Flux coordinates: Difference between revisions
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→Magnetic coordinates
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Magnetic coordinates are a particular type of flux coordinates in which the magnetic field lines are straight lines. In mathematical terms this implies that the periodic part of the magnetic field's stream function is zero in these coordinates so the magnetic field reads | Magnetic coordinates are a particular type of flux coordinates in which the magnetic field lines are straight lines. In mathematical terms this implies that the periodic part of the magnetic field's stream function is zero in these coordinates so the magnetic field reads | ||
:<math> | :<math> | ||
\mathbf{B} = \nabla\psi\times \left( \frac{\Psi_{tor}'}{2\pi}\theta_f | \mathbf{B} = \nabla\psi\times \nabla\left( \frac{\Psi_{tor}'}{2\pi}\theta_f | ||
- \frac{\Psi_{pol}'}{2\pi}\phi_f \right) | - \frac{\Psi_{pol}'}{2\pi}\phi_f \right) | ||
= \frac{\Psi_{pol}'}{2\pi\sqrt{g}}\mathbf{e}_\theta + \frac{\Psi_{tor}'}{2\pi\sqrt{g}}\mathbf{e}_\phi~. | = \frac{\Psi_{pol}'}{2\pi\sqrt{g}}\mathbf{e}_\theta + \frac{\Psi_{tor}'}{2\pi\sqrt{g}}\mathbf{e}_\phi~. | ||