= Diffusive establishment time of a wound toroidal field
{title2=$t_\eta\sim\ell^2/\eta$}
With a fixed axial seed field and prescribed localized <differential rotation>, the winding source is time independent. Early induction gives $B_\phi\sim B_0\Omega t$, while the steady balance has $B_\phi\sim B_0\Omega\ell^2/\eta$. Their comparison gives the <magnetic diffusion> time, not merely the rotation period. It diverges as conductivity becomes infinite. In an unbounded domain, this is a local equilibration estimate on scale $\ell$, not finite-time exact convergence everywhere. <Lorentz force> feedback may invalidate the prescribed-flow approximation sooner.
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