Virtual sampling in variational processing of Monte Carlo simulation in a deep neutron penetration problem

In a further study of virtually processed Monte Carlo estimates in neutron transport, a shielding problem has been studied. The use of virtual sampling to estimate the importance function at a certain point in the phase space depends on the presence of neutrons from the real source at that point. But in deep penetration problems, not many neutrons will reach regions far away from the source. In order to overcome this problem, two suggestions are considered: (1) virtual sampling is used as far as the real neutrons can reach, then fictitious sampling is introduced for the remaining regions, distributed in all the regions, or (2) only one fictitious source is placed where the real neutrons almost terminate and then virtual sampling is used in the same way as for the real source. Variational processing is again found to improve the Monte Carlo estimates, being best when using one fictitious source in the far regions with virtual sampling (option 2). When fictitious sources are used to estimate the importances in regions far away from the source, some optimization has to be performed for the proportion of fictitious to real sources, weighted against accuracy and computational costs. It has been found in this study that the optimum number of cells to be treated by ficti- tious sampling is problem dependent, but as a rule of thumb, fictitious sampling should be employed in regions where the number of neutrons from the real source fall below a specified limit for good statistics