Linear Stability of the Thermal Flux in a Reflected Core Containing Xenon and Temperature Reactivity Feedback

Abstract

The stability of the thermal flux in a reflected slab reactor due to xenon and temperature reactivity feedback is investigated using perturbation theory. A reactor with spatially constant fuel, equilibrium flux, and materials in the core is examined under various reactivity feedback situations. Stability criteria are given along with associated oscillation periods for the condition of neutrally stable equilibrium, i.e., continuous oscillation of the perturbed flux. The conditions for interaction of the xenon and temperature reactivity feedback are shown for both long and short temperature delay; the effect of delayed neutrons being considered when appropriate. A cosine fuel distribution is found to be necessary to give spatially constant equilibrium flux and this cosine fuel model is shown to predict slightly more stable conditions than the flat fuel model. Coupling of the first two (even or odd) excited modes is shown to occur (for a constant power density model) in large, high flux reactors, leading to more unstable conditions than with no coupling. (auth)