Abstract

Presented here is an application of the Response Matrix (RM${}^{†}$) method for adjoint discrete ordinates (S${}_{\mathrm{N}}$) problems in slab-geometry applied to energy-dependent neutral particle transport problems. The RM${}^{†}$ method is free from spatial truncation errors, as it generates numerical results for the adjoint angular fluxes in multilayer slabs that agree with the numerical values obtained from the analytical solution of the energy multigroup adjoint S${}_{\mathrm{N}}$ equations. The main contribution of this work is to analyze the application of the RM${}^{†}$ method to problems where it is required to solve the energy multigroup adjoint S${}_{\mathrm{N}}$ equations multiple times. This is the case of two classes of problems that can be taken care of through the adjoint technique: (i) source-detector problems; and (ii) the estimation of interior neutron source distributions that drive a subcritical system at a prescribed power density level. The efficiency (speed and accuracy) of the RM${}^{†}$ code is compared to the conventional Diamond Difference code.

摘要

这里介绍的是响应矩阵 (RM${}^{†}$) 方法用于伴随离散纵坐标 (S${}_{\mathrm{N}}$) 应用于依赖能量的中性粒子传输问题的平板几何问题。RM${}^{†}$ 该方法没有空间截断误差，因为它生成的多层板中伴随角通量的数值结果与从能量多群伴随 S 的解析解获得的数值一致${}_{\mathrm{N}}$方程。这项工作的主要贡献是分析了RM的应用${}^{†}$ 求解能量多群伴随S问题的方法${}_{\mathrm{N}}$多次方程。这是可以通过伴随技术处理的两类问题的情况：(i) 源检测器问题；(ii) 以规定的功率密度水平驱动亚临界系统的内部中子源分布的估计。RM的效率（速度和准确性）${}^{†}$ 代码与传统的钻石差异代码进行比较。