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Boozer coordinates: Difference between revisions
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:<math> | :<math> | ||
\sqrt{g_B} = \frac{V'}{4\pi^2}\frac{\langle B^2\rangle} {B^2} | \sqrt{g_B} = \frac{V'}{4\pi^2}\frac{\langle B^2\rangle} {B^2} | ||
</math> | |||
== Covariant representation of the magnetic field in Boozer coordinates == | |||
Using this Jacobian in the general form of the magnetic field in [[Flux coordinates # Magnetic coordinates|magnetic coordinates]] one gets. | |||
:<math> | |||
\mathbf{B} = 2\pi\frac{d\Psi_{pol}}{dV}\frac{B^2}{\langle B^2\rangle}\mathbf{e}_\theta + | |||
2\pi\frac{d\Psi_{tor}}{dV}\frac{B^2}{\langle B^2\rangle}\mathbf{e}_\phi | |||
</math> | </math> | ||
== Contravariant representation of the magnetic field in Boozer coordinates == | == Contravariant representation of the magnetic field in Boozer coordinates == | ||
The contravariant representation of the field is also relatively simple when using Boozer coordinates, since the angular covariant <math>B</math>-field components are flux functions in these coordinates | |||
:<math> | :<math> | ||
\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~. | ||