Takanori Kitada

Effective Convergence of Fission Source Distribution in Monte Carlo Simulation

The effective technique to accelerate the convergence of a fission source distribution in a Monte Carlo simulation is proposed as an application of a fission matrix. It is found that this acceleration method is especially useful for large core analysis where the fission source distribution is slowly converged in a Monte Carlo simulation by the source iteration method. It is found that the number of inactive cycles can be automatically determined and reduced by the acceleration method in this investigation.

Sensitivity Analysis based on Transport Theory

To estimate the uncertainty of the neutronic parameters it is required to calculate sensitivity coefficients to cross section changes. The sensitivity coefficients are usually calculated based on the diffusion theory. However, the accuracy of the sensitivity coefficients becomes doubtful because of the use of diffusion theory. The purpose of this paper is to derive the generalized perturbation theory using the transport theory, and to evaluate transport effect on the sensitivity coefficients. Sensitivity calculations were performed in 70 energy groups. The calculated sensitivity coefficients were compared with those obtained from direct transport calculations to check the accuracy of the present method, and those obtained from the generalized perturbation calculation based on the diffusion theory to investigate the transport effect on sensitivity coefficients. From the comparison, the difference was remarkably large for the neutronic parameters such as reaction rate distribution, reaction rate ratio, and reactivity worth. For example, the sensitivity coefficient of the 238U capture to 239Pu fission rate ratio in the lower core region of the under-moderated LWR core was large in the energy range 17.6–22.6 eV, and the sensitivity to 238U capture cross section calculated by the transport theory was 20% larger than that by the diffusion theory.

Evaluation of Eigenvalue Separation by the Monte Carlo Method

A new technique for evaluating an eigenvalue separation by the Monte Carlo method is proposed. This technique uses a fission matrix evaluated by an ordinary Monte Carlo calculation and enables us to evaluate higher order eigenvalues and eigenvectors that have not been able to be determined by Monte Carlo calculation. To validate it, the proposed technique was applied to the analysis of the modeled BWR core and the coupled-core reactor assembled at the C-core tank of KUCA (Kyoto University Critical Assembly). Consequently, it was found that this new technique gave good results regarding eigenvalue separation, although regional division needs to be noted in a system for evaluating a fission matrix.

Analysis of First-Harmonic Eigenvalue Separation Experiments on KUCA Coupled-Core

The first-harmonic eigenvalue separation, the difference between the fundamental and the first order eigen-values of the higher harmonic neutron transport equations, which were measured at the Kyoto University Critical Assembly (KUCA) has been analyzed. A method was proposed to calculate the first order eigenvalue based on the discrete ordinate method. The 3-D effect, energy group effect, mesh size effect, and transport effect were investigated. Among these effects, the transport effect was significant and when it was taken into account, the calculated eigenvalue separation approached the measured value on the KUCA coupled-core.

Prediction Accuracy Improvement of Neutronic Characteristics of a Breeding Light Water Reactor Core by Extended Bias Factor Methods with Use of FCA-XXII-1 Critical Experiments

Two extended bias factor methods, the LC and PE methods, were applied to the prediction accuracy evaluation of neutronic characteristics of a breeding light water reactor, using data of FCA-XXII-1 critical experiments, in order to investigate the features and effectiveness of these methods on the basis of an actual core design and existing experimental results. The present study confirms the following features of these methods. Both the LC and PE methods can improve the prediction accuracy the most when all the experimental results are used. The prediction accuracy improvement is achieved mainly by reducing uncertainty due to errors in cross sections. This is done by realizing a profile of sensitivity coefficients closer to that of the target core and suppressing the influence of errors in experiments and experimental analysis methods. The PE method always improves the prediction accuracy with the use of any combination of experimental results. It is always superior to the LC method in the improvement of the prediction accuracy. Concerning the effectiveness of using the extended bias factor methods with the data of FCA XXII-1 critical experiments, it is concluded that the experimental results regarding multiplication factor are more effective than the other experimental results, namely, reaction rate ratios of 238U capture to 239Pu fission (C28/F49) and void reactivity, in reducing prediction uncertainties of all the neutronic characteristics of the target core investigated: the multiplication factor, the C28/F49, and the void reactivity of the target core. This is due to the fact that the extended bias factor methods cannot fully utilize the potential that these experimental results have for the reduction of the uncertainties due to the errors in cross sections because of their strong correlations to the target core characteristics. This failure is due to large errors in the experiments and/or the experimental analysis methods.

Development of efficient Krylov preconditioning techniques for multi-dimensional method of characteristics

Two techniques are proposed in the preconditioning for the Krylov sub-space method called the Generalized Minimal RESidual (GMRES) method to accelerate inner iterations based on the method of characteristics (MOC). The GMRES method is an iterative method to solve a linear algebraic system byminimizing the norm of the residual vector. The proposed preconditioning technique is based on the first flight collision probability which is efficiently made by the multi-dimensional MOC code. To simplify the preconditioner, slight couplings among regions are ignored by considering the mean free path. And another proposed technique makes simplified preconditioner by the scaling matrix which can homogenize and de-homogenize the fuel region and the cladding region. The scaling technique reduces the size of the matrix and also reduces the calculation time of inverse matrix. Numerical results show that the preconditioner simplified by the mean free path efficiently reduces the number of iterations for the GMRES algorithm. And the scaling technique keeps the efficiency of preconditioner even in the multi-dimensional geometry. The total calculation time is found to be reduced when these techniques are employed.

Direction and Region Dependent Cross Sections for Use to MOX Fuel Analysis

When the continuous energy transport equation is integrated over an energy interval, the total cross section for the energy group becomes region and angular dependent, because the angular dependent neutron flux must be used as a weight. Usually the angular dependence is neglected. We investigate the approximation, and show that the error is proportional to the product of the neutron current and the difference between the flux weighted total cross section and the current weighted total cross section. The formulation of angular dependent cross section is derived in 1-dimensional slab geometry based on the multiband method. The numerical results are shown for UO2 and MOX fueled cells.

Measurement and analysis of capture reaction rate of 237Np in various thermal neutron fields by critical assembly and heavy water thermal neutron facility of Kyoto University

Abstract Capture reaction rate ratios of 237Np relative to 197Au were measured in 11 thermal neutron fields provided by the Kyoto University Critical Assembly and the Kyoto University Reactor Heavy Water Neutron Irradiation Facility. In the measurement, both samples of 237Np and 197Au were irradiated at the same time, and their gamma activities were measured. The typical experimental error was 3.5%. The analysis was performed by three steps: full-core calculation, self-shielding correction of the sample, and perturbation correction of the sample. Three full-core calculations by a continuous-energy Monte Carlo code (MVP), a transport code (TWOTRAN), and a diffusion code (CITATION) were made with the JENDL-3.2 library. The self-shielding factors were derived by an analytical formula, and the perturbation factors were calculated by another MVP calculation. The reaction rates were derived by multiplying the neutron spectrum, the two correction factors, and the capture cross sections of 237Np and 197Au. As a result, the three full-core calculations provided almost the same neutron spectra at the sample position and gave almost the same calculated-to-experimental values (C/Es) for the capture reaction rate ratios of 237Np relative to 197Au. Based on the capture cross section of 237Np taken from the JENDL-3.2 library, the C/Es were between 0.97 and 1.04, and the average C/E among the 11 cores was 1.01. On the other hand, the C/Es using the ENDF/B-VI and the JEF-2.2 were 1.02 to 1.06 for harder spectrum cores, whereas the C/Es for the softer spectrum cores were 1.08 to 1.16. It is concluded that the JENDL-3.2 library has good accuracy for the capture cross section of 237Np but the ENDF/B-VI and the JEF-2.2 libraries overestimate that of 237Np >10% in the thermal neutron energy region.

Rapid estimation of core-power ratio in coupled-core system by rod drop method

To determine rapidly the core-power ratio in a coupled-core system, a method is proposed on the basis of the control rod drop experiment. A formula of an asymmetrical two-point version was derived to deduce the core-power ratio and subcriticalities of the individual cores. It requires only a familiar measurement technique and tools for the conventional rod drop experiment to apply this formula for the purpose of obtaining these quantities. The present method was applied to the rod drop data measured in coupled-core systems, where the core-power ratio sensitively depended on the rod patterns. The validity of the proposed method was experimentally demonstrated through the comparison between the measured core-power ratios obtained by the present method and that derived from the flux distribution measurement.

Dimension-reduced cross-section adjustment method based on minimum variance unbiased estimation

ABSTRACT A new formulation of the cross-section adjustment methodology with the dimensionality-reduction technique has been derived in the light of the fact that it is often used under the condition of ill-posed problem, where the number of integral experimental quantities is less than the number of adjusted nuclear data parameters. This new formulation is proposed as the dimension-reduced conventional cross-section adjustment method (DRCA). The derivation of DRCA is based on the minimum variance unbiased estimation (MVUE), and the assumption of normal distribution is not used. The result of DRCA depends on a user-defined matrix that determines the dimension-reduced feature subspace. We examined three variations of DRCA, namely, DRCA1, DRCA2, and DRCA3, which employ (1) the nuclear data covariance matrix as the user-defined matrix, (2) the sensitivity coefficient matrix postmultiplied by the nuclear data covariance matrix, and (3) the sensitivity coefficient matrix, respectively. Mathematical investigation and numerical verification revealed that DRCA2 is equivalent to the currently widely used cross-section adjustment method. Moreover, DRCA3 is found to be identical to the cross-section adjustment method based on MVUE, which has been proposed in the previous study.