Reactor Space-Dependent Transfer Function at Low Frequency Approximated by Neutron Diffusion Theory Perturbation

The space-dependent transfer function defines the response of the neutron flux in reactor core to a periodic perturbation at a point in the core. To compute it at low excitation frequency for the ZED-2 zero power reactor, we introduce a perturbation method. The ZED-2 reactor is used to investigate the properties of CANDU (R) lattices. In CANDU (R), the low frequency noise (0.1-5 Hz) allows one to study mechanical oscillations of structures in the core, the reactor control systems, as well as delayed neutron effects. The method for computing the ZED-2 transfer function was inspired by the results of measurements in the ZED-2 reactor. They showed that, at low excitation frequency, the imaginary part of the spacedependent transfer function is, up to normalization by the steady-state neutron flux, the same over all the core, while the real part varies significantly with the position of the flux detectors or the perturber in the core. This method was then found useful to compute the response of the ZED-2 reactor core to low frequency perturbations where other methods were found hard to apply. This opens the path to generalization of this method to CANDU (R) reactors. A rough calculation shows for which types of thermal reactors this perturbation theory is not worth applying. Also, the perturbation theory introduced here can be applied to other problems described by linear operators having a second smallest eigenvalue larger in absolute value compared to the perturbation. A further development, using the perturber induced reactivity, was found to make the core response normalization unnecessary. The theoretical basis of that method is outlined.