The onset of regional instabilities in the Boiling Water Reactor has been directly related to the reactor subcritical reactivity. Because the calculation of higher harmonic modes for practical reactor problems is a significant computational expense, the research here investigated the application of perturbation methods to predict the subcritical reactivity. The method developed here is based on a second order perturbation theory for the first harmonic eigenvalue. An original contribution of this work is an innovative method to predict the rotation of the first harmonic flux after a perturbation. This provides a second order estimate of the harmonic eigenvalue, which combined with a first order estimate of the fundamental eigenvalue, yields a perturbation estimate of the subcritical reactivity that is within a few percent of exact calculations for a series of two-dimensional benchmark problems. © 1995.
Downar, T. J., & Phegley, D. A. (1995). Harmonic perturbation theory for the analysis of boiling water reactor regional instabilities. Annals of Nuclear Energy, 22(6), 339–357. https://doi.org/10.1016/0306-4549(94)00066-N