Kernel Density Estimation of Reaction Rates in Neutron Transport Simulations of Nuclear Reactors

Abstract

Kernel density estimators (KDEs) are applied to estimate neutron scalar flux and reaction rate densities in Monte Carlo neutron transport simulations of heterogeneous nuclear reactors in continuous energy. The mean free path (MFP) KDE is introduced in order to handle the issues that arise from estimating the discontinuous reaction rate densities at material interfaces. Results show the MFP KDE is more accurate at estimating reaction rates compared with previous KDE formulations. An approximate MFP (aMFP) KDE is introduced to circumvent several practical issues presented by the MFP KDE. A volume-averaged KDE is derived and used to determine the bias introduced by the aMFP KDE. A KDE is formulated for cylindrical coordinates to better represent the geometry and capture the physics in two-dimensional reactor physics problems. The results indicate that the cylindrical MFP KDE and cylindrical aMFP KDE are accurate tools for capturing reaction rates in heterogeneous reactor physics problems in continuous energy, with local biases of less than 1%.

Keywords:

• Monte Carlo
• kernel density estimator
• radiation transport

Acknowledgments

This material is based on work supported in part by the National Science Foundation Graduate Research Fellowship under grant DGE 1256260 and by the U.S. Department of Energy/National Nuclear Security Administration Advanced Scientific Computing Program at Los Alamos National Laboratory.