Undersampling diagnostics by fission matrix in Monte Carlo criticality calculations

Most Monte Carlo (MC) codes use the power iteration method for criticality calculations, where the fission bank of the previous cycle is taken as the source of the subsequent cycle. If the batch size (i.e. the neutron population per cycle) is insufficient, the power iteration may introduce biases in both keff and local tallies, which is known as the undersampling problem. Although the undersampling can be examined by independent runs with increasing batch sizes, it is important to diagnose undersampling directly upon a single calculation. In this paper, a method based on the fission matrix is proposed for undersampling diagnostics, and it is implemented in the RMC Monte Carlo code. Numerical results are presented for the “k-effective of the world” problem and the MC full-core performance benchmark. The results indicate that the fission matrix method is reliable for undersampling diagnostics. Besides, the effect of the mesh discretization on the fission matrix method is investigated.