A zero-variance-based scheme for variance reduction in Monte Carlo criticality

A zero-variance scheme is derived and proven theoretically for criticality cases, and a simplified transport model is used for numerical demonstration. It is shown in practice that by appropriate biasing of the transition and collision kernels, a significant reduction in variance can be achieved. This is done using the adjoint forms of the emission and collision densities, obtained from a deterministic calculation, according to the zero-variance scheme. By using an appropriate algorithm, the figure of merit of the simulation increases by up to a factor of 50, with the possibility of an even larger improvement. In addition, it is shown that the biasing speeds up the convergence of the initial source distribution. (authors)