Abstract

It has been well known that the analytic neutron transport solution tends to the analytic solution of a diffusion problem for optically thick systems with small absorption and source. The standard technique for proving the asymptotic diffusion limit is constructing an asymptotic power series of the neutron angular flux in small positive parameter $\epsilon$, which is the ratio of a typical mean free path of a particle to a typical dimension of the problem domain. In this paper, first, we provide an analysis of the asymptotic properties of the S_N transport eigenvalues. Then, we show that the analytical S_N transport solution satisfies the diffusion equation in the asymptotic diffusion limit based on a recently obtained closed-form analytical solution to the one-dimensional monoenergetic S_N neutron transport equation. The boundary conditions for the diffusion equation are discussed.

摘要

众所周知，对于具有小吸收和源的光学厚系统，解析中子输运解趋于扩散问题的解析解。证明渐近扩散极限的标准技术是在小正参数下构建中子角通量的渐近幂级数$\epsilon$，它是粒子的典型平均自由程与问题域的典型维度的比率。在本文中，首先，我们分析了 S _N传输特征值的渐近特性。然后，基于最近获得的一维单能 S _N中子输运方程的封闭形式解析解，我们表明解析 S _N输运解满足渐近扩散极限中的扩散方程。讨论了扩散方程的边界条件。