# On the bootstrap current in stellarators and tokamaks

## Abstract

The expression for the long-mean-free-path limit of the bootstrap current in stellarators is rederived in such a way that the expansion procedure is identical to that used in the corresponding calculation for a tokamak. In addition, the first correction due to finite collisionality is calculated and shown to vanish in quasi-isodynamic configurations without net current. This correction, which is proportional to the square root of the collisionality, is found to compare well with a numerical solution of the first-order drift kinetic equation in spherical tokamak geometry. Numerically, it appears that there is a similar correction in general stellarator geometry, which however depends on the strength of the radial electric field.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22043498

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 9; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOOTSTRAP CURRENT; CONFINEMENT; CORRECTIONS; ELECTRIC FIELDS; EXPANSION; KINETIC EQUATIONS; MEAN FREE PATH; PLASMA; SPHERICAL CONFIGURATION; STELLARATORS; TOKAMAK DEVICES

### Citation Formats

```
Helander, P., Geiger, J., and Maassberg, H.
```*On the bootstrap current in stellarators and tokamaks*. United States: N. p., 2011.
Web. doi:10.1063/1.3633940.

```
Helander, P., Geiger, J., & Maassberg, H.
```*On the bootstrap current in stellarators and tokamaks*. United States. doi:10.1063/1.3633940.

```
Helander, P., Geiger, J., and Maassberg, H. Thu .
"On the bootstrap current in stellarators and tokamaks". United States. doi:10.1063/1.3633940.
```

```
@article{osti_22043498,
```

title = {On the bootstrap current in stellarators and tokamaks},

author = {Helander, P. and Geiger, J. and Maassberg, H.},

abstractNote = {The expression for the long-mean-free-path limit of the bootstrap current in stellarators is rederived in such a way that the expansion procedure is identical to that used in the corresponding calculation for a tokamak. In addition, the first correction due to finite collisionality is calculated and shown to vanish in quasi-isodynamic configurations without net current. This correction, which is proportional to the square root of the collisionality, is found to compare well with a numerical solution of the first-order drift kinetic equation in spherical tokamak geometry. Numerically, it appears that there is a similar correction in general stellarator geometry, which however depends on the strength of the radial electric field.},

doi = {10.1063/1.3633940},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 9,

volume = 18,

place = {United States},

year = {2011},

month = {9}

}