Stability analysis of the non-linear nuclear reactor

Abstract

The stability of the nuclear reactor with temperature-dependent feedback is studied in the context of bifurcation theory of non-linear eigenvalue problems. The case of prompt Doppler effect is considered, in which the reactor temperature is proportional to the neutron flux. The multiple solutions of the non-linear boundary-value problem are constructed in the form of a perturbation expansion about the steady-state solution of the associated linear equation. The first and higher-order terms are thereby defined by inhomogeneous linear perturbation problems, which can be solved by a classical eigenfunction expansion method. The conditions for asymptotic stability, neutral stability and instability are considered. The threshold of instability ‘ in the large ’ for a solution known to be stable ‘ in the small’ is also examined.