The Multi-Step CADIS Method for Shutdown Dose Rate Calculations and Uncertainty Propagation

Shutdown dose rate (SDDR) analysis requires (a) a neutron transport calculation to estimate neutron flux fields, (b) an activation calculation to compute radionuclide inventories and associated photon sources, and (c) a photon transport calculation to estimate final SDDR. In some applications, accurate full-scale Monte Carlo (MC) SDDR simulations are needed for very large systems with massive amounts of shielding materials. However, these simulations are impractical because calculation of space- and energy-dependent neutron fluxes throughout the structural materials is needed to estimate distribution of radioisotopes causing the SDDR. Biasing the neutron MC calculation using an importance function is not simple because it is difficult to explicitly express the response function, which depends on subsequent computational steps. Typical SDDR calculations do not consider how uncertainties in MC neutron calculation impact SDDR uncertainty, even though MC neutron calculation uncertainties usually dominate SDDR uncertainty.

The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) hybrid MC/deterministic method was developed to speed SDDR MC neutron transport calculation using a deterministically calculated importance function representing the neutron importance to the final SDDR. Undersampling is usually inevitable in large-problem SDDR simulations because it is very difficult for the MC method to simulate particles in all space and energy elements of the neutron calculation. MS-CADIS can assess the degree of undersampling in SDDR calculations by determining the fraction of the SDDR response in the space and energy elements that did not have any scores in the MC neutron calculation. It can also provide estimates for upper and lower limits of SDDR statistical uncertainties resulting from uncertainties in MC neutron calculation.

MS-CADIS was applied to the ITER SDDR benchmark problem that resembles the configuration and geometrical arrangement of an upper port plug in ITER. Without using the hybrid MC/deterministic methods to speed MC neutron calculations, SDDR calculations were significantly undersampled for all tallies, even when MC neutron calculation computational time was 32 CPU-days. However, all SDDR tally results with MC neutron calculations of only 2 CPU-days converged with the standard Forward-Weighted CADIS (FW-CADIS) method and the MS-CADIS method. Compared to the standard FW-CADIS approach, MS-CADIS decreased the undersampling in the calculated SDDR by factors between 0.9% and 0.3% for computational times between 4 and 32 CPU-days, and it increased the computational efficiency of the SDDR neutron MC calculation by factors between 43% and 69%.