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Flux coordinates: Difference between revisions
→Contravariant Form of the current density
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Note that the poloidal current is now defined through a ribbon and not a disc. The two currents are related as <math>\nabla\cdot\mathbf{j} = 0</math> implies | Note that the poloidal current is now defined through a ribbon and not a disc. The two currents are related as <math>\nabla\cdot\mathbf{j} = 0</math> implies | ||
:<math> | :<math> | ||
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>. | ||