= Regular-axis alignment of steady poloidal ideal flow
{title2=$\rho\mathbf u=k(\psi)\mathbf B$}
For steady axisymmetric ideal flow with only poloidal components, induction implies $\mathbf u\times\mathbf B=C\mathbf e_\phi/R$. Axis regularity, or zero toroidal <electromotive force>, sets $C=0$. Continuity then gives $\rho\mathbf u=k(\psi)\mathbf B$, locally on connected magnetic surfaces of the <poloidal magnetic flux function>. Without the zero-circulation condition, annular domains can support steady cross-field flow.
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