Variational method for three-dimensional toroidal equilibria

A. Bhattacharjee, J. C. Wiley, R. L. Dewar

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23 Scopus citations


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 languageEnglish (US)
Pages (from-to)213-225
Number of pages13
JournalComputer Physics Communications
Issue number2-3
StatePublished - Feb 1984
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • General Physics and Astronomy


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