# Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows

## Abstract

Riemannian geometry of curves applied recently by Ricca [Fluid Dyn. Res 36, 319 (2005)] in the case of inflectional disequilibrium of twisted magnetic flux tubes is used here to compute the magnetic helicity force-free field case. Here the application of Lorentz force-free to the magnetic flux tube in tokamaks allows one to obtain an equation that generalizes the cylindrical tokamak equation by a term that contains the curvature of the magnetic flux tube. Another example of the use of the magnetic flux tube is done by taking the electron magnetohydrodynamics (MHD) fluid model (EMHD) of plasma physics that allows one to compute the velocity of the fluid in helical and almost helical flows in terms of the Frenet torsion of thin magnetic flux tubes. The cases of straight and curved twisted tubes are examined. Second-order effects on the Frenet torsion arise on the poloidal component of the magnetic field, while curvature effects appear in the toroidal component. The magnetic fields are computed in terms of the penetration depth used in superconductors. The ratio between poloidal and toroidal components of the magnetic field depends on the torsion and curvature of the magnetic flux tube. It is shown that the rotation ofmore »

- Authors:

- Departamento de Fisica Teorica, Instituto de Fisica-UERJ Rua Sao Fco. Xavier 524, Rio de Janeiro, RJ Maracana, CEP:20550-003 (Brazil)

- Publication Date:

- OSTI Identifier:
- 20782501

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 2; Other Information: DOI: 10.1063/1.2172363; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ELECTRONS; EQUATIONS; FLUID FLOW; GEOMETRY; HELICITY; LORENTZ FORCE; MAGNETIC FIELDS; MAGNETIC FLUX; MAGNETOHYDRODYNAMICS; PENETRATION DEPTH; PLASMA; PLASMA CONFINEMENT; PLASMA SIMULATION; ROTATION; TOKAMAK DEVICES; TORSION; TUBES

### Citation Formats

```
Garcia de Andrade, L.C.
```*Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows*. United States: N. p., 2006.
Web. doi:10.1063/1.2172363.

```
Garcia de Andrade, L.C.
```*Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows*. United States. doi:10.1063/1.2172363.

```
Garcia de Andrade, L.C. Wed .
"Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows". United States.
doi:10.1063/1.2172363.
```

```
@article{osti_20782501,
```

title = {Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows},

author = {Garcia de Andrade, L.C.},

abstractNote = {Riemannian geometry of curves applied recently by Ricca [Fluid Dyn. Res 36, 319 (2005)] in the case of inflectional disequilibrium of twisted magnetic flux tubes is used here to compute the magnetic helicity force-free field case. Here the application of Lorentz force-free to the magnetic flux tube in tokamaks allows one to obtain an equation that generalizes the cylindrical tokamak equation by a term that contains the curvature of the magnetic flux tube. Another example of the use of the magnetic flux tube is done by taking the electron magnetohydrodynamics (MHD) fluid model (EMHD) of plasma physics that allows one to compute the velocity of the fluid in helical and almost helical flows in terms of the Frenet torsion of thin magnetic flux tubes. The cases of straight and curved twisted tubes are examined. Second-order effects on the Frenet torsion arise on the poloidal component of the magnetic field, while curvature effects appear in the toroidal component. The magnetic fields are computed in terms of the penetration depth used in superconductors. The ratio between poloidal and toroidal components of the magnetic field depends on the torsion and curvature of the magnetic flux tube. It is shown that the rotation of the almost helical plasma flow contributes to the twist of the magnetic flux tube through the total Frenet torsion along the tube.},

doi = {10.1063/1.2172363},

journal = {Physics of Plasmas},

number = 2,

volume = 13,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}