Variationally Processed Monte Carlo Transport Theory

Monte Carlo methods are widely used in neutron and reactor studies. They commonly are accelerated by a variety of variance reduction techniques, including adjoint weighting. We propose a new use of the adjoint - in a variational principle to process the Monte Carlo results. In many cases the estimation of the adjoint function is available from the Monte Carlo simulation without further sampling. In this paper we explore a simple model, chosen for known exact results, to compare the benefit of such a variational processing over straight analogue Monte Carlo simulation. The variational Monte Carlo results, for this system, are shown to yield improvement in the accuracy for the same computational cost. Despite the fact that variational results when used during Monte Carlo runs can be biased, they are associated with large reductions in variance. Comparing the ways in which variational expressions are processed, the most gain in accuracy is obtained by completing the Monte Carlo simulation before post-processing with the variational principle.