# Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus

## Abstract

An alternative representation of an ideal magnetohydrodynamic equilibrium is developed. The representation is a variation of one given by A. Salat, Phys. Plasmas 2, 1652 (1995). The system of equations is used to study the possibility of non-symmetric equilibria in a topological torus, here an approximate rectangular parallelopiped, with periodicity in two of the three rectangular coordinates. An expansion is carried out in the deviation of pressure surfaces from planes. Resonances are manifest in the process. Nonetheless, provided the magnetic shear is small, it is shown that it is possible to select the magnetic fields and flux surfaces in such a manner that no singularities appear on resonant surfaces. One boundary surface of the parallelopiped is not arbitrary but is dependent on the equilibrium in question. A comparison of the solution sets of axisymmetric and non-axisymmetric equilibria suggests that the latter have a wider class of possible boundary shapes but more restrictive rotational transform profiles. No proof of convergence of the series is given.

- Authors:

- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)

- Publication Date:

- OSTI Identifier:
- 22252025

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; 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; APPROXIMATIONS; AXIAL SYMMETRY; COORDINATES; EQUILIBRIUM; MAGNETIC FIELDS; MAGNETIC SURFACES; MATHEMATICAL SOLUTIONS; PERIODICITY; ROTATIONAL TRANSFORM; SURFACES; TOPOLOGY

### Citation Formats

```
Weitzner, Harold.
```*Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus*. United States: N. p., 2014.
Web. doi:10.1063/1.4867184.

```
Weitzner, Harold.
```*Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus*. United States. doi:10.1063/1.4867184.

```
Weitzner, Harold. Sat .
"Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus". United States. doi:10.1063/1.4867184.
```

```
@article{osti_22252025,
```

title = {Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus},

author = {Weitzner, Harold},

abstractNote = {An alternative representation of an ideal magnetohydrodynamic equilibrium is developed. The representation is a variation of one given by A. Salat, Phys. Plasmas 2, 1652 (1995). The system of equations is used to study the possibility of non-symmetric equilibria in a topological torus, here an approximate rectangular parallelopiped, with periodicity in two of the three rectangular coordinates. An expansion is carried out in the deviation of pressure surfaces from planes. Resonances are manifest in the process. Nonetheless, provided the magnetic shear is small, it is shown that it is possible to select the magnetic fields and flux surfaces in such a manner that no singularities appear on resonant surfaces. One boundary surface of the parallelopiped is not arbitrary but is dependent on the equilibrium in question. A comparison of the solution sets of axisymmetric and non-axisymmetric equilibria suggests that the latter have a wider class of possible boundary shapes but more restrictive rotational transform profiles. No proof of convergence of the series is given.},

doi = {10.1063/1.4867184},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 2,

volume = 21,

place = {United States},

year = {2014},

month = {2}

}