Analysis of Error in Monte Carlo Transport Calculations

Equations are presented that allow the efficiencies of Monte Carlo techniques (for particle transport problems) to be calculated. This theory generalizes the theory of Amster and Djomehri to treat time-dependent multiplying systems, even when supercritical. Standard variance reducing techniques such as biased kernels, splitting, and Russian roulette are included in the theory. As concrete examples, the efficiencies of four Monte Carlo techniques for obtaining the expected number of collisions a particle makes have been analytically predicted. These predictions are stated and compared with the observed efficiencies obtained by Monte Carlo calculations using each of the four techniques.