The Diffusion Coefficient with Displacement Variance of Energetic Particles Caused by Adiabatic Focusing

J. F. Wang; G. Qin

doi:10.3847/1538-4357/ab505e

The Diffusion Coefficient with Displacement Variance of Energetic Particles Caused by Adiabatic Focusing

J. F. Wang
, G. Qin^*

^*Corresponding author for this work

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The equation κ _zz = dσ ²/(2dt) describing the relation of the parallel diffusion coefficient κ _zz with the displacement variance σ ² (hereafter DCDV) is a well-known formula. In this study, we find that DCDV is only applicable to two kinds of transport equations of the isotropic distribution function, one without cross-terms and the other without a 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.

Original language	English
Article number	89
Journal	Astrophysical Journal
Volume	886
Issue number	2
DOIs	https://doi.org/10.3847/1538-4357/ab505e
State	Published - 1 Dec 2019
Externally published	Yes

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title = "The Diffusion Coefficient with Displacement Variance of Energetic Particles Caused by Adiabatic Focusing",

abstract = "The equation κ zz = dσ 2/(2dt) describing the relation of the parallel diffusion coefficient κ zz with the displacement variance σ 2 (hereafter DCDV) is a well-known formula. In this study, we find that DCDV is only applicable to two kinds of transport equations of the isotropic distribution function, one without cross-terms and the other without a 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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T1 - The Diffusion Coefficient with Displacement Variance of Energetic Particles Caused by Adiabatic Focusing

AU - Wang, J. F.

AU - Qin, G.

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Y1 - 2019/12/1

N2 - The equation κ zz = dσ 2/(2dt) describing the relation of the parallel diffusion coefficient κ zz with the displacement variance σ 2 (hereafter DCDV) is a well-known formula. In this study, we find that DCDV is only applicable to two kinds of transport equations of the isotropic distribution function, one without cross-terms and the other without a 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.

AB - The equation κ zz = dσ 2/(2dt) describing the relation of the parallel diffusion coefficient κ zz with the displacement variance σ 2 (hereafter DCDV) is a well-known formula. In this study, we find that DCDV is only applicable to two kinds of transport equations of the isotropic distribution function, one without cross-terms and the other without a 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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DO - 10.3847/1538-4357/ab505e

M3 - 文章

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VL - 886

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 2

M1 - 89

ER -

The Diffusion Coefficient with Displacement Variance of Energetic Particles Caused by Adiabatic Focusing

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