In this paper a methodology is described to estimate multigroup neutron source distributions which must be added into a subcritical system to drive it to a steady state prescribed power distribution. This work has been motivated by the principle of operation of the ADS (Accelerator Driven System) reactors, which have subcritical cores stabilized by the action of external sources. We use the energy multigroup two-dimensional neutron transport equation in the discrete ordinates formulation (SN) and the equation which is adjoint to it, whose solution is interpreted here as a distribution measuring the importance of the angular flux of neutrons to a linear functional. These equations are correlated through a reciprocity relation, leading to a relationship between the interior sources of neutrons and the power produced by unit length of height of the domain. A coarse-mesh numerical method of the spectral nodal class, referred to as adjoint response matrix constant-nodal method, is applied to numerically solve the adjoint SN equations. Numerical experiments are performed to analyze the accuracy of the present methodology so as to illustrate its potential practical applications.
翻译:本文介绍一种方法来估计多组中子源的分布,这些分布必须添加到一个亚临界系统中,才能将中子源推向稳定的状态指定电源分布。这项工作的动机是ADS(加速驱动系统)反应堆的运作原则,这些反应堆的次临界核心由外部源的动作稳定下来。我们使用离散坐标配方(SN)和与之相连的方程式中的能源多组二维中子传输方程式,其解决方案在这里被解释为衡量中子角通量对线性功能的重要性的分布。这些方程式通过对等关系相互关联,导致中子内部源与以单位高度生成的电源之间的关系。光谱节点级的粗微数字方法,称为联合反应矩阵常态法,用于从数字角度解决离子 SN方程式。进行数值实验是为了分析当前方法的准确性,从而说明其潜在的实用应用。