A Study of the Multiplicity of Power Distributions in a Nuclear Reactor Subject to Reactivity Feedbacks

Abstract

A nonlinear reactor model is developed taking into account several feedback effects, such as moderator and fuel temperatures, xenon absorption, and soluble boron concentration, through energy relations in the core. The resulting equation belongs to a class of nonlinear boundary value problems, and it is shown through bifurcation theory that there may exist multiple steady-state solutions for a range of parameters that correspond to various design and operating conditions. Solutions are obtained numerically for ranges of the parameters by the arc-length continuation method in combination with Newton's method. Stability analysis is also applied to each solution to investigate whether the solution is stable or not. When the stable and unstable regions of the steady-state solutions are plotted for a wide range of the parameters, a range of the reactor design and operating conditions can be chosen such that the reactor does not encounter unstable situations.