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The Evaluation of Radiation Transport Forward-Adjoint Flux Integrals Using Monte Carlo Correlated Coupling Methods

S. N. Cramer

Nuclear Science and Engineering / Volume 141 / Number 3 / July 2002 / Pages 252-271

Technical Paper /

Radiation transport integrals containing both forward and adjoint fluxes are amenable to solution by the method of correlated coupling. Existing methods for surface integral coupling of forward and adjoint histories have been extended to volumetric coupling. Within the context of standard Monte Carlo usage, these integral solutions are exact, and the application to perturbation analysis requires no approximation. Coupled forward-adjoint history pairs are initiated at points selected uniformly in the perturbed volume. The energy and angular dependence of each history is dictated by the difference operator of the forward and adjoint transport equations, one equation for the perturbed system and one for the unperturbed system. The volume integral is accumulated as these history pairs score in the respective source or response regions. Some simple systems are analyzed showing that the new method gives comparable results, and a lower variance, as for existing methods. A review of current correlated coupling methodology is given, and suggestions for further study are outlined.

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