### Abstract

An equation governing potential vorticity in a magnetized plasmas is derived. The equation is analogous to Ertel's theorem. In the long wave-length limit the potential vorticity equals the ratio of the gyro-frequency plus the E × B- and diamagnetic polarization densities to the particle density. The equation is relevant for transport barriers in magnetically confined plasmas because particle density, ion temperature and the radial electric field are mutually coupled through the potential vorticity. The potential vorticity equation is derived from an energy conserving, four-field, electrostatic, full-F gyrofluid model. It is shown that the gyrofluid model possesses two exact Lagrangian invariants. In systems where mixing uniformly distribute the Lagrangian invariants we derive the corresponding turbulent equipartion states. It is shown that the system is driven towards constant potential vorticity. Given particle density and magnetic field profiles we infer ion temperature and electric potential profiles from the derived turbulent equipartion states.

Original language | English |
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Article number | 054016 |

Journal | Plasma Physics and Controlled Fusion |

Volume | 57 |

Issue number | 5 |

Number of pages | 7 |

ISSN | 0741-3335 |

DOIs | |

Publication status | Published - 2015 |

### Keywords

- gyrofluid
- potential vorticity
- transport barriers
- turbulent equipartion
- zonal flows
- Electric field effects
- Electric fields
- Electric potential
- Lagrange multipliers
- Tokamak devices
- Gyrofluids
- Potential vorticity
- Transport barrier
- Zonal flows
- Vorticity

## Cite this

Madsen, J., Juul Rasmussen, J., Naulin, V., Nielsen, A. H., & Treue, F. (2015). Gyrofluid potential vorticity equation and turbulent equipartion states: Paper.

*Plasma Physics and Controlled Fusion*,*57*(5), [054016]. https://doi.org/10.1088/0741-3335/57/5/054016