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

•The Cf-252 source driven noise analysis (CSDNA) method is investigated.•A rigorous formula including higher harmonics effect is derived.•The formula is verified by comparison with a Monte Carlo simulation.•How to obtain keff from the CSDNA method is discussed.

A theoretical formula has been derived to reconstruct the ratio of spectral densities in the 252Cf 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 keff 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 keff 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” keff using a measurement and accurate Monte Carlo simulation of CSDNA. This paper discusses the uniqueness of the inferred “experimental” keff.