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A new variance-reduction method, called the first-collision source (FCS) method, is proposed to optimize Monte-Carlo source sampling to reduce variance in deep-penetration problems. In the FCS method, Monte-Carlo samples source particles from the first-collision source distribution rather than the original source distribution. The first-collision source is generated from the original source through a transport process and a scatter process, thus it has wider phase space distribution compared with the original source. Sampling from the first-collision source is capable of obtaining source particles near the aim phase space (specific space area, energy segment, and angle segment which are most related to the aim response) to increase particle popularity in aim phase space. Moreover, a new method called the FCS-CADIS method has also been proposed to further improve the sampling efficiency and performance of variance reduction. The FCS-CADIS method combines the FCS method and the Consistent Adjoint Driven Importance Sampling (CADIS) method. Both of the FCS method and the FCS-CADIS method have been implemented in the hybrid Monte-Carlo-Deterministic particle-transport code NECP-MCX. Three problems are used to assess the performance of the FCS method and the FCS-CADIS method. The results show satisfactory improvement of Monte-Carlo calculation efficiency.

New variance reduction techniques for Monte-Carlo calculation based on first-collision source method