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Toroidal coordinates: Difference between revisions
→Magnetic field representation in flux coordinates
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:<math> | :<math> | ||
\nu(\psi,\theta,\phi) | \nu(\psi,\theta,\phi) | ||
= \frac{1}{2\pi}(\ | = \frac{1}{2\pi}(\Psi_{tor}'\theta | ||
- | - \Psi_{pol}'\phi) | ||
+ \tilde{\nu}(\psi,\theta,\phi) | + \tilde{\nu}(\psi,\theta,\phi) | ||
</math> | </math> | ||
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By very similar arguments as those used for <math>\mathbf{B}</math> (note that both <math>\mathbf{B}</math> and <math>\mathbf{j}</math> are solenoidal fields tangent to the flux surfaces) it can be shown that the general expression for <math>\eta</math> is | By very similar arguments as those used for <math>\mathbf{B}</math> (note that both <math>\mathbf{B}</math> and <math>\mathbf{j}</math> are solenoidal fields tangent to the flux surfaces) it can be shown that the general expression for <math>\eta</math> is | ||
:<math> | :<math> | ||
\eta(\psi,\theta,\phi) = \frac{1}{2\pi}({I}_{tor' | \eta(\psi,\theta,\phi) = \frac{1}{2\pi}({I}_{tor}'\theta | ||
- {I}_{pol}'\phi) | - {I}_{pol}'\phi) | ||
+ \tilde{\eta}(\psi,\theta,\phi)~. | + \tilde{\eta}(\psi,\theta,\phi)~. | ||