Time-varying modes in space-dependent nuclear reactor kinetics by a perturbation approach

Modal methods in space-dependent nuclear reactor kinetics can accommodate for continuous time variation of modes and adjoints. A perturbation theory based approach is developed in this paper as a tool to continuously update time-dependent modes, eigenvalues and adjoints to be used in modal inhour space reactor kinetics. The rise and fall of very large distortions in the mode shape can be obtained and eigenvalue variations can be evaluated to a very good accuracy. The modal equations look like a natural generalization of the point or adiabatic models of reactor kinetics, with a very low number of coupling terms. Precursor modal variables obeying the physical property of no cross-coupling between different decay groups can be defined also in the time-varying-modes setting. This allows for an easy implementation of six (or more) delayed neutron groups and the interpretation of excursion-shutdown transients for which a detailed account of the individual delayed neutron groups contributions according to their different decay constants is needed. 15 refs., 9 figs., 1 tab