Power distributions in a nuclear reactor core under various operating conditions and their safety implications

A nonlinear reactor model has been developed considering typical feedback effects such as the moderator and fuel temperatures, xenon, and soluble boron. The resulting equation belongs to a class of nonlinear boundary value problems, and it was numerically shown using the arc-length continuation method that the nonlinear feedback equation may have multiple steady-state solutions due to existence of branch points for a range of parameters and feedback coefficients which are determined by various design and operating conditions. Solution diagrams of three distinct types were obtained depending on the values of feedback constants and stability was characterized for each solution. The starting point of instability (first limit point) in the solution diagram decreases as the temperature coefficients become large or the boron concentration increases, which means decrease of stability. When solution diagrams which are divided into stable and unstable regions are obtained for a wide range of feedback coefficients, we can choose the range of the reactor design and operating conditions such that the reactor does not encounter unstable situations