# Expansions of non-symmetric toroidal magnetohydrodynamic equilibria

## Abstract

Here, expansions of non-symmetric toroidal ideal magnetohydrodynamic equilibria with nested flux surfaces are carried out for two cases. The first expansion is in a topological torus in three dimensions, in which physical quantities are periodic of period 2π in y and z. Data is given on the flux surface x = 0. Despite the possibility of magnetic resonances the power series expansion can be carried to all orders in a parameter which measures the flux between x = 0 and the surface in question. Resonances are resolved by appropriate addition resonant fields. The second expansion is about a circular magnetic axis in a true torus. It is also assumed that the cross section of a flux surface at constant toroidal angle is approximately circular. The expansion is in an analogous flux coordinate, and despite potential resonance singularities, may be carried to all orders. Non-analytic behavior occurs near the magnetic axis. Physical quantities have a finite number of derivatives there. The results, even though no convergence proofs are given, support the possibility of smooth, well-behaved non-symmetric toroidal equilibria.

- Authors:

- New York Univ. (NYU), New York, NY (United States)

- Publication Date:

- Research Org.:
- New York Univ. (NYU), New York, NY (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1467570

- Alternate Identifier(s):
- OSTI ID: 1258497

- Grant/Contract Number:
- FG02-86ER53223

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 6; 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

```
Weitzner, Harold.
```*Expansions of non-symmetric toroidal magnetohydrodynamic equilibria*. United States: N. p., 2016.
Web. doi:10.1063/1.4954048.

```
Weitzner, Harold.
```*Expansions of non-symmetric toroidal magnetohydrodynamic equilibria*. United States. doi:10.1063/1.4954048.

```
Weitzner, Harold. Tue .
"Expansions of non-symmetric toroidal magnetohydrodynamic equilibria". United States. doi:10.1063/1.4954048. https://www.osti.gov/servlets/purl/1467570.
```

```
@article{osti_1467570,
```

title = {Expansions of non-symmetric toroidal magnetohydrodynamic equilibria},

author = {Weitzner, Harold},

abstractNote = {Here, expansions of non-symmetric toroidal ideal magnetohydrodynamic equilibria with nested flux surfaces are carried out for two cases. The first expansion is in a topological torus in three dimensions, in which physical quantities are periodic of period 2π in y and z. Data is given on the flux surface x = 0. Despite the possibility of magnetic resonances the power series expansion can be carried to all orders in a parameter which measures the flux between x = 0 and the surface in question. Resonances are resolved by appropriate addition resonant fields. The second expansion is about a circular magnetic axis in a true torus. It is also assumed that the cross section of a flux surface at constant toroidal angle is approximately circular. The expansion is in an analogous flux coordinate, and despite potential resonance singularities, may be carried to all orders. Non-analytic behavior occurs near the magnetic axis. Physical quantities have a finite number of derivatives there. The results, even though no convergence proofs are given, support the possibility of smooth, well-behaved non-symmetric toroidal equilibria.},

doi = {10.1063/1.4954048},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 6,

volume = 23,

place = {United States},

year = {2016},

month = {6}

}