Scattering-coupled adaptive source biasing for deep-penetration neutron arrival-spectrum calculations

Reliable neutron arrival spectra are needed for space radiation assessment and radiation protection, but deep-penetration Monte Carlo calculations often yield highly uneven uncertainties across energy groups. In analog Monte Carlo simulations, the nonuniform source spectrum and the energy-dependent transport behavior of neutrons can lead to relative uncertainties that differ by tens or even hundreds of times among arrival energy groups. To address this imbalance in arrival-spectrum uncertainties for deep-penetration transport, this study proposes a scattering-coupled adaptive source biasing (SC-ASB) method that uses a source-to-target response matrix to retain scattering-induced coupling from high-energy source neutrons to lower-energy arrival groups. The biased source distribution is derived by minimizing the sum of relative statistical errors (RSEs) subject to normalization and two-sided error-balance constraints, while the original source expectation is preserved by weight correction. Atmospheric neutron transport calculations showed that SC-ASB improved the relative-error distribution and increased computational efficiency. For a 15 km source height case, the figure of merit was 276 times that of analog simulation. Compared with uniform source biasing, SC-ASB showed better adaptability across source heights. In contrast to the WW variance-reduction method, SC-ASB provides more effective balancing of the RSEs across different energy groups. The method provides a variance-reduction framework for spectrum-resolved deep-penetration neutron transport.