High-Order Perturbation Theory for Incident Flux Response Expansion Methods

In this work, a high-order perturbation method is developed to generate/compute response functions for the coarse mesh transport (COMET) method, which provides whole-core neutron transport solutions to various reactor core types. In this approach, the response functions are first generated at a reference eigenvalue point, and the response functions at an arbitrary eigenvalue are computed as a high-order perturbation from the reference point. The method has been tested at both the lattice level (response function generation) and the core level (whole-core transport calculations). At the lattice level, it is found that the response functions predicted by the perturbation method agree very well with those directly computed by the Monte Carlo method. The average relative difference in the surface-to-surface response functions is 0.29% to 0.46% when the eigenvalue k ranges from 0.6667 to 1.5. In whole-core transport calculations, the COMET calculations using the high-order perturbation method are almost identical to those using the interpolation method. The eigenvalue, assembly, and pin fission densities predicted by COMET agree very well with the MCNP reference solution. This indicates that the high-order perturbation response function generation method can achieve the same accuracy as the interpolation method while significantly improving the computational efficiency of the precomputation phase.