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Subspace approximation to the cosmic ray Fokker-Planck equation with perpendicular diffusion
Astrophysics and Space Science ( IF 1.9 ) Pub Date : 2021-07-26 , DOI: 10.1007/s10509-021-03976-w
A. Shalchi 1
Affiliation  

The Fokker-Planck equation describing the diffusion of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not useful for applications. In the past a subspace approximation was proposed which allows to compute important quantities such as the characteristic function as well as certain expectation values. This previous approach was applied to solve the one-dimensional Fokker-Planck equation which contains only a pitch-angle scattering term. In the current paper we extend this approach in order to solve the Fokker-Planck equation for the three-dimensional case including a perpendicular diffusion term. Several expectation values are computed based on our new solution.



中文翻译:

具有垂直扩散的宇宙射线福克-普朗克方程的子空间近似

描述与湍流相互作用的高能粒子扩散的 Fokker-Planck 方程很难解析求解。数值解当然是可能的,但它们对应用程序没有用。过去提出了一种子空间近似,它允许计算重要的量,例如特征函数以及某些期望值。这种先前的方法用于求解仅包含俯仰角散射项的一维 Fokker-Planck 方程。在当前的论文中,我们扩展了这种方法,以解决包含垂直扩散项的三维情况的 Fokker-Planck 方程。根据我们的新解决方案计算了几个期望值。

更新日期:2021-07-26
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