Award type：Award from publisher, newspaper, foundation, etc. 

Tomohiro Endo have been selected as one of the "Outstanding Reviewers" for the year of 2022 in recognition of your outstanding efforts, dedication and professionalism.

Country：Japan

Country：Japan

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

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

DOI： 10.1016/j.anucene.2018.10.032

Web of Science

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

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

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

DOI： 10.1080/00223131.2023.2231931

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

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

DOI： 10.1080/00223131.2019.1580625

Web of Science

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

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

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

DOI： 10.1080/00223131.2015.1034216

Web of Science

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

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

DOI： 10.1016/j.anucene.2011.01.007

Scopus

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

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

DOI： 10.1080/18811248.2007.9711368

Scopus

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

Reactor laboratory experiments are conducted in zero-powered research reactor facilities, at the University Teaching and Research Reactor (UTR in Kindai University: UTR-KINKI) and at Kyoto University Critical Assembly (KUCA), together with nuclear education through reactor physics experiments for university students. The experimental programs designed for undergraduate and graduate students at UTR-KINKI are classified into basic, intermediate, and advanced levels according to student coursework in subjects related to reactor physics and radiation detection; also developed is a curriculum of experimental programs to meet student needs. A new educational program is provided at KUCA, covering exponential experiments and uranium enrichment measurements. The range of the systematic development of programs for reactor laboratory experiments is extensive, covering reactor physics experiments and radiation detection. Notably, incorporating subcriticality measurements by the Feynman-α method in the UTR-KINKI core into the program offers outstanding opportunities for direct experience with measurement and data processing methods that involve critical approach monitoring of fuel debris. Introducing subcritical measurements is conducive to the fostering experts with an interest in criticality safety.

DOI： 10.1016/j.anucene.2024.110531

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

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

DOI： 10.1080/00295639.2023.2230414

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

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

DOI： 10.1080/00223131.2024.2341776

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

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

DOI： 10.1080/00223131.2023.2231462

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

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

DOI： 10.1080/00223131.2023.2244512

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

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

DOI： 10.1080/00223131.2023.2231464

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

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

DOI： 10.1080/00223131.2023.2203707

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

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

DOI： 10.1080/00223131.2023.2201603

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

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

DOI： 10.1080/00223131.2023.2204102

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

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

DOI： 10.1080/00223131.2023.2278600

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

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

DOI： 10.1080/00295639.2023.2246779

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

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

DOI： 10.1364/optcon.492445

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

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

DOI： 10.1080/00223131.2022.2138601

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

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

DOI： 10.1080/00223131.2022.2130463

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

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

DOI： 10.1080/00223131.2022.2097963

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

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

DOI： 10.1080/00223131.2022.2095051

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

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

DOI： 10.1080/00295639.2022.2087833

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

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

DOI： 10.1080/00295639.2022.2067447

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

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

DOI： 10.1080/00295639.2021.2025297

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

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

DOI： 10.1080/00295639.2021.1982549

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

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

DOI： 10.1080/00295639.2021.1968225

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

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

DOI： 10.1080/00223131.2021.1944930

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

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

DOI： 10.1080/00223131.2021.1940341

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

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

DOI： 10.1080/00223131.2021.1921631

Web of Science

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

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

DOI： 10.1080/00223131.2021.1902416

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

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

DOI： 10.1080/00295639.2020.1863066

Web of Science

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

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

DOI： 10.1080/00223131.2020.1814891

Web of Science

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

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

DOI： 10.1080/00295639.2020.1781482

Web of Science

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

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

DOI： 10.1080/00295639.2020.1774230

Web of Science

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

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

DOI： 10.1080/00223131.2020.1783382

Web of Science

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

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

DOI： 10.1016/j.anucene.2020.107614

Web of Science

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

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

DOI： 10.1016/j.anucene.2020.107493

Web of Science

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

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

DOI： 10.1016/j.anucene.2020.107341

Web of Science

Scopus

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

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

DOI： 10.1080/00295639.2020.1722512

Web of Science

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

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

DOI： 10.1080/00223131.2019.1709993

Web of Science

Scopus

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

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

DOI： 10.1080/00223131.2019.1699190

Web of Science

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

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

DOI： 10.1080/00223131.2019.1706658

Web of Science

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

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

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

DOI： 10.1080/00223131.2019.1700844

Web of Science

Scopus

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

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

DOI： 10.1080/00223131.2019.1647893

Web of Science

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

Useful and valuable measurement data obtained at the solid-moderated core for the development of accelerator-driven systems (ADSs) have been accumulated at the Kyoto University Critical Assembly (KUCA), and some of them have been open to the public. In order to efficiently utilize these data, experimental analyses with deterministic calculation procedures are helpful. In the present manuscript, a numerical benchmark problem is established. This benchmark problem can be utilized by users of the ADS-related measurement data obtained at the KUCA A-core to verify their own numerical tools devoted to experimental analyses. Material and geometrical specifications with reference solutions obtained by a continuous-energy Monte Carlo code MVP-II are provided.<br />
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In addition, numerical results obtained by a deterministic code system CBZ are also presented as an example. Through careful investigation about discretization on space and angle, guideline for proper discretization is provided. The CBZ results tend to underestimate the reference Monte Carlo solutions about 0.5%∆k/kk&#039;, and calculations of simplified core models suggest that this is caused by neutron leakage treatment in finite systems or resonance self-shielding treatment in CBZ.

DOI： 10.1080/00223131.2019.1647892

Web of Science

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

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

DOI： 10.1080/00223131.2019.1647895

Web of Science

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

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

DOI： 10.1080/00223131.2019.1666057

Web of Science

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

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

DOI： 10.1080/00295639.2019.1579514

Web of Science

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

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

DOI： 10.1080/00223131.2019.1618406

Web of Science

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

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

DOI： 10.1080/00223131.2019.1618405

Web of Science

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

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

DOI： 10.1080/00223131.2019.1598509

Web of Science

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

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

DOI： 10.1080/00295639.2018.1516961

Web of Science

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

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

DOI： 10.1016/j.anucene.2018.09.022

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

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

DOI： 10.1080/00295639.2018.1501978

Web of Science

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

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

DOI： 10.1080/00223131.2018.1513875

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

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

DOI： 10.1080/00223131.2018.1479988

Web of Science

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

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

DOI： 10.1080/00223131.2018.1432426

Scopus

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

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

DOI： 10.1080/00223131.2017.1403387

Research data storage URL： http://hdl.handle.net/2237/27279

Scopus

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

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

DOI： 10.1016/j.pnucene.2017.08.007

Scopus

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

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

DOI： 10.1016/j.net.2017.06.012

Scopus

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

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

DOI： 10.1016/j.net.2017.06.016

Web of Science

Scopus

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

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

DOI： 10.1016/j.anucene.2017.03.030

Scopus

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

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

DOI： 10.1080/00223131.2017.1299052

Scopus

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

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

DOI： 10.1080/00223131.2017.1286271

Scopus

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

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

DOI： 10.1080/00295639.2016.1273002

Scopus

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

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

DOI： 10.3139/124.110671

Scopus

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

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

DOI： 10.1080/00223131.2016.1202793

Scopus

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

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

DOI： 10.1080/00223131.2016.1171172

Research data storage URL： http://hdl.handle.net/2237/25272

Web of Science

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

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

DOI： 10.1080/00223131.2015.1127185

Scopus

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

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

DOI： 10.13182/NSE16-53

Scopus

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

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

DOI： 10.1080/00223131.2015.1113898

Research data storage URL： http://hdl.handle.net/2237/25270

Scopus

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

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

DOI： 10.13182/NSE15-102

Scopus

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

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

DOI： 10.13182/NSE14-152

Web of Science

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

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

DOI： 10.1080/00223131.2014.948520

Web of Science

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

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

DOI： 10.1080/00223131.2014.919882

Scopus

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

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

DOI： 10.1080/00223131.2014.903212

Scopus

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

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

DOI： 10.1080/00223131.2014.882801

Scopus

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

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

DOI： 10.1080/00223131.2014.864248

Scopus

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

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

DOI： 10.13182/NT13-7

Scopus

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

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

DOI： 10.1080/00223131.2013.820155

Web of Science

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

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

DOI： 10.1080/00223131.2013.807753

Scopus

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

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

DOI： 10.1080/00223131.2013.785271

Web of Science

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

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

DOI： 10.1080/00223131.2012.723174

Scopus

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

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

DOI： 10.1080/00223131.2012.693890

Scopus

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

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

DOI： 10.1080/00223131.2012.677126

Scopus

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

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

DOI： 10.1080/18811248.2011.9711837

Scopus

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

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

DOI： 10.1080/18811248.2011.9711792

Scopus

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

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

DOI： 10.13182/NSE10-50

Scopus

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

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

DOI： 10.1080/18811248.2011.9711707

Scopus

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

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

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

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

DOI： 10.1080/18811248.2011.9711698

Scopus

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

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

DOI： 10.1080/18811248.2011.9711700

Scopus

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

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

DOI： 10.5516/NET.2010.42.5.500

Web of Science

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

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

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

DOI： 10.1016/j.anucene.2007.09.014

Web of Science

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

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

DOI： 10.13182/NSE155-276

Web of Science

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

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

DOI： 10.1016/j.anucene.2006.09.010

Web of Science

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

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

DOI： 10.1016/j.anucene.2006.05.005

Web of Science

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

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

DOI： 10.1016/j.anucene.2006.02.002

Web of Science

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

DOI： 10.13182/T128-41580

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

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

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

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

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

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

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

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

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

DOI： 10.13182/T125-36787

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

DOI： 10.13182/T125-36788

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.

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

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

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

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

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

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

DOI： 10.13182/T124-35116

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

DOI： 10.13182/T124-35126

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

DOI： 10.13182/T124-35323

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

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

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

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

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.

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

DOI： 10.13182/T123-33367

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

DOI： 10.13182/T123-33370

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

DOI： 10.13182/T122-32047

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

DOI： 10.13182/T122-32039

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

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

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

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

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

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

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.

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

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

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

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

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

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

Authorship：Lead author   Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)   Publisher：Atomic Energy Society of Japan  

DOI： 10.3327/jaesjb.61.10_734

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.

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 &quot;time-domain decomposition based integral method (TDDI)&quot; 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 &quot;sandwich formula.&quot; 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.

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.

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.

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

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

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

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

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

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 &quot;measured&quot; 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 &quot;characteristics planes&quot; 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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

DOI： 10.11484/jaea-conf-2014-003

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

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

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 &quot;characteristics planes(CP)&quot; 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

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

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

DOI： 10.11484/jaea-conf-2014-003

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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 &quot;noise&quot; 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.

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.

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.

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.

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

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

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

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.

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

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

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

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.

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.

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

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

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

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

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

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.

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

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

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

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

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

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 &gt;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.

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.

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

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

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

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

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.

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

Event date： 2023.10

Language：English   Presentation type：Oral presentation (general)  

Venue：Sendai international center, Miyagi, Japan   Country：Japan  

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.

Event date： 2023.9

Language：English   Presentation type：Oral presentation (general)  

Venue：Nagoya University Higashiyama Campus   Country：Japan  

For efficient uncertainty quantification, we focused on a deterministic sampling method using the simplex ensemble. By combining the scaling method, we improved the deterministic sampling method so that the input parameters can be arbitrarily perturbed according to the user's purpose.

Event date： 2023.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：The University of Tokyo, Komaba Campus   Country：Japan  

When neutrons are detected under a near-critical condition, the probability distribution of neutron counts follows the Pál-Mogil'ner-Zolotukhin-Bell-Babala distribution. Based on the statistical property, we investigated whether criticality can be determined under a low neutron count rate condition.

Event date： 2022.9

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Online   Country：Japan  

This presentation will review our recent research about the applicability of the prompt neutron decay constant α to the data assimilation in order to reduce the nuclear data-induced uncertainty of the neutron multiplication factor keff for a target system.
In the field of reactor physics, the data assimilation has been effectively utilized to improve the accuracy and precision of numerically predicted core characteristics parameters and to update a priori nuclear data that are used as input parameters in the core analysis. For the data assimilation using the integral experiments, critical experimental results collected in databases such as the International Criticality Safety Benchmark Evaluation Project (ICSBEP) are often utilized. For the following reasons, we focus on the utilization of other integral experiments for the data assimilation process: (1) Construction of a new facility for critical experiments is not easy; (2) Because a typical experimental system (e.g., geometry and combination of fuel and other materials) for the critical experiment tends to be complicated, a simpler experimental system is desirable to effectively update the a posteriori target data based on the data assimilation technique.
One of the alternative integral experiments is the prompt neutron decay constant α, which corresponds to a time constant for the fundamental mode of exponential decay of prompt neutron flux. Even not only for the subcritical system with fissile nuclides but also for the non-neutron multiplication system without any fissile nuclide, the α value can be directly measured using the pulsed neutron source method or reactor noise analysis method (e.g., Rossi-α or Feynman-α methods).
As the improvement of the measurement technique for the fundamental mode of α value, we clarified that the robust estimation of the α value can be achieved by applying dynamic mode decomposition to the time series data (e.g., time histograms of the pulsed neutron and Rossi-α methods) measured by the multiple neutron detectors.
Furthermore, in order to accomplish the data assimilation using the α value, we developed the efficient sensitivity analysis of α based on the first-order perturbation theory. In this presentation, we will present application examples of the data assimilation of α using the sensitivity coefficients and covariance matrix of nuclear data.

Event date： 2022.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Ibaraki University on Hitachi Campus   Country：Japan  

In order to robustly estimate the reactivity using the inverse kinetics method in a case where the neutron generation time for the target system has a large uncertainty and the outliers in the input signal of neutron counts are exists, the following studies are investigated: (1) improvement of the “Simplest Reactivity Estimator (SRE)” without explicitly using the neutron generation time, and (2) the application of the median filter to the input signal.

Event date： 2022.9

Language：Japanese   Presentation type：Oral presentation (invited, special)  

Venue：Ibaraki University on Hitachi Campus   Country：Japan  

Event date： 2022.5

Language：English   Presentation type：Oral presentation (general)  

Venue：Pittsburgh, PA   Country：United States  

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.

Event date： 2022.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Online   Country：Japan  

For the training of human resources in the future nuclear industry, an advanced educational program for the reactor physics experiments is newly developed by utilizing the Japanese educational reactor (UTR-KINKI) with recent radiation measurement techniques. In this presentation, the overview of this educational program will be explained. This program is supported by global nuclear human resource development initiative by MEXT.

Event date： 2021.10

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Virtual Meeting   Country：United States  

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.

Other Link： https://doi.org/10.13182/M&C21-33627

Event date： 2021.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Online   Country：Japan  

As the neutron count rates and/or the total measurement time of the reactor noise increases, the total number of detection data becomes huge. Thereby, it is difficult to straightforwardly apply the reactor noise analysis method to all of the detection data. Furthermore, the statistical uncertainty quantification for such a reactor noise analysis is a challenging issue. To address this issue, we investigate the practical method for the Rossi-α method with dynamic mode decomposition to estimate the statistical uncertainty using the bootstrap method, where many resamples are virtually generated from divided binary files of detection data.

Event date： 2021.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Online   Country：Japan  

Event date： 2021.6

Language：English   Presentation type：Oral presentation (general)  

Venue：zoom   Country：United States  

The present study developed an in-house code of a deterministic α-eigenvalue calculation code for a non-neutron-multiplication system such as a water-only system. Besides, sensitivity analysis of α with respect to nuclear data was carried out based on the first-order perturbation theory.

Other Link： https://doi.org/10.13182/T124-35323

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Online   Country：Japan  

To quantify the nuclear data-induced uncertainty of prompt neutron decay constant α for a non-neutron multiplication system, we developed an inhouse calculation code using SN method and power iteration. Based on the first-order perturbation theory, sensitivity analysis and uncertainty quantification of α with respect to nuclear data were carried out for pulsed neutron source experiments, which were conducted for water tank systems in the following study: https://doi.org/10.1080/18811248.1966.9732325

Event date： 2020.11

Language：English   Presentation type：Oral presentation (general)  

Venue：zoom   Country：United States  

This study aims to apply the unscented Kalman filter (UKF) to the subcriticality monitoring for a subcritical system where multi state-parameters (e.g., subcriticality −ρ, external neutron source strength S, and point kinetics parameters Λ and βeff) can vary in time.

Other Link： https://doi.org/10.13182/T123-33367

Event date： 2020.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Online   Country：Japan  

To discuss whether the prompt neutron decay constant α can be estimated from measured time-series data of gamma-ray counts, we derived the theoretical formula of Feynman-α method based on the neutron-photon coupling probability generating function (PGF) equations. As a result, it is confirmed that the conventional theoretical formula should be modified by adding the constant background component because the detected gamma-rays have additional correlation due to the multiplicities of photon-sources and the photo-atomic reactions. By fitting the derived theoretical formula to virtual reactor noise data (time-series data of Compton scattering counts) using the PHITS code, we try estimating the prompt neutron decay constant.

Event date： 2020.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Fukushima University   Country：Japan  

A transient experiment due to reactivity- and source-changes was carried out at the Kyoto University Criticality Assembly (KUCA) with the DT accelerator neutron source. To estimate the subcriticality in this source-driven subcritical system, we aim to apply the unscented Kalman filter (UKF) to the time-series data of neutron count measured at KUCA.

Event date： 2019.12

Language：English   Presentation type：Oral presentation (general)  

Venue：Osaka, Japan   Country：Japan  

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.

Event date： 2019.9

Language：English   Presentation type：Oral presentation (general)  

Venue：Paris, France   Country：France  

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.

Event date： 2019.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：University of Toyama, Gofuku Campus   Country：Japan  

For a Cf-252 spontaneous fission source surrounded by the polyethylene reflector, a reactor noise experiment was carried out for a non-multiplication system, using a special Transparent RUbber SheeT type Eu:LiCAF (TRUST Eu:LiCAF) detector, which is relatively small and has a high geometrical detection efficiency. By the third-order neutron correlation technique with the moving block bootstrap method, it was demonstrated that the statistically significant difference from the unique combination number "3" could be actually observed.

Event date： 2019.8

Language：English   Presentation type：Oral presentation (general)  

Venue：Portland, Oregon, USA   Country：United States  

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.

Event date： 2019.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Iraraki University, Mito Campus   Country：Japan  

By utilizing the Feynman-α method with the bootstrap method, the prompt neutron decay constant α and the experimental error were measured at the Kyoto University Critical Assembly (KUCA) in the shutdown state. On the basis of data assimilation techniques such as the bias factor and cross-section adjustment methods using (1) the measurement value of α and (2) sensitivity coefficients of α and keff that were estimated by the first-order perturbation theory, we try reducing the nuclear-data-induced uncertainty of predicted keff for another KUCA experimental core.

Event date： 2018.11

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Kyoto University Institute for Integrated Radiation and Nuclear Science   Country：Japan  

The Feynman-α method using the bootstrap method is improved to estimate experimental covariance of the second order neutron-correlation factor Y(T) due to the bunching method.

Event date： 2018.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Okayama University, Tsushima Campus   Country：Japan  

In this study, the prompt neutron decay constant α is numerically estimated using the Sn neutron transport code PARTISN for the Godiva experimental benchmark (HEU-MET-FAST-001), where the α value at critical state is measured by the Rossi-α method. Furthermore, the relative sensitivity coefficients of α to nuclear data are evaluated on the basis of the first-order perturbation theory, followed by the nuclear data-induced uncertainty quantification of α with SCALE6.2 covariance data (252groupcov7.1).

Event date： 2018.4

Language：English   Presentation type：Oral presentation (general)  

Venue：Cancun, Mexico   Country：Mexico  

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.

Event date： 2018.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Osaka University, Suita Campus   Country：Japan  

For the data assimilation using subcritical experiment, we investigate (a) bias factor method using random The prompt neutron decay constant α can be measured by subcritical experiments such as the reactor noise analysis and the pulsed neutron source method. For the uncertainty quantification of α and for the data assimilation using α, the sensitivity analysis method for the prompt neutron decay constant is newly developed using the first order perturbation theory, which utilizes the adjoint eigenfunction of ω-eigenvalue calculation.

Event date： 2017.11

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Research Reactor Institute, Kyoto University   Country：Japan  

For any step-wise transient of (−ρ, βeff, Λ, S), the subcriticality in dollar units can be approximately measured using the integral and the extrapolation methods. Note that the estimated subcriticality depends on the spatial position of neutron detector.

Event date： 2017.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Hokkaido University   Country：Japan  

For the data assimilation using subcritical experiment, we investigate (a) bias factor method using random sampling technique and (b) Bayesian inference using likelihood function. Using measurement results of prompt neutron decay constant α, we try to reduce nuclear data-induced uncertainties of core characteristics parameters (effective neutron multiplication factor, neutron generation time and effective delayed neutron fraction) in the Pi-Bi loaded ADS benchmark problems at the Kyoto University Critical Assembly (KUCA).

Event date： 2017.4

Language：English   Presentation type：Oral presentation (general)  

Venue：Fukui and Kyoto, Japan   Country：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.

Event date： 2017.4

Language：English   Presentation type：Oral presentation (general)  

Venue：Jeju, Korea   Country：Korea, Republic of  

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.

Event date： 2017.4

Language：English   Presentation type：Oral presentation (general)  

Venue：Jeju, Korea   Country：Korea, Republic of  

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.

Event date： 2017.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Tokai University, Shonan Campus   Country：Japan  

In the subcriticality measurement for the accelerator-driven system (ADS), prompt neutron decay constant and area ratio are measured using the pulsed neutron method. In this study, the numerical analysis methods for the prompt neutron decay constant and the area ratio are investigated using the deterministic method.

Event date： 2016.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Kurume City Plaza   Country：Japan  

これまでの研究において、モンテカルロ法に基づいた固有値計算で推定される統計誤差について、その統計誤差過小評価割合を評価するための理論式を導出した。この統計誤差過小評価割合を評価するためには、λモード固有値方程式の高次モードが必要である。本研究では、固有値が縮退したforward/adjoint固有関数についても正規直交条件を満足するような、多群拡散計算に基づいた高次モード計算コードを開発した。

Event date： 2016.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Tohoku University, Kawauchi Campu   Country：Japan  

Applicability of the bootstrap method is investigated to estimate the statistical error, i.e. confidence interval, of the third order neutron-correlation technique using only a single measurement of reactor noise. Through a numerical experiment which virtually simulates the reactor noise experiment, we verify the coverage probability of the estimated confidence interval.

Event date： 2015.11

Language：English   Presentation type：Oral presentation (general)  

Country：United States  

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

Event date： 2015.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Shizuoka University, Shizuoka Campus   Country：Japan  

面積比法の実験で測定される"面積比"について、検出中性子増倍率kdetに基づいて面積比の理論式を導出し、keff固有値方程式の固有関数との関係を明らかにした。京都大学臨界集合体実験装置(KUCA)で過去に実施したDT中性子源を用いた面積比法実験を解析することで、kdet≒keffとなる位置に検出器を配置することで、数値解析による空間補正効果の少ない、ロバストな面積比法実験が可能であることを見出した。

Event date： 2015.7

Language：English   Presentation type：Oral presentation (general)  

Venue：Research Reactor Institute, Kyoto University   Country：Japan  

Event date： 2015.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Ibaraki University, Hitachi Campus   Country：Japan  

4ループPWR平衡炉心を対象として、ランダムサンプリング法に基づいたバイアス因子法について検討した。

Event date： 2014.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Research Reactor Institute, Kyoto University   Country：Japan  

Event date： 2014.11

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Conference hall, Hokkaido University   Country：Japan  

Event date： 2014.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Disneyland Hotel Anaheim, CA   Country：United States  

Event date： 2014.9 - 2014.10

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2014.9 - 2014.10

Language：English   Presentation type：Oral presentation (general)  

Venue：The Westin Miyako Kyoto Hotel, Kyoto   Country：Japan  

DOI： 10.11484/jaea-conf-2014-003

Event date： 2014.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Kyoto University, Yoshida Campus   Country：Japan  

ランダムサンプリング法に基づいた不確かさ定量評価の統計誤差(信頼区間)の推定方法として、ブートストラップ法の適用可能性について検討を行った。

Event date： 2014.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Tokyo City University, Setagaya Campus   Country：Japan  

分散対平均法に対してブートストラップ法を適用することで、1回の時系列データ測定から求められた二次相関量Y値および即発減衰定数αの統計誤差を推定することが可能かどうか、京都大学臨界集合体実験装置(KUCA)にて未臨界炉雑音実験を実施し検証を行った。

Event date： 2013.12

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Research Reactor Institute, Kyoto University   Country：Japan  

Event date： 2013.4

Language：English   Presentation type：Oral presentation (general)  

Venue：Lotte Hotel Jeju, Jeju Island   Country：Korea, Republic of  

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.

Event date： 2013.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Kindai University, Higashi Osaka Campus   Country：Japan  

DOI： 10.11561/aesj.2013s.0.144.0

Other Link： http://www.aesj.or.jp/meeting/2013s/j/13Spr_program17-41.pdf#page=14

Event date： 2012.11

Language：English   Presentation type：Oral presentation (general)  

Venue：Town & Country Hotel & Resort, San Diego, CA   Country：United States  

Event date： 2012.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Hiroshima University, Higashi-Hiroshima campus   Country：Japan  

DOI： 10.11561/aesj.2012f.0.155.0

Other Link： http://www.aesj.or.jp/meeting/2012f/j/12Fall_program16-43.pdf#page=27

Event date： 2012.4

Language：English   Presentation type：Oral presentation (general)  

Venue：Knoxville Convention Centor, Knoxville, TN   Country：United States  

Average burnup of damaged fuels loaded in Fukushima Dai-ichi reactors is estimated, using the Cs134/Cs137 ratio method for measured radioactivities of Cs134 and Cs137 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 134Cs/137Cs 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.

Event date： 2012.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：University of Fukui, Bunkyo Campus   Country：Japan  

Cs134/Cs137放射能比法を用いることにより、事故時に環境中に放出されたCs134,Cs137の放射能比の実測値から、原子炉内破損燃料の燃焼度を逆推定することができる。このように逆推定された燃焼度を活用することによって、炉内破損燃料の同位体組成比を評価することができ、環境中に放出された放射性核種の同位体比の推定や、燃料デブリ取出作業時の燃焼度クレジットの適用に資することができる。 本発表では、文部科学省の「放射線量等分布マップの作成プロジェクト」により得られたCs134,Cs137土壌濃度マップの測定結果に基づいて、Cs134/Cs137放射能比法により福島第一原子力発電所1～3号機破損燃料の燃焼度推定を行う。こうして推定された燃焼度に対して、原子炉内の燃焼度分布がどのような影響を与えるのか、Cs133,Cs134,Cs137の燃焼度方程式に基づいて理論的な考察を行う

DOI： 10.11561/aesj.2012s.0.138.0

Other Link： http://www.aesj.or.jp/meeting/2012s/j/12Spr_program18-44.pdf#page=6

Event date： 2011.11

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Techno Plaza Ricotti ,Tokai-mura, Ibaraki-ken   Country：Japan  

Average burnup of damaged fuels loaded in Fukushima Dai-ichi reactors is estimated by using the Cs134/Cs137 ratio method for actually measured radioactivities of Cs134 and Cs137 in contaminated soils within the range of 100 km from the Fukushima Dai-ichi nuclear power plants. The numerical analysis of radioactivity ratio of Cs134/Cs137 is carried out by two deterministic codes (SRAC2006/PIJ, SCALE6.0/TRITON) and a Monte Carlo code (MVP-BURN). Moreover, the void fraction effect for Cs134/Cs137 ratio is also investigated with two recent evaluated nuclear data libraries (JENDL-4.0, ENDF-B/VII.0). As a result, the measured Cs134/Cs137 ratio from the contaminated soil is 0.996±0.07 as of March 11th, 2011. By using the Cs134/Cs137 ratio method, the estimated burnup of Fukushima Dai-ichi units 1, 2, and 3 is approximately 17.2±1.5 [GWd/t] in the present research.

Event date： 2011.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Kitakyushu International Conference Center   Country：Japan  

DOI： 10.11561/aesj.2011f.0.173.0

Other Link： http://www.aesj.or.jp/meeting/2011f/j/11Fall_program16-45.pdf#page=25

Event date： 2011.6

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：The Westin Diplomat Resort and Spa, Hollywood, Florida   Country：United States  

Event date： 2011.5

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：O2 Resort, Taebaek   Country：Korea, Republic of  

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.

Event date： 2010.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：Hokkaido University   Country：Japan  

DOI： 10.11561/aesj.2010f.0.205.0

Other Link： http://www.aesj.or.jp/meeting/2010f/j/10Fall_program16-50.pdf#page=35

Event date： 2009.11

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Omni Shoreham Hotel, Washington D.C.   Country：United States  

Event date： 2009.9

Language：English   Presentation type：Oral presentation (general)  

Venue：Richland, Washington   Country：United States  

Event date： 2008.9