# Electromagnetic effect on geodesic acoustic mode with adiabatic electrons

## Abstract

The geodesic acoustic mode (GAM) is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the second order and the finite β effect. The general dispersion relation is derived from the gyro-kinetic equations in the presence of nonzero δA _{∥}, the parallel component of the perturbed magnetic vector potential. Transparent and concise expressions for the GAM frequency and Landau damping rate in the presence of the second order FOW effect and finite β effect are first presented. It is clearly shown that the m = ±2 harmonics dominant δA _{∥} and the kinetic expression of δA _{∥} have the same form as the fluid one. For the real frequency, the electromagnetic effect introduces a term on the order of q ^{2}β, which is comparable to the second order electrostatic terms, namely, the terms introduced by the second order FOW resonance effect. While for the collisionless damping rate, δA _{∥} does not directly introduce β–dependent terms, but affects the damping rate via modifying the real frequency. Besides, our analytical result shows good agreement with the numerical examinations.

- Authors:

- Anhui Univ. of Technology, Anhui (China)
- Univ. of Science and Technology of China, Hefei (China)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Mound Plant, Miamisburg, OH (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1545355

- Alternate Identifier(s):
- OSTI ID: 1569668

- Report Number(s):
- LLNL-JRNL-789248

Journal ID: ISSN 1070-664X

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 26; Journal Issue: 2; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Huang, Wenlong, Ren, Haijun, and Xu, X. Q. Electromagnetic effect on geodesic acoustic mode with adiabatic electrons. United States: N. p., 2019.
Web. doi:10.1063/1.5080271.
```

```
Huang, Wenlong, Ren, Haijun, & Xu, X. Q. Electromagnetic effect on geodesic acoustic mode with adiabatic electrons. United States. doi:10.1063/1.5080271.
```

```
Huang, Wenlong, Ren, Haijun, and Xu, X. Q. Tue .
"Electromagnetic effect on geodesic acoustic mode with adiabatic electrons". United States. doi:10.1063/1.5080271. https://www.osti.gov/servlets/purl/1545355.
```

```
@article{osti_1545355,
```

title = {Electromagnetic effect on geodesic acoustic mode with adiabatic electrons},

author = {Huang, Wenlong and Ren, Haijun and Xu, X. Q.},

abstractNote = {The geodesic acoustic mode (GAM) is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the second order and the finite β effect. The general dispersion relation is derived from the gyro-kinetic equations in the presence of nonzero δA∥, the parallel component of the perturbed magnetic vector potential. Transparent and concise expressions for the GAM frequency and Landau damping rate in the presence of the second order FOW effect and finite β effect are first presented. It is clearly shown that the m = ±2 harmonics dominant δA∥ and the kinetic expression of δA∥ have the same form as the fluid one. For the real frequency, the electromagnetic effect introduces a term on the order of q2β, which is comparable to the second order electrostatic terms, namely, the terms introduced by the second order FOW resonance effect. While for the collisionless damping rate, δA∥ does not directly introduce β–dependent terms, but affects the damping rate via modifying the real frequency. Besides, our analytical result shows good agreement with the numerical examinations.},

doi = {10.1063/1.5080271},

journal = {Physics of Plasmas},

number = 2,

volume = 26,

place = {United States},

year = {2019},

month = {2}

}

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