The method of characteristics applied to solving slowing down equation to estimate the self-shielded resonance cross sections with an explicit geometrical effect

Abstract

The conventional resonance treatment in the transport lattice codes requires resonance integral tables in which resonance integrals are tabulated as a function of the background cross sections to be a measure of dilution. Typically self-shielded resonance cross sections in the resonance integral table are generated by performing slowing down calculations with point-wise cross sections defined on an ultra fine energy grid for one-dimensional cylindrical pin cells. Collision probability, interface current method and discrete ordinate method have been used for the one-dimensional cylindrical slowing down calculations. These resonance integral tables are to be used in estimating the self-shielded resonance cross sections for the rectangular or hexagonal pin cells, which results in a reactivity difference due to the geometrical effect on the effective resonance cross sections. In order to improve this problem, the method of characteristics has been applied to the slowing down calculations for two-dimensional square pin cells. The geometrical effect on the reactivity has been quantitatively analyzed by using the Monte Carlo code MCNP and the transport lattice code KARMA. The method of characteristics has been implemented into the MERIT code developed at KAERI for slowing down calculations. The computation results show that the reactivity differences and the discrepancies of the effective resonance cross sections due to the geometrical inconsistency could be significantly improved by using the method of characteristics.