Tally efficiency analysis for Monte Carlo Wielandt method

The Monte Carlo Wielandt method has the potential to eliminate most of a variance bias because it can reduce the dominance ratio by properly controlling the estimated eigenvalue (ke). However, it requires increasingly more computation time to simulate additional fission neutrons as the estimated eigenvalue becomes closer to the effective multiplication factor (keff). Therefore, its advantage over the conventional Monte Carlo (MC) power method in the calculation efficiency may not always be ensured. Its efficiency of the tally estimation needs to be assessed in terms of a figure of merit based on a real variance as a function of ke. In this paper, the real variance is estimated by using an inter-cycle correlation of the fission source distribution for the MC Wielandt calculations. Then, the tally efficiency of the MC Wielandt method is analyzed for a 2 × 2 fission matrix system and weakly coupled fissile array problems with different dominance ratios (DRs). It is shown that the tally efficiency of the MC Wielandt method depends strongly on ke, there is a ke value resulting in the best efficiency for a problem with a large DR, and the efficiency curve as a function of L, the average number of fission neutrons per history, follows a long tail after the best efficiency.