On the Accuracy of a Common Monte Carlo Surface Flux Grazing Approximation

Particle fluxes on surfaces are difficult to calculate with Monte Carlo codes because the score requires a division by the surface-crossing angle cosine, and grazing angles lead to inaccuracies. We revisit the standard practice of dividing by half of a cosine “cutoff” for particles whose surface-crossing cosines are below the cutoff. We concentrate on the flux crossing an external boundary, deriving the standard approach in a manner that explicitly points out three assumptions: (a) that the external boundary surface flux is isotropic or mostly isotropic, (b) that the cosine cutoff is small, and (c) that the minimum possible surface-crossing cosine is 0. We find that the requirement for accuracy of the standard surface flux estimate is more restrictive for external boundaries (a very isotropic surface flux) than for internal surfaces (an isotropic or linearly anisotropic surface flux). Numerical demonstrations involve analytic and semianalytic solutions for monoenergetic point sources irradiating surfaces with no scattering. We conclude with a discussion of potentially more robust approaches.