Flux coordinates: Difference between revisions

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*<math> \int_{\mathcal{V}}\nabla\cdot\Gamma\; d\mathcal{V} =  \langle\Gamma\cdot\nabla V\rangle = V'\langle\Gamma\cdot\nabla \psi\rangle</math>
*<math> \int_{\mathcal{V}}\nabla\cdot\Gamma\; d\mathcal{V} =  \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(\mathbf{x}), ~ \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(\mathbf{x}), ~ \mathrm{if}~ \nabla\cdot\mathbf{B} = 0 ~\mathrm{and}~ \nabla \psi\cdot\mathbf{B} = 0 </math>


*<math> \langle \nabla \psi\cdot\nabla\times \mathbf{A} \rangle = 0~.
*<math> \langle \nabla \psi\cdot\nabla\times \mathbf{A} \rangle = 0~.
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