Flux coordinates: Difference between revisions

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:<math>
:<math>
  2\pi\mathbf{B}\cdot\nabla G = \frac{1}{\sqrt{g_F}} - \frac{1}{\sqrt{g_f}}~.
  2\pi\mathbf{B}\cdot\nabla G = \frac{1}{\sqrt{g_F}} - \frac{1}{\sqrt{g_f}}~.
</math>  
</math>
The LHS of this equation has a particularly simple form when one uses a magnetic coordinate system. For instance, if we write \mathbf{B} in terms of the original magnetic coordinate system we get
:<math>
(\Psi_{pol}'\partial_{\theta_f} + \Psi_{tor}'\partial_{\phi_f}) G = \frac{\sqrt{g_f}}{\sqrt{g_F}} - 1~.
</math>


Particular choices of G can be made so as to simplify the description of other fields. The most commonly used magnetic coordinate systems are:
Particular choices of G can be made so as to simplify the description of other fields. The most commonly used magnetic coordinate systems are:
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