Toroidal coordinates: Difference between revisions

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It is worthwhile to note that the Clebsch form of <math> \mathbf{B} </math> corresponds to a [[:Wikipedia: Magnetic potential|magnetic vector potential]]
It is worthwhile to note that the Clebsch form of <math> \mathbf{B} </math> corresponds to a [[:Wikipedia: Magnetic potential|magnetic vector potential]]
<math> \mathbf{A} = \nu\nabla\psi </math> (or <math> \mathbf{A} = \psi\nabla\nu </math> as they differ only by the Gauge transformation <math> \mathbf{A} \to \mathbf{A} - \nabla (\psi\nu)</math>).
<math> \mathbf{A} = \nu\nabla\psi </math> (or <math> \mathbf{A} = \psi\nabla\nu </math> as they differ only by the Gauge transformation <math> \mathbf{A} \to \mathbf{A} - \nabla (\psi\nu)</math>).
The general form of the stream function is
:<math>
\nu(\psi,\theta,\phi)
= \frac{1}{2\pi}(\dot{\Psi}_{tor}\theta
- \dot{\Psi}_{pol}\phi)
+ \tilde{\nu}(\psi,\theta,\phi)
</math>
where <math>\tilde{\nu}</math> is a differentiable function periodic in the two angles. This general form can be derived by using the fact that  <math> \mathbf{B}</math> is a physical function (and hence singe-valued). The specific form for the coefficients in front of the secular terms (i.e. the non-periodic terms) can be obtained from the FSA properties [[Useful properties of the FSA]].


== Magnetic ==
== Magnetic ==
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