### Abstract

A variational method is developed for three-dimensional toroidal equilibria, characterized by the mapping between two coordinate systems: the cylindrical system (R, φ, Z) and the magnetic system (v, θ, ζ), where v is a radial flux surface label, θ a poloidal angle and ζ a toroidal angle. Two types of mapping, namely, the inverse mapping (v, θ, ζ) → (R, φ, Z) and the mixed mapping (v, θ, φ) → (R, ζ, Z) are considered. The dependent variables are Fourier-analysed in θ and ζ (or φ), and a set of ordinary differential equations are derived for the amplitudes in v from the variational principle. Truncation of the infinite Fourier series leads to a reduced set of equations which we solve numerically by collocation to obtain two- and three-dimensional toroidal equilibria.

Original language | English (US) |
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Pages (from-to) | 213-225 |

Number of pages | 13 |

Journal | Computer Physics Communications |

Volume | 31 |

Issue number | 2-3 |

DOIs | |

State | Published - Feb 1984 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Hardware and Architecture
- Physics and Astronomy(all)

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## Cite this

*Computer Physics Communications*,

*31*(2-3), 213-225. https://doi.org/10.1016/0010-4655(84)90046-8