A three-dimensional theoretical investigation of the local and global component of neutron noise in bare homogeneous water moderated reactors and applications

Abstract

Starting from the time-dependent three-dimensional two-group diffusion equations for a bare homogeneous critical reactor, it is shown that the fluctuations of the neutron population can be uniquely separated into a local and a global component with each component satisfying a second-order differential equation. It is shown that under certain limitations, the two-group treatment of the neutron noise and the subsequent derivation of the two components, is equivalent to the one-group theory in which the slowing down of the fast neutrons is taken into account through an appropriately chosen slowing down kernel. The theory so developed, is applied in order to investigate the local component of the neutron noise induced by a randomly vibrating infinitely thin absorber in a two-dimensional cylindrical reactor and the neutron noise due to axially propagating perturbations of the moderator density, in a multi-channel model of a three-dimensional slab reactor.