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Flux coordinates: Difference between revisions
→Covariant Form
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If we consider an equilibrium magnetic field such that <math> \mathbf{j}\times\mathbf{B} \propto \nabla\psi</math>, where <math> \mathbf{j}</math> is the current density , then both <math> \mathbf{B}\cdot\nabla\psi = 0</math> and <math> \nabla\times\mathbf{B}\cdot\nabla\psi = 0</math> and the magnetic field can be written as | If we consider an equilibrium magnetic field such that <math> \mathbf{j}\times\mathbf{B} \propto \nabla\psi</math>, where <math> \mathbf{j}</math> is the current density , then both <math> \mathbf{B}\cdot\nabla\psi = 0</math> and <math> \nabla\times\mathbf{B}\cdot\nabla\psi = 0</math> and the magnetic field can be written as | ||
:<math> | :<math> | ||
\mathbf{B} = \ | \mathbf{B} = -\eta\nabla\psi + \nabla\chi | ||
</math> | </math> | ||
where <math>\chi</math> is identified as the magnetic ''scalar'' potential. Its general form is | where <math>\chi</math> is identified as the magnetic ''scalar'' potential. Its general form is | ||
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</math> | </math> | ||
where the integral is performed along the magnetic axis. | where the integral is performed along the magnetic axis. | ||
== Magnetic coordinates == | == Magnetic coordinates == | ||