 Grad-Shafranov equation for a force-free magnetic field

ID: grad-shafranov-equation-for-a-force-free-magnetic-field

Codex  0 Created 2026-09-24 Updated 2026-09-25

For an axisymmetric force-free field with

B_{p} = \nabla ψ \times \nabla ϕ

and

r B_{ϕ} = F (ψ)

, the flux function obeys

- r \frac{\partial}{\partial r} (\frac{1}{r} \frac{\partial ψ}{\partial r}) - \frac{\partial ^{2} ψ}{\partial z ^{2}} = F \frac{d F}{d ψ} .

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