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Toroidal coordinates: Difference between revisions
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→Useful properties of FSA
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:<math> \int_{V}\nabla\cdot\Gamma\; dV = \langle\Gamma\cdot\nabla V\rangle = V'\langle\Gamma\cdot\nabla \psi\rangle</math> | :<math> \int_{V}\nabla\cdot\Gamma\; dV = \langle\Gamma\cdot\nabla V\rangle = V'\langle\Gamma\cdot\nabla \psi\rangle</math> | ||
:<math> \langle \mathbf{B}\cdot\nabla f \rangle = 0~,\qquad \forall~ \mathrm{single~valued~} f, ~ \mathrm{if}~ \nabla\cdot\mathbf{B} = 0 ~\mathrm{and}~ \nabla V\cdot\mathbf{B} = 0 </math> | :<math> \langle \mathbf{B}\cdot\nabla f \rangle = 0~,\qquad \forall~ \mathrm{single~valued~} f, ~ \mathrm{if}~ \nabla\cdot\mathbf{B} = 0 ~\mathrm{and}~ \nabla V\cdot\mathbf{B} = 0 </math> | ||
:<math> \langle \sqrt{g}^{-1}\rangle = \frac{4\pi^2}{V'} | |||
</math> | |||
=== Magnetic field representation in flux coordinates === | === Magnetic field representation in flux coordinates === | ||