3D coupled electron-photon deterministic importance using the discrete ordinates method - 125

The ADEIS (Angular-dependent adjoint Driven Electron-photon Importance Sampling) methodology has been developed to perform variance reduction for coupled electron-photon Monte Carlo (MC) calculations. This methodology estimates the angular lower-weight bounds for a modified version of the weight-window technique of MCNP5. The importance functions are calculated using the CEPXS/ONELD package which performs one-dimensional coupled electron-photon transport calculation. One of the major challenges in extending this work to three-dimensional geometries is obtaining reasonably accurate (yet approximate) 3D importance distributions in a relatively short time. As a preliminary investigation, we analyzed the use of a 3D Cartesian discrete ordinates code, PENTRAN in conjunction with cross-sections generated by both CEPXS and CEPXS-GS through a series of sensitivity studies. CEPXS generates effective cross-sections that effectively solve the Boltzmann-CSD transport equation for electrons and the Boltzmann transport equation for photons while CEPXS-GS provides a simultaneous solution of the continuous-slowing-down and elastic-scattering portions of the scattering source by the Goudsmit-Saunderson theory. PENTRAN is a 3D SN code with adaptive differencing schemes and capability to perform full domain decomposition, for parallel process. Two aspects have to be considered in the evaluation of the method used to estimate the 3D importance distributions in the context of the ADEIS methodology; i) its accuracy, and ii) the amount of computation time. Since CEPXS and CEPXS-GS in conjunction with ONELD have been extensively tested in 1D geometries, it is appropriate to compare PENTRAN results to those obtained with ONELD. Even though 1D geometries are modeled, the various numerical discretizations used in PENTRAN retain their three-dimensional nature. Therefore, the goal of the sensitivity studies presented here is to only analyze the accuracy of the solution when both CEPXS and CEPXS-GS cross-section are used in conjunction with 3D Cartesian numerics. The following set of sensitivity studies were considered: i) the fine mesh distribution, ii) SN and PN order, iii) quadrature set, and iv) differencing scheme. Scalar fluxes, dose profiles and solution convergence behavior are used for comparison. The results will show that, as expected, the CEPXS methodology is rather sensitive to choice of discretization parameters (due to the strong coupling between the energy and spatial variables) and does not appears to give adequate results for 3-D calculations in conjunction with PENTRAN. However, it is well documented that CEPXS methodology was designed for use with 1-D SN code. Therefore, the full paper will also present present results obtained with CEPXS-GS cross-sections since this methodology is not limited to 1-D geometry. The use of CEPXS-GS should allow distinguishing between the effects related to 3-D numerical considerations in electron transport (such as differencing scheme, quadrature set and order, scattering expansion, etc.) from CEPXS related effects