Modeling and analysis of reactor noise by stochastic differential equations

Reactor noise, caused both by the probabilistic nature of the fission chains and external reactivity noises, is one of the basic topics in nuclear science and engineering, both in theory and practice. Modeling reactor noise (and neutron flux fluctuation in general) is traditionally performed by two main approaches: the stochastic transport equation for the probability generating function and the transfer function response to random perturbations. This paper suggest a new modeling approach, corresponding to an intermediate regime, where noise is modeled by Brownian motion. A derivation of the model is presented, physically justified by the great number of particles involved, and mathematically supported by the method of diffusion approximations. The model is described by means of a stochastic differential equation, that is analyzed in the case of prompt reactivity. As a first application of our approach we present a straightforward derivation of the well-known Feynman-Y formula. Further, we propose an alternative to the traditional sampling scheme of the Feynman-Y function, based on mean absolute deviation, known from the statistics literature to be more robust than the mean square deviation estimator. Further applications of the proposed approach and its advantages over existing diffusion scale approximations are discussed. keywords: Point reactor kinetics; diffusion approximations; stochastic differential equations