Non-regionwise weight cancellation for Monte Carlo higher order criticality calculations using kernel density estimator

In the Monte Carlo power iteration method, a higher k-eigenfunction is represented by both positive and negative particle weights. A special technique is required for these signed particle weights to cancel each other. Unlike some regionwise exact or approximate cancellation techniques that have been developed thus far, a newly developed cancellation technique using the kernel density estimator (KDE) eliminates the cumbersome regional division process. Density functions for fission source sites with positive and negative weights are represented by positive and negative kernel density estimators, respectively. After they cancel each other, the fission source sites for the next iteration cycle are determined by the rejection sampling. The new technique with KDE has shown feasibility of providing as accurate calculation results as other existing cancellation techniques by choosing a small enough kernel bandwidth.

► Higher k-eigenfunction calculations by Monte Carlo requires positive and negative weights.
► The kernel density estimator (KDE) has been applied to the cancellation for Monte Carlo method.
► KDE has been successfully implemented into Monte Carlo higher k-eigenfunction calculations.
► A small bandwidth is preferable to reduce the bias caused by KDE implementation.