Mitigation of statistical fluctuations in electron-photon tallies obtained with the use of the splitting/rouletting VR techniques - 124

Monte Carlo (MC) coupled electron-photon transport calculations are often performed to determine characteristics such as energy or charge deposition. However, these calculations may require large amount of computational resources to obtain adequate statistics in a reasonable amount of time. Therefore, the study of variance reduction techniques for this class of problem is necessary. In our previous work, the ADEIS (Angular-dependent adjoint Driven Electron-photon Importance Sampling) methodology was used to show that angular/space/energy transport biasing (i.e., splitting/rouletting technique) through a deterministic importance-based weight-window technique can produce significant speedups for coupled electron-photon simulation. However, it was also shown that for certain cases, the presence of 'discontinuities' in the importance distributions and the strong coupling between the photon and electrons can produce statistical fluctuations in the tallies. This paper will present various strategies that were considered in ADEIS to eliminate or mitigate these statistical fluctuations. These strategies are made as general as possible in order to minimize the number of assumptions related to the nature of the problem. Statistical fluctuations can be attributed to 'discontinuities' in the importance distributions caused by the physical behavior of particles, unphysical oscillations in the deterministic importance functions, and strong coupling between the electron and photons. The strategies considered for mitigating these fluctuations can be classified in two categories; i) reducing/eliminating the 'discontinuities' in the importance distributions and ii) partially removing the coupling between the particles. To reduce 'discontinuities', three strategies are considered: a) refining the spatial discretization of the importance, b) the use of CEPXS-GS cross-sections since it has been proven that the use of these cross-sections eliminates CEPXS/ONELD numerical oscillations in cases with a very small spatial mesh size, and c) a better smoothing/interpolation (space and energy) algorithm. By completely removing the coupling between the particles, it is possible to introduce a bias if the physical characteristics of the problem are not well understood. Therefore, it is preferable to partially decouple the problem. In deterministic calculations, in addition to the scattering from electron-to-photon groups and/or photon-to-electron groups, the coupling between the electrons and the photons is achieved through the objective function (adjoint source). Therefore, through the proper selection of an objective function, the particle importance distributions can be partially decoupled. It will be shown that refining the spatial meshing mitigates the fluctuations and that the computational cost of this refinement can be reduced by using a better smoothing/interpolating algorithm. Note that this spatial refinement introduces additional unphysical oscillation when the CEPXS cross-sections are used. Therefore, the full paper will also include results showing the impact of using the CEPSX-GS cross-sections on the fluctuations. Finally, the impact of partial decoupling of the particles through the adjoint source will also be examined