High-Order Stochastic Perturbation Method for Updating Response Functions for Changes in Material Density and Isotopic Atom Density

In this paper, a new high-order stochastic perturbation method is developed to update the COMET surface-to-surface and fission response functions due to any change in arbitrary magnitude in the density of materials or isotopic atom densities. The method is developed by deriving the relation between the weights of a particle making multiple collisions in the perturbed and unperturbed systems and tallying the Chebyshev expansion moments of the response functions. As a result, the response functions can be updated on the fly during COMET core calculations to account for any arbitrary change in the material density or isotopic atom density. The method is benchmarked in a full-length Advanced High-Temperature Reactor (AHTR) single-assembly problem.

A comparison between the COMET solution using the perturbation method and that using the response function library generated directly by Monte Carlo reveals excellent agreement between the two COMET solutions (i.e. the corresponding eigenvalues and fission density distributions). The difference in the eigenvalues is 2 pcm, which is less than one standard deviation (1 of the stochastic uncertainty in the COMET calculations (7 pcm), and the average relative difference in the stripewise fission densities is 0.12%, which is less than 3 . The perturbation method eliminates the need for precomputing the perturbed responses for the perturbed COMET calculation. This is a savings of the library precomputation time by a factor of 3.66.