Calculation of the Total Flux at a Point by the Monte Carlo Track Rotation Estimator

The mathematical validity of the track rotation estimator (TRE) as an unbiased point flux estimator is presented in detail. The mathematical formulation of the TRE is developed for the cases of spherical symmetry, spherically symmetrical media with nonisotropic source, and nonsymmetrical media. Various methods for biasing the angular distribution to obtain a bounded variance are developed. The results of calculations in which the TRE is applied to test problems—infinite media, sphere, and sphere with nonisotropic source—as well as a three-dimensional finite slab with point source are presented and compared with the uncollided flux (UCF) and the once-collided flux (OCF) estimators. The results indicate substantially superior quality factors for the TRE over the UCF and the OCF estimators, especially when the absorption cross section is small.