Satoru Katsuragi

Higher Order Perturbation Method in Reactor Calculation

The higher order perturbation theory is applied to the one-dimensional multi-group diffusion equation. The method of calculating the eigenvalue, eigenfunction and adjoint function of the higher mode is established for a non-Hermetian matrix. The diffusion equation is solved by the higher order perturbation method, through the use of the eigenvalues, eigenfunctions and adjoint functions of the higher modes. The newly developed method is applied to the estimation of reactivity effect in a reactor.

A Method of Calculation of Detailed Power Distribution in Fuel Assemblies

Abstract A method has been developed that effectively estimates the detailed distribution of power generation in the fuel or blanket assemblies in nuclear reactors. A two-dimensional, one-group diffusion model is applied to a region of homogeneous composition enclosed in a contour devoid of concavity viewed from outside. The diffusion equation is reduced to the form of Helmholtz equation, and a non-homogeneous boundary condition of Dirichlet or Neumann type is given on the contour, using neutron fluxes previously obtained in coarse mesh diffusion criticality calculations covering the whole reactor. This boundary value problem in two-dimensional space is made to yield a solution in the form of a potential due to a single or double layer. The method is applied to a hexagonal cell of a fast reactor. The results of calculation are amply accurate in comparison with the corresponding values from the usual fine-mesh diffusion scheme and with much shorter computing time.

Transport solutions for multilayer slab-cell systems

Abstract Cases method is applied to one-speed neutron-transport problems in multiplayer slab cells. A set of singular integral equations for the eigen-function-expansion coefficients of the angular neutron flux is derived, and two methods of solution suitable for numerical calculation are presented. In the first method the solution of the Hilbert problem is obtained in the form of power series for a coupling parameter. In the second method the singular integral equations are reduced to a set of Fred Holms integral equations. The numerical results are given.

EXPERIMENTAL AND THEORETICAL STUDIES OF HEAVY-WATER HOMOGENEOUS TWO-REGION SYSTEM

A series of critical experiments and theoretical analyses has been made on two-region systems in which a heavy water solution of uranyl sulfate with 235U enrichment of about 20% is surrounded by heavy water, poisoned with B or mixed with ThO2. D-to-235U atomic ratios in the core solutions ranged 4,500–1,000, depending on the core diameter and the blanket concentration. The theoretical effective multiplication factor is decreased by treating the leakage of fast neutrons from the core rigorously, and is increased by using spatial-dependent effective cross sections. These treatments are justified by the agreement found between the calculated and measured values for the Cd ratio and the thermal flux distribution. The disagreement seen in the effective multiplication factor between the theoretical and experimental values may be attributed to uncertainty in the resonance integral of 235U. The discrepancy in the effective multiplication factors does not exceed 1%, when the accepted value of νI f -I a is reduced ...