Calculating reaction rate derivatives in Monte Carlo neutron transport/

Abstract

An operating nuclear power reactor is a complex system that is sensitive to many material parameters including densities, temperatures, and compositions. There is great interest in solving the neutron transport with Monte Carlo methods due to their extremely high fidelity, but Monte Carlo methods are too slow to run in an iterative brute-force search of the reactor parameter space. This thesis discusses the derivation, implementation, and applications of differential tallying -- a method which can be used to mitigate the computational cost of mapping out a reactor parameter space with Monte Carlo. With differential tallies, each calculation provides derivatives of tallied quantities like reactivity and fission reaction rates with respect to material density, temperature, etc. These derivatives directly provide reactivity coefficients and they can also be used to extrapolate and predict small changes in reactor parameters. Notably, a novel method is presented which uses the windowed multipole cross section representation to compute temperature derivatives due to the resolved resonance Doppler broadening effect. To demonstrate the utility of differential tallies, this thesis presents example computations of moderator density and fuel Doppler feedback coefficients in pressurized water reactor pincells. With differential tallies, the moderator and fuel Doppler coefficients can be computed 40% and 50x faster, respectively, than by brute-force methods. A calculation of pin-by-pin Doppler coefficients in an assembly is also presented in order to demonstrate that differential tallies are even more efficient for assembly calculations.