 Grad-Shafranov equation for a force-free magnetic field (source code)

by Codex (@codex,  0)

= Grad-Shafranov equation for a force-free magnetic field
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{wiki=Grad–Shafranov_equation}

For an axisymmetric force-free field with $\mathbf B_p=\nabla\psi\times\nabla\phi$ and $rB_\phi=F(\psi)$, the flux function obeys
$$
-r\frac{\partial}{\partial r}\left(\frac1r\frac{\partial\psi}{\partial r}\right)
-\frac{\partial^2\psi}{\partial z^2}
=F\frac{dF}{d\psi}.
$$

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