= Magnetocentrifugal launching criterion in a flattened power-law potential
{title2=$\alpha_{\rm crit}=\arctan(|\lambda|/\sqrt{\beta+2})$}
In a <flattened power-law gravitational potential> $\Phi=\Phi_0R_0^\beta(R^2+\lambda^2z^2)^{-\beta/2}$, a magnetic surface corotating with its disk footpoint has an <effective potential> with meridional <Hessian matrix> $\Omega_f^2\operatorname{diag}[-(\beta+2),\lambda^2]$ there. A cold outward displacement along a field inclined by $\alpha$ to the vertical is downhill when $\tan^2\alpha>\lambda^2/(\beta+2)$. Equality is marginal and can depend on higher derivatives and field-line curvature; this is a local launching criterion, not a guarantee of a global escaping wind.
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