# Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

## Abstract

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

- Authors:

- Research Department of Biomedical Engineering, Institute of Electrical Engineering, Chinese Academy of Science, Beijing 100190 (China)
- School of Science, Harbin Institute of Technology, Shenzhen 518055 (China)

- Publication Date:

- OSTI Identifier:
- 22663233

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 845; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTROPHYSICS; COSMIC RADIATION; DIFFUSION; INCLINATION; MAGNETIC FIELDS; NONLINEAR PROBLEMS; PLASMA; POWER SERIES; SCATTERING; SIMULATION; TRANSPORT THEORY; TURBULENCE

### Citation Formats

```
Wang, J. F., Ma, Q. M., Song, T., Yuan, S. B., and Qin, G., E-mail: wangjunfang@mail.iee.ac.cn, E-mail: qingang@hit.edu.cn.
```*Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA7FB6.

```
Wang, J. F., Ma, Q. M., Song, T., Yuan, S. B., & Qin, G., E-mail: wangjunfang@mail.iee.ac.cn, E-mail: qingang@hit.edu.cn.
```*Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing*. United States. doi:10.3847/1538-4357/AA7FB6.

```
Wang, J. F., Ma, Q. M., Song, T., Yuan, S. B., and Qin, G., E-mail: wangjunfang@mail.iee.ac.cn, E-mail: qingang@hit.edu.cn. Sun .
"Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing". United States. doi:10.3847/1538-4357/AA7FB6.
```

```
@article{osti_22663233,
```

title = {Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing},

author = {Wang, J. F. and Ma, Q. M. and Song, T. and Yuan, S. B. and Qin, G., E-mail: wangjunfang@mail.iee.ac.cn, E-mail: qingang@hit.edu.cn},

abstractNote = {The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.},

doi = {10.3847/1538-4357/AA7FB6},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 2,

volume = 845,

place = {United States},

year = {2017},

month = {8}

}