# Gyrokinetic magnetohydrodynamics and the associated equilibria

## Abstract

The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee, and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, Φ, and the vector potential, A, and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when Φ → 0 and A becomes constant in time, which, in turn, gives ∇· (J _{∥}+J _{⊥}) = 0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. In conclusion, these gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.

- Authors:

- Princeton Univ., Princeton, NJ (United States). Princeton Plasma Physics Lab.

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1415462

- Alternate Identifier(s):
- OSTI ID: 1414982

- Grant/Contract Number:
- AC02-09CHI1466

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 12; 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

### Citation Formats

```
Lee, W. W., Hudson, S. R., and Ma, C. H.
```*Gyrokinetic magnetohydrodynamics and the associated equilibria*. United States: N. p., 2017.
Web. doi:10.1063/1.5008257.

```
Lee, W. W., Hudson, S. R., & Ma, C. H.
```*Gyrokinetic magnetohydrodynamics and the associated equilibria*. United States. doi:10.1063/1.5008257.

```
Lee, W. W., Hudson, S. R., and Ma, C. H. Wed .
"Gyrokinetic magnetohydrodynamics and the associated equilibria". United States. doi:10.1063/1.5008257. https://www.osti.gov/servlets/purl/1415462.
```

```
@article{osti_1415462,
```

title = {Gyrokinetic magnetohydrodynamics and the associated equilibria},

author = {Lee, W. W. and Hudson, S. R. and Ma, C. H.},

abstractNote = {The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee, and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, Φ, and the vector potential, A, and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when Φ → 0 and A becomes constant in time, which, in turn, gives ∇· (J∥+J⊥) = 0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. In conclusion, these gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.},

doi = {10.1063/1.5008257},

journal = {Physics of Plasmas},

number = 12,

volume = 24,

place = {United States},

year = {Wed Dec 27 00:00:00 EST 2017},

month = {Wed Dec 27 00:00:00 EST 2017}

}