Modeling of neutron fluctuations with temperature feedback using stochastic differential equations

Neutron fluctuations, also coined zero power noise, is concerned with the study of the random fluctuations observed in the neutron population evolving in a fissile medium, due to the fundamentally intrinsic stochastic nature of the neutrons’ interactions in matter. The canonical theoretical modeling of such fluctuations rely on the establishment of a microscopic probability balance equation, from which one can extract, with the highest precision, all of the information about the stochastic behavior of the neutron population. An approximate yet practical scheme has been gaining in popularity in recent years. It relies on a coarse grained approach of the problem, where the evolution of the neutron population is modeled through (Itô prepoint) Stochastic Differential Equations (SDE). In this simplified scheme, the crux is to find the SDE that best approximates the fluctuations of the underlying microscopic stochastic process . In the present work, an alternative approach to the scheme usually found in the neutronics literature is proposed. A family of SDE that best approximate the fine grain behavior of the neutron population is derived from an explicit truncation of the translation operators found in the microscopic master equation of the problem. The approach is developed over a concrete and relatively original application case, namely that of the point reactor model including mono-energetic neutrons, one group of precursors, and a temperature feedback process. • A model of neutron fluctuations including a thermal feedback mechanism is proposed. • A Fokker–Planck equation associated to the microscopic stochastic process is derived. • Stochastic Differential Equations describing the neutron fluctuations are obtained.