TY - JOUR

T1 - Variational method for three-dimensional toroidal equilibria

AU - Bhattacharjee, A.

AU - Wiley, J. C.

AU - Dewar, R. L.

N1 - Funding Information:
This work was primarily supported by the United States Department of Energy under con- tract # DE-ACO5-79ET-53-36 at the Institute for Fusion Studies and contract * DE-FGO5O8OET-53088 at the Fusion Research Center.

PY - 1984/2

Y1 - 1984/2

N2 - 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.

AB - 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.

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U2 - 10.1016/0010-4655(84)90046-8

DO - 10.1016/0010-4655(84)90046-8

M3 - Article

AN - SCOPUS:0020703586

VL - 31

SP - 213

EP - 225

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

IS - 2-3

ER -