Higher harmonic analyses of the [252]Cf source driven noise analysis method

Abstract

A theoretical formula has been derived to reconstruct the ratio of spectral densities in the [252]Cf source driven noise analysis (CSDNA) method from the higher harmonic eigenvalues and eigenfunctions of the α-mode neutron transport equations. The formula closely reproduces each power spectral density and the ratio of spectral densities calculated by Monte Carlo simulations, thereby verifying the theoretical formula. The reactivity or k{eff} of a subcritical system is related to the ratio of spectral densities by the fundamental mode approximation in which the higher harmonic modes are neglected. However, the ratio of spectral densities measured in the CSDNA method yields an ambiguous reactivity or k{eff} that depends on the locations of detectors due to the effect of the higher harmonics. A more elaborate method developed by Mihalczo and Valentine et al. infers an “experimental” k{eff} using a measurement and accurate Monte Carlo simulation of CSDNA. This paper discusses the uniqueness of the inferred "experimental" k{eff}.