Review of Hybrid Methods for Deep-Penetration Neutron Transport

Abstract

Methods for deep-penetration radiation transport remain important for radiation shielding, nonproliferation, nuclear threat reduction, and medical applications. As these applications become more ubiquitous, the need for accurate and reliable transport methods appropriate for these systems persists. For such systems, hybrid methods often obtain reliable answers in the shortest time by leveraging the speed and uniform uncertainty distribution of a deterministic solution to bias Monte Carlo transport and reduce the variance in the solution. This work reviews the state of the art among such hybrid methods. First, we summarize variance reduction (VR) for Monte Carlo radiation transport and existing efforts to automate these techniques. Relations among VR, importance, and the adjoint solution of the neutron transport equation are then discussed. Based on this exposition, the work transitions from theory to a critical review of existing VR implementations in modern nuclear engineering software. At present, the Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint-Driven Importance Sampling (FW-CADIS) hybrid methods are the gold standard by which to reduce the variance in problems that have deeply penetrating radiation. The CADIS and FW-CADIS methods use an adjoint scalar flux to generate VR parameters for Monte Carlo radiation transport. Additionally, efforts to incorporate angular information into VR methods for Monte Carlo are summarized. Finally, we assess various implementations of these methods and the degree to which they improve VR for their target applications.

Keywords:

• Neutron transport
• hybrid methods
• review
• deep-penetration neutron transport
• variance reduction

Acknowledgments

We are grateful for the strong field of method development and method developers that necessitated this review. In particular, Tara Pandya, Seth Johnson, Steven Hamilton, and Tom Evans at ORNL have been instrumental for us. We would also like to thank Ed Larsen for graciously providing his personal notes on contributon theory to supplement our understanding of the material. Last, Kathryn Huff was indispensable in preparing this manuscript from its original form as a dissertation chapter. We are grateful for her contribution to this work and her help in getting this manuscript in its current form. Critical review of this review came from Massimiliano Fratoni, Tara Pandya, and John Harte in its early stage. Time to prepare this publication was supported in part by the Gordon and Betty Moore Foundation’s Data-Driven Discovery Initiative through grant GBMF4561 to Matthew Turk. This material is based on work supported by the U.S. Department of Energy under award number DE-NE0008286.

Notes

^a While Booth defined importance related to particles leaving the cell in Eq. [7], in a later paper with Hendricks,¹⁰ importance was defined as related to particles and their weights entering the cell. As long as the bookkeeping remains consistent, the importance estimates should be comparable.