Relationship of Transport Coefficients with Statistical Quantities of Charged Particles

In previous studies, a general spatial transport equation was derived from the Fokker-Planck equation. The latter equation contains an infinite number of spatial derivative terms T _n = K _nz ∂ⁿ F/∂z ⁿ with n = 1, 2, 3, ⋯ . Due to the complexity of the general equation, some simplified equations with finitely many spatial derivative terms have been used by astrophysical researches, e.g., the diffusion equation, the hyperdiffusion equation, subdiffusion transport equation, etc. In this paper, the simplified transport equations with the 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, the skewness - and the kurtosis - are determined by some transport coefficients. The results can help one to use various transport coefficients determined by the statistical quantities, including many that are relatively newfound in this paper, to study charged particle parallel transport processes.