An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part II: Flux and Eigenvalue Sensitivities to Nuclear Cross Sections and Resonance Parameters

Abstract

A benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension was established. For the first time, the analytic solution of the flux amplitude was derived in the particular case of an infinite-homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). In this paper, the benchmark is extended to the adjoint transport problem, and a solution to the adjoint flux is derived. The adjoint flux solution is then combined with the forward flux to obtain expressions for an arbitrary-order cross section and resonance parameter sensitivity coefficients. Finally, numerical solutions are provided for a benchmark problem constituted of the first resonance of ²³⁹Pu, the 6.67-eV resonance of ²³⁸U, and a scattering isotope with a flat cross section, allowing for computational verification of the sensitivity coefficients and nuclear data uncertainty of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the sensitivity analysis of neutron transport criticality calculations.

Keywords:

• Neutron transport
• neutron flux
• nuclear data uncertainty
• nuclear cross-section resonances
• analytic benchmark