Monte Carlo Fission Matrix Acceleration Method with Limited Inner Iteration

We propose a modified method to improve the stability of the Monte Carlo fission matrix acceleration (FM) method. In the existing FM method, the weights of fission neutrons are adjusted by the fundamental-mode eigenvector of the fission matrix, which can be calculated by power iteration (PI). In this paper, the PI procedure to calculate the fundamental-mode eigenvector of the fission matrix in each cycle is called the inner iteration to distinguish it from the Monte Carlo iteration cycles. In our proposed method, the fission source distribution tallied during the Monte Carlo simulation is taken as the initial vector for the inner iteration. The weights of the fission neutrons are not adjusted by the fundamental-mode eigenvector of the fission matrix but by the vector obtained with only a few inner iteration steps. We call the proposed method the Monte Carlo fission matrix acceleration method with limited inner iteration (FM_lii). The FM_lii method possesses the following properties: It is more stable than the existing fission matrix acceleration method, and it preserves considerable acceleration efficiency. Moreover, we analyze the stability property of the proposed method for the case of two weakly coupled fissile arrays. A number of numerical tests for practical large-scale, loosely coupled systems are presented that demonstrate the theoretical analysis and efficiency of our scheme.