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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
$$
-r\frac{\partial}{\partial r}\left(\frac1r\frac{\partial\psi}{\partial r}\right)
-\frac{\partial^2\psi}{\partial z^2}
=F\frac{dF}{d\psi}.
$$


Grad-Shafranov equation for a force-free magnetic field

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 314 / 4 / d / Solution

Grad-Shafranov equation for a force-free magnetic field

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Grad-Shafranov equation for a force-free magnetic field

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