Exact Monte Carlo Perturbation Analysis by Forward-Adjoint Coupling in Radiation Transport Calculations

An exact perturbation analysis method in Monte Carlo radiation transport calculations is investigated utilizing the coupling of forward and adjoint simulations. The vehicle chosen for this investigation is correlated-coupling for time-independent neutron or photon transport problems, which has been applied to material perturbation isolated from both the source and detector. By initiating forward and adjoint simulation histories (trajectories) in opposite directions at a position sampled from the interface between the perturbed and unperturbed materials, the correlated-coupling can exclusively construct the physical particle histories traversing the perturbed material. In other words, only those histories that have influence on the variation of the detector response are simulated. There exists no approximation in the sense that all the higher order perturbed terms in the response variation are kept. Moreover, the statistical error is estimated in the same way as in the confidence interval estimation in a standard forward or adjoint calculation. The theoretical basis lies in response decomposition with an enclosure containing both the source and detector. Numerical results are shown for multi-energy group problems.