Xenon-Induced Oscillations

The xenon-induced oscillations in the power level (fundamental mode) and in the power distribution (first harmonic) have been studied for a slab reactor with prompt power reactivity feedback. One-group space-dependent kinetics equations and linearized theory are used throughout. The linear analysis rigorously predicts the onset of xenon oscillations; however, it does not say anything on how much the oscillation amplitude grows or decays. Explicit formulas giving the effects of the coupling of the infinite number of reactor modes with the fundamental mode and first harmonic are obtained and used for the first time to explain mode-coupling effects both qualitatively and quantitatively. Mode-coupling effects are quite small at the thermal flux levels of present power reactors [10¹³−10¹⁴ n/(cm²sec)]. At higher fluxes [10¹⁵ n/(cm²sec)] mode coupling is destabilizing and might be significant; here the negative feedback reactivity needed to provide stability must be increased by ≈ 10%, relative to the value obtained from a calculation where coupling is neglected. A study has been made on the influence of the equilibrium power distribution on both types of oscillations; this study gives information concerning the effects of a reflector on reactor kinetics. A new result is that, depending on flux level, a reflected reactor may be more stable than a bare reactor against fundamental mode oscillations.