The role of the eigenvalue separation in reactor dynamics and neutron noise theory

Abstract

ABSTRACT The concept of eigenvalue separation (ES) was introduced in the past for the characterisation of the space-time kinetics of reactor transients, and the stability properties of large loosely coupled cores. However, most of the investigations reported so far concern the determination of the ES itself either from static calculations, or from measurements of the flux tilt or neutron noise cross-correlations. Conclusions on system behaviour were only drawn from the properties of the static eigenfunctions, comparing non-perturbed and perturbed systems, without explicitly solving the time- or frequency-dependent problem. In this paper, we explore the role of the ES on the neutronic response of a critical core to small stochastic perturbations (neutron noise); in particular, the spatial and frequency characteristics of the arising neutron noise as a function of the ES, as well as the spatial structure of the perturbation. It is shown that for systems with small ES and non-uniform perturbations, point kinetics will not dominate even for very low frequencies. The results lend some further insight into the origin and properties of the various types of boiling water reactor instabilities.