Monte Carlo sensitivity calculation in fixed source problems with the derivative source method

Abstract

This paper proposes a new Monte Carlo sensitivity analysis method for fixed source radiation transport problems, which is dubbed the derivative source method (DSM). This method is a variation of the formerly proposed perturbation source method. A transport equation of a derivative particle representing a derivative of a flux with respect to a parameter such as a cross section is derived by differentiating the fixed source radiation transport equation. This paper presents a Monte Carlo algorithm to solve this transport equation. The derivative particle is emitted from a region of interest (ROI) when a radiation particle undergoes a collision in the ROI. The derivative particle is tracked in the same manner as the ordinary radiation particles. The derivative particle that undergoes a collision in the ROI can yield another derivative particle whose derivative order is increased by one from the colliding particle. This higher-order derivative particle can be used for calculating the higher-order derivative of a flux. The differential operator sampling method (DOS), which is commonly used for Monte Carlo sensitivity analyses, suffers from poor performance when an ROI is small. For a small ROI, the efficiency of the DSM can be improved by adding a pseudo scattering cross section in the ROI, thereby increasing the pseudo scatterings and the number of derivative particles emitted from the ROI. The efficiency of the new method is evaluated by comparing the DSM to the DOS. Numerical tests are performed for a two-dimensional geometry containing a small inclusion. The results reveal that the DSM definitely outperforms the DOS for these test problems. The efficiency of the DSM depends strongly on the pseudo scattering cross section added to the inclusion.