标题： 各向同性康普顿散射的数值计算 显示英文标题

标题： Numerical computation of isotropic Compton scattering

摘要： 康普顿散射参与了许多天体物理情形。 它众所周知，并且在过去五十年里被详细研究过。 不同截面的精确公式常常很复杂，过去基本上使用的是渐近表达式。 数值计算能力现在已经发展到可以直接在处理等离子体中各种相互作用的复杂代码中使用精确公式。 尽管康普顿截面的数值计算在原则上很简单，但其实用评估常常容易出现精度问题。 这些问题在某些天体物理情形下可能很严重，但往往没有得到适当解决。 本文研究了与康普顿散射对相互作用光子和粒子群时间演化贡献相关的数值问题。 推导出了一种无数值抵消的各向同性康普顿截面的精确形式。 其准确性被调查并与其他公式进行了比较。 然后，研究了几种利用该截面求解动力学方程的方法。 给出了现有截面可以数值计算的范围。 我们发现，这里推导出的截面允许对任何光子和电子能量进行准确而快速的数值评估。 求解动力学方程的最有效方法是一种结合直接积分光子和粒子分布的截面以及福克-普朗克近似的组合方法。 给出了描述这种组合的表达式。 显示英文摘要

摘要： Compton scattering is involved in many astrophysical situations. It is well known and has been studied in detail for the past fifty years. Exact formulae for the different cross sections are often complex, and essentially asymptotic expressions have been used in the past. Numerical capabilities have now developed to a point where they enable the direct use of exact formulae in sophisticated codes that deal with all kinds of interactions in plasmas. Although the numerical computation of the Compton cross section is simple in principle, its practical evaluation is often prone to accuracy issues. These can be severe in some astrophysical situations but are often not addressed properly. In this paper we investigate numerical issues related to the computation of the Compton scattering contribution to the time evolution of interacting photon and particle populations. An exact form of the isotropic Compton cross section free of numerical cancellations is derived. Its accuracy is investigated and compared to other formulae. Then, several methods to solve the kinetic equations using this cross section are studied. The regimes where existing cross sections can be evaluated numerically are given. We find that the cross section derived here allows for accurate and fast numerical evaluation for any photon and electron energy. The most efficient way to solve the kinetic equations is a method combining a direct integration of the cross section over the photon and particle distributions and a Fokker-Planck approximation. Expressions describing this combination are given.