Real and Virtual Sampling in Variational Processing of Stochastic Simulation in Neutron Transport: the One-Dimensional Rod

We are seeking to combine conventional analogue Monte Carlo simulation that might be used in realistic three-dimensional problems, with variational processing to reduce variance and improve the ratio of accuracy to computing costs. At this stage we investigate a one-dimensional transport problem with left and right scattering, for which exact solutions are available for comparison. We can show that the usual Monte Carlo simulation can be used not only to estimate the forward flux but also the importance or adjoint flux of neutrons sampled, where the importance is to be used in the variational processing. Hence the single simulation potentially holds information to improve the accuracy. The efficiency is improved by the use of virtual rather than fictitious sampling. Virtual sampling is introduced, which consists of marking every location of a neutron as a virtual source, and found to be more efficient than fictitious sampling to determine the importances