204
edits
Flux coordinates: Difference between revisions
→Transforming between Magnetic coordinates systems
| Line 260: | Line 260: | ||
:<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: | ||