Boozer coordinates: Difference between revisions
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→Contravariant representation of the magnetic field in Boozer coordinates
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\mathbf{B} = -\tilde\eta\nabla\psi + \frac{I_{tor}}{2\pi}\nabla\theta + \frac{I_{pol}^d}{2\pi}\nabla\phi~. | \mathbf{B} = -\tilde\eta\nabla\psi + \frac{I_{tor}}{2\pi}\nabla\theta + \frac{I_{pol}^d}{2\pi}\nabla\phi~. | ||
</math> | </math> | ||
It then follows that | |||
:<math> | |||
\nabla\psi\times\mathbf{B} = \nabla\psi\times\nabla\left(\frac{I_{tor}}{2\pi}\theta + \frac{I_{pol}^d}{2\pi}\phi\right)~, | |||
</math> | |||
and then the 'diamagnetic' lines are straight in Boozer coordinates and given by <math>{I_{tor}}\theta + {I_{pol}^d}\phi = \mathrm{const.}</math>. | |||
It is also useful to know the expression of the following object in Boozer coordinates | |||
:<math> | |||
\frac{\nabla V\times\mathbf{B}}{B^2} = -\frac{2\pi I_{pol}^d}{\langle B^2\rangle}\mathbf{e}_\theta + \frac{2\pi I_{tor}}{\langle B^2\rangle}~,\mathbf{e}_\phi | |||
</math>. | |||