Eigenvalue implicit sensitivity and uncertainty analysis with the subgroup resonance-calculation method

Response sensitivity coefficients with respect to nuclide cross sections consist of two parts, explicit sensitivity coefficients and implicit sensitivity coefficients. The explicit sensitivity coefficients, which account the direct impact of cross sections on the responses through neutron transport equation, can be calculated efficiently with the classical Perturbation Theory. The implicit sensitivity coefficients, which account the indirect impact of cross sections on the responses through resonance self-shielding, are either omitted in most sensitivity analysis codes, or accounted for based on simple resonance-calculation methods which are not applicable for complex fuel designs. In order to expand the implicit sensitivity analysis method to wider application domain, a method based on the Generalized Perturbation Theory (GPT) is proposed in this paper to calculate the implicit sensitivity coefficients by using the subgroup method in the resonance self-shielding calculation. Based on the in-house-developed 2-D general-geometry method-of-characteristic neutron-transport code AutoMOC and subgroup resonance self-shielding code SUGAR, the proposed method has been implemented in the COLEUS code for the sensitivity and uncertainty analysis. Numerical analysis is then performed to investigate the impact of the implicit sensitivity coefficients of eigenvalue on non-resonance nuclide cross sections in two single-cell cases with different enrichments. The eigenvalue sensitivity coefficients predicted by the COLEUS code are consistent with those calculated by the direct-perturbation method, the reference solution. The results show that the implicit sensitivity has an important impact on both sensitivity and uncertainty in some analyzed cases.