Characteristics of neutron diffusion coefficient as a function of energy group in the one-dimensional multi-group diffusion equation of finite slab reactor core

Abstract

One of the most straightforward approaches that widely used to solve the neutron transport equation is the diffusion equation approach. The diffusion equation describes the individual behavior of the average neutron trajectory when interacting with matter. Usually, the neutron diffusion equation is obtained under the assumption that scattering is isotropic in the laboratory system of coordinates, and neutrons have the same energy and region is homogeneous; this called a one-speed diffusion equation. It leads to the diffusion coefficient to be independent of the spatial position; the volume of the reactor is constant, and the number density of the fuel atoms is also relatively constant. In this study, multi-group neutron diffusion characteristics were introduced in two ways. First, they vary with energy in the finite slab reactor core using a one-dimensional multi-group diffusion equation with the Gauss-Seidel iteration method. Second, using Fick’s law directly. The study used macroscopic cross-sections in the U-PuN fuel cell level as initial input for 70 energy groups. The data library used is JFS-3-J33 for 70 energy groups, which is the library data of SLAROM computer codes from JAEA Japan. The first way indicates the diffusion coefficient characteristics of U-235 and Pu-239 fuel isotopes firmly have the same pattern in each group energy. They have fluctuations throughout the fast, intermediate, and thermal energy group regions because both isotopes are fertile material. On the other hand, the diffusion coefficient of U-238 fuels isotope tends to be stable in each energy group. This event occurs because the isotope of U-238 is natural uranium, which is included as a fertile material. The second way shows the diffusion coefficients characteristics of the nuclear fuel isotopes firmly have the same pattern in each energy group, especially in the fast and thermal energy group region. They have fluctuations only throughout the intermediate energy group regions because, in this area, there is a resonant region.