Stability of Nuclear Reactors with Changes in Eigenvalue

The stability of a nuclear reactor with prompt feedback is examined when its eigenvalue (size, material buckling) is increased or decreased. Two models describing the temperature dependence of the Doppler coefficients T^-1 and T^-3/2 are used in the analysis, and their relative effectiveness in maintaining stability is compared. Both the eigenvalue and neutron flux of the nonlinear reactor are expanded in the perturbation parameter ∈, defined as the spatially weighted average of the change in neutron flux relative to the flux of the linear reactor. For a change in reactor eigenvalue, the equilibrium states of the neutron flux are obtained, accurate to the first order of feedback, but to an arbitrary order of perturbation. The stability of each state is examined.It is found that even for an overall negative prompt feedback, there exists a limit to the increase in reactor eigenvalue (or in neutron flux), beyond which instability may result. This limit depends on the initial conditions of the perturbed reactor. The neutron flux is shown to be more sensitive to a change ∈ than the reactor eigenvalue, and this sensitivity depends on the temperature variation of feedback. It is also shown that the T^-1 variation of the negative Doppler coefficient is more effective than the T^-3/2 variation in maintaining reactor stability when the reactor eigenvalue is increased.