Modeling neutron count distribution in a subcritical core 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. Classical approaches to modeling this noise and neutron count distribution in the detection system rely on the stochastic transport equation for the probability generating function and on transfer function response to random perturbations. In recent years, a third modeling approach has been proposed, relying on Ito stochastic differential equations, which enjoys the tractability that the first aforementioned approach has, and at the same time accounts for fluctuations, by modeling noise in terms of Brownian motion. This paper develops the latter approach to incorporate the stochasticity in the detection process to the model equations. The resulting neutron count distributions are explicitly computable. As an application of our approach we present a straightforward derivation of the well-known Feynman-Y formula. We then propose an alternative to the traditional sampling scheme of this formula, based on mean absolute deviation, known from the statistics literature to be more robust than the mean square deviation estimator. The study focuses on a single energy point model and neglects the effect of the delayed neutrons. Extensions of the approach to multiple energy levels and the incorporation of delayed neutrons are discussed, as well as further applications of the approach and its advantages over existing diffusion scale approximations.