论文标题
带电颗粒的传输方程的迭代操作的扩散系数的不变性
The invariance of the diffusion coefficient with the iterative operations of charged particles' transport equation
论文作者
论文摘要
空间平行扩散系数（SPDC）是描述充电颗粒传输的重要数量之一。 SPDC有三个不同的定义，即，位移方差定义$κ_{zz}^{dv} = \ lim_ { $ x = \ partial {f}/\ partial {z} $和tgk公式定义$κ_{zz}^{tgk} = \ int_0^{\ int_0^{\ infty} dt \ langle v_z（t）v_z（t）v_z（0）\ rangle $。对于恒定平均磁场，SPDC的三个不同定义给出了相同的结果。但是，对于聚焦场，可以证明不同定义的结果不是相同的。在本文中，从Fokker-Planck方程式中，我们发现不同的方法，例如一般的傅立叶扩展和扰动理论，可以给出各向同性分布函数（EIDFS）的不同方程。但这表明，一个EIDF可以通过一些衍生迭代操作（DIOS）转化为另一个EIDF。如果SPDC的一个定义对于Dios来说是不变的，则显然该定义也是不同EIDF的不变性，因此，它是EIDF（DMES）不同派生方法的不变量。对于聚焦字段，我们建议TGK定义$κ_{zz}^{tgk} $只是大约公式，而fick的定律定义$κ_{zz}^{fl} $对某些dios并不不变。但是，至少对于特殊条件，在本文中，我们表明定义$κ_{zz}^{dv} $是Dios种类的不变数量。因此，对于空间变化，位移方差定义$κ__{zz}^{dv} $，而不是fick的定义定义$κ__{zz}^{fl} $ and tgk公式定义$κ__{zz {zz}^{zz}^{tgk {tgk} $，是最适当的定义。
The Spatial Parallel Diffusion Coefficient (SPDC) is one of the important quantities describing energetic charged particle transport. There are three different definitions for the SPDC, i.e., the Displacement Variance definition $κ_{zz}^{DV}=\lim_{t\rightarrow t_{\infty}}dσ^2/(2dt)$, the Fick's Law definition $κ_{zz}^{FL}=J/X$ with $X=\partial{F}/\partial{z}$, and the TGK formula definition $κ_{zz}^{TGK}=\int_0^{\infty}dt \langle v_z(t)v_z(0) \rangle$. For constant mean magnetic field, the three different definitions of the SPDC give the same result. However, for focusing field it is demonstrated that the results of the different definitions are not the same. In this paper, from the Fokker-Planck equation we find that different methods, e.g., the general Fourier expansion and perturbation theory, can give the different Equations of the Isotropic Distribution Function (EIDFs). But it is shown that one EIDF can be transformed into another by some Derivative Iterative Operations (DIOs). If one definition of the SPDC is invariant for the DIOs, it is clear that the definition is also an invariance for different EIDFs, therewith it is an invariant quantity for the different Derivation Methods of EIDF (DMEs). For the focusing field we suggest that the TGK definition $κ_{zz}^{TGK}$ is only the approximate formula, and the Fick's Law definition $κ_{zz}^{FL}$ is not invariant to some DIOs. However, at least for the special condition, in this paper we show that the definition $κ_{zz}^{DV}$ is the invariant quantity to the kinds of the DIOs. Therefore, for spatially varying field the displacement variance definition $κ_{zz}^{DV}$, rather than the Fick's law definition $κ_{zz}^{FL}$ and TGK formula definition $κ_{zz}^{TGK}$, is the most appropriate definition of the SPDCs.
