= Self-similar magnetic mode in a stagnation flow
{title2=$B_z=f(t)b(r/g(t))\cos(m\phi)$}
For <magnetic concentration by an incompressible stagnation flow>, one possible normalization gives $(g^2)'=2\eta-2\omega g^2$, $f'/f=2\omega-\lambda\eta/g^2$, and $b''+(q^{-1}+q)b'+(\lambda-m^2/q^2)b=0$. The mode parameter $\lambda$ is not fixed by decay at infinity alone. The regular axisymmetric Gaussian has $\lambda=2$, $b=e^{-q^2/2}$ and conserved axial <magnetic flux>, with energy proportional to $g^{-2}$. The radial equation also has regular algebraic-tail solutions.
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