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Flux coordinates: Difference between revisions
→Transforming between Magnetic coordinates systems
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(\Psi_{pol}'\partial_{\theta_f} + \Psi_{tor}'\partial_{\phi_f}) G = \frac{\sqrt{g_f}}{\sqrt{g_F}} - 1~. | (\Psi_{pol}'\partial_{\theta_f} + \Psi_{tor}'\partial_{\phi_f}) G = \frac{\sqrt{g_f}}{\sqrt{g_F}} - 1~. | ||
</math> | </math> | ||
which can be turned into an algebraic equation on the fourier components of <math>G</math> | |||
:<math> | |||
G_{nm} = \frac{-i}{\Psi_{pol}'n + \Psi_{tor}'m}\left(\frac{\sqrt{g_f}}{\sqrt{g_F}}\right)_{nm}~. | |||
</math> | |||
where | |||
:<math> | |||
G(\psi, \theta_f, \phi_f) = \sum_{n,m} G_{nm}(\psi) e^{i(n\theta_f + m\phi_f)} | |||
</math> | |||
and <math>G_{00} = 0 </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: | ||