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Toroidal coordinates: Difference between revisions
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<ref>Morse and Feshbach, ''Methods of theoretical physics'', McGraw-Hill, New York, 1953 ISBN 007043316X</ref> | <ref>Morse and Feshbach, ''Methods of theoretical physics'', McGraw-Hill, New York, 1953 ISBN 007043316X</ref> | ||
<ref>[[:Wikipedia:Toroidal coordinates]]</ref> | <ref>[[:Wikipedia:Toroidal coordinates]]</ref> | ||
:<math>R = R_p \frac{\sinh \zeta}{\cosh \zeta - \cos \eta}</math> | :<math>R = R_p \frac{\sinh \zeta}{\cosh \zeta - \cos \eta}</math> | ||
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The coordinate ''η'' is a poloidal angle and runs from 0 to 2π. | The coordinate ''η'' is a poloidal angle and runs from 0 to 2π. | ||
This system is orthogonal. | This system is orthogonal. | ||
The Laplace equation separates in this system of coordinates, thus allowing an expansion of the vacuum magnetic field in toroidal harmonics. | |||
<ref>F. Alladio, F. Chrisanti, ''Analysis of MHD equilibria by toroidal multipolar expansions'', Nucl. Fusion '''26''' (1986) 1143</ref> | |||
<ref>[http://dx.doi.org/10.1016/0010-4655(94)90112-0 B.Ph. van Milligen and A. Lopez Fraguas, ''Expansion of vacuum magnetic fields in toroidal harmonics'', Computer Physics Communications '''81''', Issues 1-2 (1994) 74-90]</ref> | |||
== Magnetic == | == Magnetic == | ||