Importance Function Biasing of the Deep Penetration Monte Carlo Calculation

The formal basis of the use of calculated importance information for biasing forward and adjoint Monte Carlo deep penetration shielding problems is presented. The distinction between the “point value” and “event value” functions for adjoint problems is discussed. The analysis reveals that the emergent particle density, and not the particle flux density, is the proper choice of biasing function for the selection of the ad junctor's next collision site. This is analogous to the choice of the event value as the value function for the biased selection of the next collision site in the forward analysis. A numerical illustrative problem consisting of a concrete cylinder with an axial duct, a plane source on the bottom surface, and four joint detectors outside the emergent top surface is used to demonstrate this theory.