Method for control drum position critical search with Monte Carlo codes

Abstract

The use of Monte Carlo codes when performing optimization or root-finding routines can lead to complications due to the statistical uncertainty associated with calculated results. Monte Carlo codes are often needed to model the complex geometries associated with microreactors so when a critical search is performed to find the rotational position of the control drums which yield a critical core, the noise in calculated criticalities can disrupt the progression of the search. In addition, gradient-based root-finding algorithms are most appropriate for this critical search due to the monotonicity of the control drum position versus criticality relationship but these algorithms are particularly susceptible to the noise in calculated criticalities. Therefore, these weaknesses are specifically addressed with a few variants of secant-like methods that are presented in this paper and evaluated on control drum worth curves generated from the eVinciTM and Holos-Quad microreactors. In the end, a single secant-like method is recommended for implementation due to superior performance on these worth curves. In general, these root-finding methodologies are created with ease-of-implementation as a significant motivator such that they can be implemented using only calculated criticalities, with uncertainty, from any Monte Carlo neutronics code without the need for source code access. The scripting framework required to implement this method only requires the programming of 3 explicit mathematical equations with expressions clearly provided in this paper and an outline to use this method to find burnup dependent critical drum positions is provided with an application to the eVinciTM microreactor.