A generalized approach to the biased adjoint Monte Carlo calculation

The application of the forward (or adjoint) Monte Carlo method to the solution of deep-penetration radiation transport problems requires the use of a biasing technique such as "importance sampling". A systematic approach to obtain the importance information is to solve the adjoint (or forward) transport equation and to use the solution as the importance information. In this work, a two-dimensional discrete ordinates calculation in the forward mode was used to obtain appropriate importance information for the adjoint Monte Carlo calculation. Then, methods of biasing three-dimensional deep penetration adjoint Monte Carlo calculations using the angular flux and the emergent particle density as importance information were studied. The biasing techniques investigated include collision energy biasing and collision angular probability biasing - these procedures alter the collision kernel using the total flux or the angular flux as the importance information. Path length biasing was accomplished using the emergent particle density as the importance information. Adjoint source energy and source angular biasing by the total flux and the angular flux respectively are also studied.

The effects of applying the biasing techniques to adjoint Monte Carlo calculations have been investigated for neutron transport through a thick concrete shield with a penetrating duct. Source angular biasing, source energy biasing, collision energy biasing, collision angular probability biasing, and path length biasing were employed individually or in various combinations. Results of the biased adjoint Monte Carlo calculations using DOT-calculated importance information were compared with standard forward and adjoint Monte Carlo calculations. Based on the figure-of-merit, σ²t, the adjoint calculations with importance in formation biasing are a factor of 8 to 20 better than the calculation with the adjoint source angular step biasing, ST, which in turn is much better than the adjoint Monte Carlo calculation with only the weighting-in-lieu-of-absorption survival biasing. Hence, the effectiveness and the applicability of importance function biasing in deep penetration, three-dimensional adjoint Monte Carlo calculations are clearly demonstrated. Results of the adjoint Monte Carlo calculations show that the combination of source angular biasing, source energy biasing, and collision energy biasing in the standard test problem gave much better results as compared with the other calculations.

In summary, this dissertation proposes a new and rigorous basis for the "importance function" biasing of the adjoint Monte Carlo calculation; develops practical methodology for incorporated the biasing procedures and DOT-calculated importance information into the MORSE-CG Monte Carlo code; and presents a comprehensive computational evaluation of the proposed theory and biasing methodology.