Improving tally efficiency and accuracy of multi-group scattering matrix calculations in the Monte Carlo code NECP-MCX

Abstract

Two issues arise in the calculation of the multi-group scattering matrix when employing a continuous-energy Monte Carlo code for generating homogenized multi-group cross-sections. Firstly, the analog estimator is used to evaluate group-to-group elements, which leads to large statistical uncertainty. Secondly, employing the scalar flux as the weighting function in generating the high-order scattering matrix introduces errors in fast reactor calculations. For the first issue, the repeated collision approach and pre-tabulated cross-section approach are adopted to improve the tally efficiency. For the second issue, the average scattering cosine is calculated based on the conservation of the mean square displacement of neutrons, which is then used to correct the first-order self-scattering cross-section. To evaluate the effectiveness of the above approaches, a PWR pin-cell problem and fast reactor core problems are tested. The results demonstrate that: 1) The figure of merit for multi-group scattering matrix calculations was improved by 8–12 times with the pre-tabulated cross-section approach. 2) Biases of k_eff were reduced from over 500 pcm to less than 300 pcm when using the corrected self-scattering cross-section. 3) The corrected self-scattering cross-section also yielded higher accuracy for the assembly power calculations, where the maximum biases are reduced from 5 % to 1 %.