Improving the SN Adjoint Source and Geometry Representation Capabilities in the SCALE Hybrid Shielding Analysis Sequence

The hybrid Monte Carlo (MC)/deterministic techniques, CADIS [1] and FW-CADIS [2] have proved to provide a factor of >1000 increase in the efficiency of the neutronics modeling of problems with immense geometry and massive shielding [3,4,5]. These methods use approximate forward and/or adjoint SN calculation(s) to develop the variance reduction parameters for a subsequent MC calculation. Despite that the deterministic calculation(s) are only used in the primary steps of the modeling sequence, the efficiency of the final MC calculation depends on the accuracy of the results of the SN calculation(s). The material definitions for SN calculations have been based on a simple approximation. This work studies the benefits of a new approach which provides a better representation of the MC geometry in the SN calculation(s). The effectiveness of the hybrid techniques is measured in their time savings compared to using either the deterministic or the MC methods individually. For saving human and computer time, the deterministic calculation has to be fast and automated. The computer time required by the deterministic calculation has an approximately linear scaling with the total number of mesh elements. Therefore, it is desirable to minimize the number of elements used, while maintaining a mesh that preserves the main geometric features of the problem. The automation of the deterministic input file creation requires an algorithm for defining the material and densities of each deterministic mesh element based on the MC geometry. Prior to this work, the implementation of the hybrid techniques used the cell center (CC) approach, which assigns the materials and densities to the SN mesh cells based on the MC materials existing at the center points of the mesh cells. This approach did not conserve relevant quantities such as material volumes. The macro-material (MM) approach [6] was developed for better representation of the MC geometry in the deterministic calculation. The approach depends on querying the MC geometry for the materials at multiple points within each mesh element and defining a new material based on the partial volume fractions of the original MC materials. For the deterministic calculations of CADIS and FW-CADIS an adjoint source, representing the MC tally, has to be defined. The MM approach was implemented in the adjoint source definition for additive responses such as radiation dose or nuclear heating in mesh elements that include heterogeneities. The materials’ responses are weighted by the MM fraction of each mesh cell before summing them to build the adjoint source spectrum representing the response of the tally to be optimized. The goal of this work is to investigate the effect of using the MM approach in both the materials assignments and in the adjoint source definition on the time and memory requirement of the deterministic calculation and on the figures of merit (FOM) of the final MC calculation.