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Hamada coordinates: Difference between revisions
→Form of the Jacobian for Hamada coordinates
(Created page with 'Hamada coordinates are a set of magnetic coordinates in which the equilibrium current density <math>\mathbf{j}</math> lines are straight…') |
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In a coordinate system where <math>\mathbf{j}</math> is straight <math>\tilde{\eta}</math> is a function of <math>\psi</math> only, and therefore LHS of this equation must be zero in such a system. It therefore follows that the Jacobian of the Hamada system must satisfy | In a coordinate system where <math>\mathbf{j}</math> is straight <math>\tilde{\eta}</math> is a function of <math>\psi</math> only, and therefore LHS of this equation must be zero in such a system. It therefore follows that the Jacobian of the Hamada system must satisfy | ||
:<math> | :<math> | ||
\sqrt{g_H | \sqrt{g_H} = \langle\sqrt{g_H}^{-1}\rangle^{-1} = \frac{V'}{4\pi^2}~, | ||
</math> | </math> | ||
where the last idenity follows from the [[Flux coordinates#Useful properties of the FSA|properties of the flux surface average]]. | where the last idenity follows from the [[Flux coordinates#Useful properties of the FSA|properties of the flux surface average]]. | ||