Toroidal coordinates
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Co-ordinate systems used in toroidal systems:
Eulerian
(X, Y, Z)
Cylindrical
(R, φ, Z), where
- R2 = X2 + Y2, and
- tan φ = Y/X.
Simple toroidal
(r, φ, θ), where
- R = R0 + r cos θ, and
- Z = r sin θ
(R0 corresponding to the axis of the torus)
Toroidal
where Rp is the pole of the coordinate system. Surfaces of constant ζ are tori with major radii R = Rp/tanh ζ and minor radii r = Rp/sinh ζ. At R = Rp, ζ = ∞, while at infinity and at R = 0, ζ = 0. The coordinate η is a poloidal angle and runs from 0 to 2π. This system is orthogonal.
Magnetic
See Flux surface.
References
- ↑ Morse and Feshbach, Methods of theoretical physics, McGraw-Hill, New York, 1953 ISBN 007043316X
- ↑ Wikipedia:Toroidal_coordinates
- ↑ F. Alladio, F. Chrisanti, Analysis of MHD equilibria by toroidal multipolar expansions, Nucl. Fusion 26 (1986) 1143