The use of an SDE model for subcritical reactor noise experiment design and its comparison to a traditional Monte Carlo computational method

Abstract

Noise experiments, and the Feynman-α method in particular, are used to measure the decay rate of the neutron population in a source driven subcritical assembly, such as that of a shut down nuclear reactor core. These experiments allow for a direct measurement of the reactivity of the assembly or other kinetic parameters such as the delayed neutron fraction βeff. These experiments can take a significant amount of time to perform, as the neutron population in the system is commonly small, and thus the detection rate is low. Simulation of these experiments can be used to design the experimental setup in advance. The design space includes parameters such as the required source intensity, detector efficiency or measurement time. However, direct simulation of the branching process itself is relatively expensive, even in a point reactor model, as many particle histories must be simulated for each configuration. Previous work has shown that the branching process’ mean count rate and variance can be accurately modeled using a system of stochastic differential equations (SDEs). By solving these SDEs, one can simulate an ”experiment signal” whose mean and variance match that of the branching process, which fully simulates all the information required for a Feynman-α experiment. Using these inexpensive simulations, the variance in the extracted reactivity from many sampled detection signals is obtained for many possible experimental setups. From this analysis, we show the dependence of the relative error in one’s measurements on their setup parameters, and that for any reactivity value, there exist source intensities and detection probabilities such that any further improvement in these parameters will only have negligible impact on the error. The relationship between these two parameters for equally low relative errors is also examined. A publicly available, open source Python implementation is provided for other researchers to use in future studies.