Derivative Source Method for Monte Carlo Transport Calculation of Sensitivities to Material Densities and Dimensions

The Derivative Source Method (DSM) takes derivatives of a particle transport equation with respect to selected parameters and solves them via the standard Monte Carlo random walk simulation along with the original transport problem. The Monte Carlo solutions of the derivative equations make the sensitivities of quantities of interest to the selected parameters. In this paper, we show that DSM can be embedded in Monte Carlo simulation to simultaneously calculate sensitivities of transport phase-space solution to multiple object dimensions and material densities. We verify and assess the efficiency of DSM by solving a multigroup neutronic system of a source-driven fuel-moderator-absorber slab lattice and calculating the fast and slow flux sensitivity coefficient distributions to the fuel and absorber dimensions, as well as the fuel, moderator, and absorber densities. The results are compared to those obtained from conventional finite difference sensitivity calculations. A figure of merit, defined as the product inverse of runtime and square of relative error, is used to assess method efficiencies. For a couple of the calculated sensitivities, well-configured finite difference calculations are the most efficient, followed closely by DSM. However, since seeking such well-configured finite difference is not always practical, in the rest of the cases, including the all-parameter simultaneous sensitivity calculation, DSM has the highest efficiency, demonstrating its robustness.