Excitation of Neutron Flux Waves in Reactor Core Transients

An analysis of the excitation of neutron flux waves in reactor core transients has been performed. A perturbation theory solution has been developed for the time-dependent thermal diffusion equation in which the absorption cross section undergoes a rapid change, as in a pressurized water reactor rod ejection accident. In this analysis the unperturbed reactor flux states provide the basis for the spatial representation of the flux solution. Using a simplified space-time representation for the cross-section change, the temporal integrations have been carried out and analytic expressions for the modal flux amplitudes determined. The first-order modal excitation strength is determined by the spatial overlap between the initial and final flux states and the cross-section perturbation. The flux wave amplitudes are found to be largest for rapid transients involving large reactivity perturbations.