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.

摘要

建立了验证沿能量维度的中子输运临界求解器准确性的基准。在质心各向同性散射和任意数量的无阈值中性粒子反应共振（例如，辐射捕获）的无限均匀介质的特殊情况下，首次推导出通量幅度的解析解、裂变和共振散射）。在本文中，基准扩展到伴随传输问题，并推导出伴随通量的解决方案。然后将伴随通量解与前向通量组合以获得任意阶横截面和共振参数灵敏度系数的表达式。最后，为由第一次共振构成的基准问题提供了数值解²³⁹ Pu、²³⁸ U的 6.67-eV 共振以及具有平坦横截面的散射同位素，允许对当前中子输运临界代码的灵敏度系数和核数据不确定性进行计算验证。通过这些新颖的结果，该分析基准可以作为验证中子输运临界计算灵敏度分析的参考。