Higher order mode analyses in Feynman-α method

Using a generalized formula for the space and energy dependent Feynman-α method, which was originally derived by Endo et al. and Muñoz-Cobo et al., the effect of higher order modes of the α-mode eigenvalue problem on the Feynman Y function has been investigated. To deal with a large number of higher order modes, the diffusion approximation is adopted instead of the transport theory for a one-dimensional homogeneous infinite slab. By making a transport correction to low order mode eigenvalues and eigenfunctions, the formula can accurately reproduce the Monte Carlo simulation results of the Feynman-α method. By virtue of these efforts, an accurate numerical application of the generalized formula, which has not been performed due to the difficulty in solving the higher order α-mode eigenvalue problem, has been made possible. Sample numerical examples for a near-critical system and a deeply-subcritical system quantitatively demonstrate how the Feynman Y functions are decomposed into the higher order mode components. While the higher order mode components in the Feynman Y function can be negligible in a near-critical system, the Feynman Y function in a deeply-subcritical system is found to be severely contaminated by the higher order modes.

► A higher order mode effect on the Feynman Y function has been investigated. ► A generalized space and energy dependent Feynman-a formula is used for this study. ► To deal with a large number of higher order modes, the diffusion approximation is adopted. ► By transport corrections, the formula can accurately reproduce Monte Carlo simulation results. ► An accurate numerical application of the generalized formula has been made possible.