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Flux coordinates: Difference between revisions
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→Transforming between Magnetic coordinates systems
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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 | The LHS of this equation has a particularly simple form when one uses a magnetic coordinate system. For instance, if we write <math>\mathbf{B}</math> in terms of the original magnetic coordinate system we get | ||
:<math> | :<math> | ||
(\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~. | ||