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Toroidal coordinates: Difference between revisions
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→Contravariant From
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==== Contravariant From ==== | ==== Contravariant From ==== | ||
Any | Any [[:Wikipedia: solenoidal vector field| solenoidal vector field]] <math>\mathbf{B}</math> can be written as | ||
<math> \mathbf{B} = \nabla\alpha\times\nabla\nu </math> | <math> \mathbf{B} = \nabla\alpha\times\nabla\nu </math> | ||
called its Clebsch representation. For a magnetic field with flux surfaces <math>(\psi = \mathrm{const}\; , \; \nabla\psi\cdot\mathbf{B} = 0)</math> we can choose, say, <math>\alpha</math> to be the flux surface label <math>\psi</math> | called its Clebsch representation. For a magnetic field with flux surfaces <math>(\psi = \mathrm{const}\; , \; \nabla\psi\cdot\mathbf{B} = 0)</math> we can choose, say, <math>\alpha</math> to be the flux surface label <math>\psi</math> | ||