Relationship of transport coefficients with statistical quantities of charged particles. (arXiv:2306.13839v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Wang_J/0/1/0/all/0/1">J. F. Wang</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Qin_G/0/1/0/all/0/1">G. Qin</a>
In the previous studies, from the Fokker-Planck equation the general spatial
transport equation, which contains an infinite number of spatial derivative
terms $T_n=kappa_{nz}partial^n{F}/ partial{z^n}$ with $n=1, 2, 3, cdots$,
was derived. Due to the complexity of the general equation, some simplified
equations with finite spatial derivative terms have been used in astrophysical
researches, e.g., the diffusion equation, the hyperdiffusion one, subdiffusion
transport one, etc. In this paper, the simplified equations with the highest
order spatial derivative terms up to the first-, second-, third-, fourth-, and
fifth-order are listed, and their transport coefficient formulas are derived,
respectively. We find that most of the transport coefficients are determined by
the corresponding statistical quantities. In addition, we find that the
well-known statistical quantities, skewness $mathcal{S}$ and kurtosis
$mathcal{K}$, are determined by some transport coefficients. The results can
help one to use different transport coefficients determined by the statistical
quantities, including many that are relatively new found in this paper, to
study charged particle parallel transport processes.
In the previous studies, from the Fokker-Planck equation the general spatial
transport equation, which contains an infinite number of spatial derivative
terms $T_n=kappa_{nz}partial^n{F}/ partial{z^n}$ with $n=1, 2, 3, cdots$,
was derived. Due to the complexity of the general equation, some simplified
equations with finite spatial derivative terms have been used in astrophysical
researches, e.g., the diffusion equation, the hyperdiffusion one, subdiffusion
transport one, etc. In this paper, the simplified equations with the highest
order spatial derivative terms up to the first-, second-, third-, fourth-, and
fifth-order are listed, and their transport coefficient formulas are derived,
respectively. We find that most of the transport coefficients are determined by
the corresponding statistical quantities. In addition, we find that the
well-known statistical quantities, skewness $mathcal{S}$ and kurtosis
$mathcal{K}$, are determined by some transport coefficients. The results can
help one to use different transport coefficients determined by the statistical
quantities, including many that are relatively new found in this paper, to
study charged particle parallel transport processes.
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