Nonlinear stability and limit cycles in xenon-induced reactor oscillations

Xenon oscillations in pressurized water reactors were analyzed, using linear stability analysis and weak nonlinear analysis based on the multiple time-scales method. The dynamics are described by a spatio-temporal nonlinear model, which includes feedback processes of xenon absorption, as well as fuel and coolant temperature changes. It is shown that the homogeneous steady-state solution that describes nominal operation of a large reactor can go through uniform Hopf bifurcations at several values of the neutron flux, and the long-wavelength modes that can grow beyond the instability thresholds are identified. In order to study the dynamics beyond the Hopf bifurcation, a nonlinear equation for the amplitude of the growing oscillatory mode is derived. The amplitude equation is used to identify parameter ranges of bounded periodic oscillations and of oscillations with diverging amplitudes. The approach described may be used to broaden the operational limits required to suppress xenon oscillations for safe operation.