Calculation Method of LN Function Cross-section Implicit Sensitivity Coefficient

Abstract

For many new reactors, the uncertainty caused by nuclear data has become the main source of uncertainty in reactor physics design due to the higher uncertainty of measurement cross-section in the high energy region. Previously, uncertainty analysis for fast spectrum reactors mainly focused on explicit sensitivity coefficient calculation and uncertainty analysis, with less analysis of implicit effects and little analysis of the magnitude of their impact. The implicit effect of sensitivity coefficient is related to the processing method of resonance self-shielding cross-section, and due to the complexity of resonance self-shielding calculation, the implicit effect of sensitivity coefficient also becomes more complex. For example, for the problem of pressurized water reactors, implicit effects can be considered by solving the continuous energy spectrum slowing equation or changing the effective resonance integral table in the library. For thermal reactors, due to the need for neutron moderation to pass through the intermediate energy region with strong resonance self-shielding effect, the implicit sensitivity effect is relatively significant. When calculating the sensitivity coefficient, the implicit effect needs to be considered. For fast spectrum reactors (fast reactors), although the implicit effect is not very significant in theory, there has been no good method for calculating the implicit effect of sensitivity coefficients. The resonance self-shielding processing method based on background cross-section iteration is widely used in many reactor physics programs. A new implicit sensitivity effect analysis method based on the Bondarenko background cross-section iteration method was proposed in this study. The LN function was used to interpolate the background cross-section to represent the influence of cross-section disturbance on neutron spectra, and the influence was transmitted to the explicit sensitivity coefficient, thereby obtaining the sensitivity coefficient considering the implicit effect. Due to the fact that the implicit sensitivity coefficient of the cross-section is mainly related to the LN function, it is called as the LN function implicit sensitivity calculation method (LNIS method). A simple fast energy spectrum benchmark problem was proposed for the above method, and the implicit effect of the cross-section calculated by the new method was analyzed using the benchmark problem, proving the correctness of the method by comparison with the results of MCNP. For the proposed fast spectral benchmark problem, multi-group cross-section calculation was used. In the energy group with strong resonance self-shielding effect, the implicit effect correction of some nuclear cross-section sensitivity coefficients can reach a maximum of 50%. For the few-group cross-section, for most reaction channels, the accuracy of the keff relative sensitivity coefficient and uncertainty calculation after considering the implicit effect was significantly improved, but there were some reaction channels. Perhaps due to issues with Bondarenko and narrow resonance approximation itself, the improvement in sensitivity coefficient and uncertainty accuracy is not significant.

Keywords

• reactor
• implicit sensitivity coefficient
• sensitivity coefficient calculation
• uncertainty