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Boozer coordinates: Difference between revisions
→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> | ||
The covariant <math>B</math>-field components are then | |||
:<math> | |||
B_\psi = -\tilde{\eta} | |||
\quad | |||
, | |||
\quad | |||
B_\theta =\frac{I_{tor}}{2\pi} | |||
\quad | |||
\text{and} | |||
\quad | |||
B_\phi = \frac{I_{pol}^d}{2\pi}~. | |||
</math> | |||
It then follows that | It then follows that | ||
:<math> | :<math> | ||