Nonlinear Oscillations and Stability of a Nuclear Reactor with Two Reactivity Feedbacks

The space-independent reactor kinetics equations with two reactivity feedbacks are analyzed for stability and nonlinear oscillations. Expressions are derived using Fourier series methods for determining the frequency and fundamental amplitudes of the oscillations in reactivity and power. These results are compared with exact solutions of the system equations and agree in all cases for equilibrium power levels near the critical power level. The system of equations is examined for the effect of delayed neutrons on oscillatory solutions. When delayed neutrons are included, unstable limit cycles are found as well as stable limit cycles.