A stochastic differential equation for neutron count with detector dead time and applications to the Feynman-α formula

Detector dead time, caused by both physical components in the detection system and the electronic data acquisition, may have a dramatic effect on the regulation system and in-pile experiments. For example, when conducting the Feynman-α experiments in a marginally sub-critical configuration, the dead time effect is known to bias the variance to mean ratio. Analytic computations of the influence of the dead time on the detection count distribution are hard. Therefore, conducting Feynman-α experiments, or other noise experiments, in the presence of a noticeable dead time effect, is challenging. In the present study, we develop the stochastic differential equations approach to stochastic transport, by providing a model for the detection count in a sub-critical configuration under a non-paralyzing detector dead time. The analysis is based on tools from renewal processes and on a nonlinear filter for detection losses. After constructing the full model, a second order approximation is provided and solved, suggesting a novel first order correction to the Feynman-Y function. The proposed correction is compared with experimental results and past known results, showing improvement and high accuracy.