An enquiry into noise-induced reactivity shifts in the point-kinetics equations

Neutron noise analysis within the point-kinetics model is traditionally formulated using linear response theory under small-amplitude sinusoidal perturbations. Although this approach has proven successful in providing a conceptual foundation for neutron noise measurement and diagnostics, it neglects potential non-linear effects that may, for example, modify the stationary state of the reactor. In particular, effective reactivity shifts can be generated by non-linear interactions, which are not captured by the standard linearized treatment. These effects are nevertheless generally assumed to remain negligible under deterministic forcing. This assumption may break down in the presence of stochastic fluctuations. Multiplicative noise can indeed induce systematic drift terms in the effective dynamics, leading to noise-induced reactivity shifts that drive the mean neutron population away from stationarity. The present work investigates the impact of non-linear neutron noise within the point-kinetics model, considering both deterministic and stochastic excitations. The magnitude of the resulting reactivity shifts is quantified, and the respective roles of stochastic forcing and delayed neutron precursors are analysed, providing an assessment of their potential operational significance. • Sinusoidal perturbations induces a reactivity shift of the neutron population. • Another reactivity shift is observed in the case of multiplicative noise. • Delayed neutrons introduce correlation-dependent drift.