Modeling Zero Power Reactor Noise and Neutron Count Distribution: A Stochastic Differential Equations Approach

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. In a recent study, a new modeling approach was introduced, corresponding to an intermediate regime, where noise is modeled by Brownian motion, describing the dynamics by means of Stochastic Differential Equations (SDE). In the present study we further develop the SDE approach by considering a model that preserves the discrete nature of detections, specifically, via the binomial distribution. The new formalism thus results in a non-normal distribution of the neutron count in a given time interval. We provide an explicit formula for the distribution of the neutron count, and provide simplified formulas for its high moments. Comparison between the analytic prediction and experimental results show a very high correspondence, with a bias of less than 0.98% for the first four moments.