Monte Carlo Variance Reduction Using Nested Dxtran Spheres

Dxtran is a deterministic transport method typically used for increasing the sampling in a spherical region that would otherwise not be adequately sampled because the probability of scattering toward the region is often very small. Essentially, the dxtran method splits the particle into two pieces at each source or collision point: a piece that arrives (without further collisions) at the dxtran sphere and a piece that does not. One difficulty with the dxtran method is that it can introduce a large weight fluctuation between particles colliding just before the sphere and particles colliding after crossing the sphere. New work shows that it is possible to mitigate this difficulty by extending the dxtran sphere concept to a set of nested dxtran spheres. Each dxtran sphere then shields its interior from particles whose weights are too large so that weights are more commensurate with their locations. Shielding against the large weights not only increases the efficiency of the calculation but the reliability as well. The effectiveness of the technique in MCNP was demonstrated on a 1-km air transport problem and on a concrete duct problem.