Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles

Transformations of radiation-matter interaction parameters that result in similar radiation distributions are referred to as similarity relations. A class of similarity relations for monoenergetic, or single energy group, neutral particle transport is derived from fundamental transport considerations. One specific relation, defined as the moments similarity relation, is examined as a biased sampling method for Monte Carlo simulations. The moments similarity relation most effectively reduces computation time for simulations involving deep penetration and highly forward peaked scattering. The method involves substantial reductions in the total scattering cross section that can be employed with greatest accuracy away from sources and boundaries. A specific case study for diffuse transmittance and reflectance in a highly scattering medium is presented to illustrate the method and evaluate its computational effectiveness.