Hamada coordinates: Difference between revisions
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→Form of the Jacobian for Hamada coordinates
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- \mathbf{B}\cdot\nabla\tilde{\eta} = p'~. | - \mathbf{B}\cdot\nabla\tilde{\eta} = p'~. | ||
</math> | </math> | ||
Taking the [[Flux coordinates#flux surface average|flux surface average]] <math>\langle\cdot\rangle</math> of this equation we find <math>(- | Taking the [[Flux coordinates#flux surface average|flux surface average]] <math>\langle\cdot\rangle</math> of this equation we find <math>(-{I}'_{tor}{\Psi}'_{pol} + {I}'_{pol}{\Psi}'_{tor})= 4\pi^2{p}'\langle(\sqrt{g_f})^{-1}\rangle^{-1}</math>, so that we have | ||
:<math> \mathbf{B}\cdot\nabla\tilde{\eta} = {p}'\left(\frac{\langle(\sqrt{g_f})^{-1}\rangle^{-1}}{\sqrt{g_f}}-1\right) | :<math> \mathbf{B}\cdot\nabla\tilde{\eta} = {p}'\left(\frac{\langle(\sqrt{g_f})^{-1}\rangle^{-1}}{\sqrt{g_f}}-1\right) | ||