The neutron population in a reactor fluctuates due to the random nature of neutron emission and various sources of mechanical vibrations, which can impact macroscopic neutron cross sections. The reactor can be seen as a system with a transfer function that connects an excitation (such as a vibration or the random nature of neutron emissions from fission) to the neutron population. The study and measurement of this transfer function allow us to deduce essential neutron parameters related to the kinetics of delayed neutron emission or even the source of thge vibrations. However, the theoretical expression of this transfer function is often based on the kinetics of the point reactor, which in some cases does not reliably exploit the measurements.
In this thesis work, we propose to study various extensions of the neutron transfer function formalism using Monte Carlo simulations. First, we will simulate fluctuations using a simplified C++ model to confirm the assumptions of theoretical equations for "neutron noise" that can be used to "measure" the effective fraction of delayed neutrons. We will then seek to optimize the positioning of detectors in a reactor and interpret certain effects related to positioning already observed in past experiments conducted by CEA.