Higher order mode analyses of power spectral density and Feynman-α method in accelerator driven system with periodically pulsed spallation neutron source

This paper deals with the theory of higher order modes in the Feynman Y function and the cross power spectral density (CPSD) in an accelerator-driven system (ADS) where pulsed spallation neutrons are injected at a constant frequency. A theoretical formula that considers the effect of higher order modes of the correlated and uncorrelated components in the Feynman Y function for an ADS is newly derived in this paper. Although the formula for the correlated and uncorrelated components of a CPSD was derived in a recent publication of the author of this paper, the verification has not been done yet. These formulae for the Feynman Y function and CPSD are applied to a subcritical multiplying system with a one-dimensional infinite slab geometry. The Feynman Y functions and CPSD calculated with the theoretical formulae are compared with the Monte Carlo simulations of these noise techniques. The theoretical formulae reproduce the Monte Carlo simulations very well, thereby substantiating the theoretical formulae derived in this paper. The correlated and uncorrelated components of the Feynman Y functions and CPSD are decomposed into the sum of the fundamental mode and other higher order modes. The higher order mode effect in the uncorrelated component is much more significant than in the correlated component.