T; Yamamoto, A

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY Vol. 62 ( 2 ) page： 179 - 196 2025.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

This study newly established a direct coupling code system consisting of the nuclear data processing code FRENDY version 2, and the three-dimensional heterogeneous transport code GENESIS (FRENDY-V2/GENESIS) for easy implementation of the random-sampling-based uncertainty quantification considering the implicit effect due to nuclear cross-section (XS) perturbations. The multi-group macroscopic XSs prepared for GENESIS were generated by FRENDY version 2, where the Dancoff factor was calculated by the neutron current method. Then the background XSs were evaluated based on the Carlvik two-term rational approximation. The infinite multiplication factor (k-infinity) and the fission reaction rate distribution in UO<inf>2</inf> and MOX lattice geometries were compared with MVP3 to verify the calculation accuracy of FRENDY-V2/GENESIS. The sensitivity analyses on the discretization conditions such as the ray tracing of the method of characteristics were also carried out. Through several comparisons between FRENDY-V2/GENESIS and MVP3, FRENDY-V2/GENESIS with the SHEM 361-group structure calculates the k-infinity within approximately 50 pcm and the fission reaction rate distribution within approximately 0.1% by the root mean square, respectively. Consequently, the applicability of FRENDY-V2/GENESIS was verified, and FRENDY-V2/GENESIS can be used to discuss the implicit effect due to multi-group XS perturbations.

DOI： 10.1080/00223131.2024.2410918

Absolute measurement of subcriticality in dollar units based on lag-1 autocovariance of zero-power reactor noise

Hirota R., Moribe T., Endo T., Yamamoto A., Watanabe K., Wakabayashi G., Shiga H., Sakon A., Oda K., Kaneko J.H.

Journal of Nuclear Science and Technology 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

The zero-power reactor noise analysis is often utilized to measure a kinetic parameter of the prompt neutron decay constant (Formula presented.) for a target subcritical system in a steady state. There will be large uncertainties in the point kinetics parameters when detailed information on the target system is not available in advance. Therefore, if the subcriticality is converted from the measured (Formula presented.) value, the estimated subcriticality will inevitably have a large uncertainty. To address this problem, the present study aims to propose an absolute measurement technique of subcriticality in a steady state without the point kinetics parameters. The proposed method utilizes the lag-1 autocovariance of the reactor noise, which can emphasize the delayed neutron component better than the conventional reactor noise analysis methods such as the autocorrelation and Feynman- (Formula presented.) methods. By searching for the model parameters of the analytical formula of the lag-1 autocovariance for the measured values using the nonlinear least squares fitting method or Bayesian Monte Carlo, the subcriticality in dollar units can be inversely estimated together with the ratio of (Formula presented.). The validity of the proposed method is demonstrated for a zero-power reactor noise measurement at UTR-KINKI under a shutdown state.

DOI： 10.1080/00223131.2025.2530788

Discussion on the 3S for peaceful use of nuclear energy for future generations (1) Open Access

Yamamoto Akio

Journal of the Atomic Energy Society of Japan Vol. 67 ( 4 ) page： 218 - 221 2025

Fundamental properties and characteristics of flux distribution tallies using proper orthogonal decomposition Open Access

Kondo R., Yamamoto A., Endo T.

EPJ Nuclear Sciences and Technologies Vol. 11 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：EPJ Nuclear Sciences and Technologies

The flux distribution tallies using the proper orthogonal decomposition (POD) called the POD tallies have been developed in our previous study. The POD tallies can achieve dimensionality and statistical uncertainty reduction for a finely discretized flux distribution. Some characteristics of the POD tallies, which are left by our previous work, are revealed in the present study. Firstly, the POD tallies with the track length estimator are newly implemented. Since the statistical uncertainty of the POD tallies is reduced compared with the cell tallies, the POD tallies with the track length estimator can obtain the most precise result among the present implantations. Secondly, the basis vectors obtained by the deterministic and the stochastic methods are compared. The statistical uncertainty of the snapshot data invokes the degradation of the extracted basis vectors. This result indicates that the deterministic method might be more efficient for the snapshot calculation. Finally, the impact of the covariances of expansion coefficients on the statistical uncertainty of expanded flux distribution is investigated. The reconstructed statistical uncertainty considering only the variances of the expansion coefficients differs from the reference. This result reveals that the covariances of the expansion coefficients are important to estimate the statistical uncertainty of the local flux in the flux distribution.

DOI： 10.1051/epjn/2025019

A deterministic transport calculation method of α-eigenvalue for non-multiplying system using framework of k-eigenvalue calculation Open Access

Yamamoto A., Tsujita K., Endo T.

Journal of Nuclear Science and Technology 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

A new α-eigenvalue calculation method for a non-multiplying system using the framework of conventional k-eigenvalue calculation of a deterministic transport code is proposed. The time-derivative or the time-absorption term in α-eigenvalue calculation is moved to the right-hand side of the transport equation and is considered as a virtual fission source. The present method is applied to a simple three-dimensional problem with the one-group cross-section and a small water tank system with the 252-group cross-section. The calculation results indicate that the present method provides accurate α-eigenvalue with rapid convergence and no numerical instability.

DOI： 10.1080/00223131.2025.2507866

Verification of in-core power distribution reconstruction based on POD for high-temperature gas-cooled reactors using ex-core detectors

Urase Y., Yamamoto A., Endo T.

Journal of Nuclear Science and Technology 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

A reconstruction method of in-core power distribution using the proper orthogonal decomposition (POD) and the signal from ex-core detectors is proposed. POD can efficiently reconstruct the in-core power distribution from a small number of constraints (i.e. detectors) by expressing the power (≈ neutron flux) distribution in terms of a small number of POD bases and expansion coefficients. The number of unknowns required to reconstruct the power distribution is reduced from the number of spatial meshes in the core calculation to the number of POD expansion coefficients. A new method using the linear regression is proposed to calculate the POD expansion coefficients in addition to the method based on the generalized inverse matrix. In this study, the applicability of the in-core power distribution reconstruction method based on the ex-core detector signals and POD is verified in a two-dimensional system simulating the High-Temperature Engineering Test Reactor (HTTR). As a result of the verification, it was confirmed that the in-core power distribution can be reconstructed with a limited number of ex-core detector signals. The influence of statistical errors in the detector signals was also evaluated, and the in-core power distribution can be appropriately reconstructed when the order of the detector counts is approximately less than 3%. The linear regression method was numerically more stable than the generalized inverse matrix method in calculating POD expansion coefficients.

DOI： 10.1080/00223131.2025.2533530

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

Endo T., Hirota R., Yamamoto A., Watanabe K., Wakabayashi G., Oda K., Kaneko J.H.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 2028 - 2037 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025

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 K<inf>eff</inf>-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 β<inf>eff/</inf>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

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

Hirota R., Endo T., Yamamoto A., Watanabe K., Wakabayashi G., Oda K., Kaneko J.H.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 2038 - 2047 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025

The reactor noise analysis method can measure the prompt neutron decay constant α 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 β<inf>eff</inf> are needed to estimate the reactivity in dollar units by conversion from the measured α value. To address the above-mentioned problem, this study aims to develop the estimation technique of the reactivity in dollar units ρ/β<inf>eff</inf>, 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 ρ/β<inf>eff</inf> 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).

DOI： 10.13182/MC25-46969

Fast Burnup Calculation Method Based on Neutron Spectrum Reconstruction with Proper Orthogonal Decomposition and Regression Model

Watanabe T., Aizawa N., Chiba G., Tada K., Yamamoto A.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 288 - 297 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025

A fast burnup calculation method based on neutron spectrum reconstruction using the proper orthogonal decomposition (POD) and regression model is studied. In this method, a large number of burnup-dependent multigroup neutron fluxes are prepared as snapshot data by detailed burnup calculations with randomly sampled parameter sets, such as fuel pin pitch and enrichment. Dimensionality reduction is applied to the neutron fluxes by POD and the regression models connecting the dimensionality-reduced neutron fluxes with the parameters are established. By substituting arbitrary input parameters into the regression models, the multigroup neutron flux is reconstructed and used to calculate one-group cross sections for burnup calculations. The above procedure performs burnup calculations with different sets of input parameters without calculating neutron spectra by neutron transport calculations at each burnup step. In this study, the feasibility of the method is examined by numerical calculations using a UO2 fuel pin-cell model of PWR. Results show that the nuclide inventories of randomly prepared target cases can be calculated with a prediction error of a few percent. The prediction error is dominated by the regression models in the present calculation condition.

DOI： 10.13182/MC25-46817

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

Haga A., Endo T., Yamamoto A., Chiba G.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 472 - 481 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025

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

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

Yamamoto A., Endo T.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025 page： 544 - 553 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering M and C 2025

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 and used in the UFG calculation in heterogeneous geometry to achieve short computation time. Verification developed 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

Sub-pin level distribution tallies and statistical error estimation with POD tallies in two-dimensional C5G7 benchmark

Kondo R., Yamamoto A., Endo T.

Journal of Nuclear Science and Technology 2025

Language：English Publishing type：Research paper (scientific journal) Publisher：Journal of Nuclear Science and Technology

The flux distribution tallies using proper orthogonal decomposition, called POD tallies, have been developed to address issues of high-fidelity Monte Carlo simulations. The POD tallies can reduce both dimensionality and statistical error. The present study verifies the applicability of the POD tallies to sub‑pin level flux distribution in the two‑dimensional C5G7 benchmark. Statistical error estimation is also proposed by applying the circular block bootstrap method to the POD tallies to estimate the statistical error of the flux distribution in a single Monte Carlo eigenvalue calculation. In the verification, the dimensionality of the finely discretized distribution is reduced by more than 90% compared with conventional cell tallies. The statistical error is reduced by more than half as the average value of all tally regions. It is confirmed that the statistical error of flux distribution can be properly estimated considering both the inter‑cycle correlation and the correlation between the expansion coefficients of different POD orders by the proposed approach.

DOI： 10.1080/00223131.2025.2554969

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