Biasing Parameter Limits for Synergistic Monte Carlo in Deep-Penetration Calculations

The Monte Carlo scheme for deep-penetration problems, where both transport and collision kernels are biased synergistically, leads to minimum variance. Obtaining a proper biasing parameter is still a problem. For certain values of biasing parameter, the variance could be infinite even in a very simple problem. Using moment equations of statistical error prediction, a critical biasing parameter is obtained. A biasing parameter greater than the critical parameter may lead to an unbounded second moment in a simple one-dimensional homogeneous shield problem. A prescription is provided that may help to avoid a poor selection of the biasing parameter.