Analysis of Example Problems for Monte Carlo Surface Flux Tallies

Particle fluxes on surfaces are difficult to calculate with Monte Carlo methods because the score requires a division by the surface-crossing angle cosine, and grazing angles lead to inaccuracies. The traditional method for dealing with this problem was recently extended by recognizing the assumptions that were implicit in its derivation. More recently, a kernel density estimator (KDE) has been proposed to replace the traditional method. In this technical note, example problems from the KDE development are analyzed, and the failure of the traditional method is shown to be due to the invalidity of one of the implicit assumptions, as previously predicted, and the extended theory is used to correct the traditional method.