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Flux coordinates: Difference between revisions
→Covariant Form
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I_{pol} + I_{pol}^d = \oint_{\psi=0}\mathbf{B}\cdot d\mathbf{l} \Rightarrow I_{pol}' + (I_{pol}^d)' = 0 ~, | I_{pol} + I_{pol}^d = \oint_{\psi=0}\mathbf{B}\cdot d\mathbf{l} \Rightarrow I_{pol}' + (I_{pol}^d)' = 0 ~, | ||
</math> | </math> | ||
where the integral is performed along the magnetic axis and therefore does not depend on <math>\psi</math>. | where the integral is performed along the magnetic axis and therefore does not depend on <math>\psi</math>. This can be used to show that a expanded version of <math>\mathbf{B}</math> is given as | ||
:<math> | |||
\mathbf{B} = -\tilde\eta\nabla\psi + \frac{I_{tor}}{2\pi}\nabla\theta + \frac{I_{pol}^d}{2\pi}\nabla\phi + \nabla\tilde\chi~. | |||
</math> | |||
== Magnetic coordinates == | == Magnetic coordinates == | ||