Simultaneous optimization of tallies in difficult shielding problems

Monte Carlo is quite useful for calculating specific quantities in complex transport problems. Many variance reduction strategies have been developed that accelerate Monte Carlo calculations for specific tallies. However, when trying to calculate multiple tallies or a mesh tally, users have had to accept different levels of relative uncertainty among the tallies or run separate calculations optimized for each individual tally. To address this limitation, an extension of the Consistent Adjoint Driven Importance Sampling (CADIS) method, which is used for difficult source/detector problems, has been developed to optimize several tallies or the cells of a mesh tally simultaneously. The basis for this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. This method utilizes the results of a forward discrete ordinates solution, which may be based on a quick coarse-mesh calculation, to develop a forward- weighted source for the adjoint calculation. The importance map and the biased source computed from the adjoint flux are then used in the forward Monte Carlo calculation to obtain approximately uniform relative uncertainties for the desired tallies. This extension is called forward-weighted CADIS, or FW-CADIS. methodology that has been successfully applied to both MCNP with the ADVANTG patch^2,3 and MAVRIC (Refs. 4 and 5) in SCALE 6 (Ref. 6). The implementations of CADIS use an approximate adjoint discrete ordinates calculation to determine both the transport weight-window target values and the biased source distribution to optimize one tally of interest in the Monte Carlo calculation. The needs of specific applications have recently motivated efforts to develop approaches for optimizing Monte Carlo calculations for distributions, such as flux or dose- rate distributions (e.g., mesh tallies), as well as response at multiple localized tallies. These efforts have led to the development of an extension to the CADIS method that has been demonstrated to be effective for obtaining mesh tallies with approximately uniform relative uncertainties- simultaneous optimization. The effectiveness of this new method, referred to as forward-weighted CADIS (FW- CADIS), has been demonstrated for selected applications in previous papers.^7-9 This paper demonstrates the FW-CADIS method on a difficult problem of particular interest to the radiation protection and shielding community, namely, the problem of determining the spatial dose distribution surrounding an array of commercial spent nuclear fuel casks for the determination of the site boundary dose. 785-792.