绝热聚焦下含能粒子扩散系数随位移变化的研究
Diffusion coefficient with displacement variance of energetic particles with adiabatic focusing
摘要：
方程$κ_{zz}=dσ^2/(2dt)$（以下称为DCDV）是描述平行扩散系数$κ_{zz}$与平行位移方差$σ^2$的关系的高能粒子的公知公式。在本研究中，我们发现DCDV只适用于两种各向同性分布函数的输运方程，一种是不含交叉项的输运方程，另一种是不含对流项的输运方程。这里，通过采用更一般的输运方程，即，由Fokker-Planck方程导出的变系数微分方程，得到了一个新的$κ_{zz}$作为$σ^2$的函数的方程。我们发现DCDV是新方程的特例。此外，还初步研究了另一个与电报方程相对应的$κ_{zz}$作为$σ^2$的函数的方程.
英文摘要：
The equation $κ_{zz}=dσ^2/(2dt)$ (hereafter DCDV) is a well-known formula of energetic particles describing the relation of parallel diffusion coefficient $κ_{zz}$ with the parallel displacement variance $σ^2$. In this study, we find that DCDV is only applicable to two kinds of transport equations of isotropic distribution function, one is without cross terms, the other is without convection term. Here, by employing the more general transport equation, i.e., the variable coefficient differential equation derived from the Fokker-Planck equation, a new equation of $κ_{zz}$ as a function of $σ^2$ is obtained. We find that DCDV is the special case of the new equation. In addition, another equation of $κ_{zz}$ as a function of $σ^2$ corresponding to the telegraph equation is also investigated preliminarily.
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