 Thirty-degree magnetocentrifugal launching criterion

For a cold corotating field line anchored in a circular point-mass orbit, the effective potential has meridional Hessian ${\omega }^2\mathrm{diag}(-3,1)$. Along a straight line inclined by $\alpha$ to the vertical its quadratic curvature is ${\omega }^2(1-4{\sin }^2\alpha )$. Negative curvature gives the strict local launching criterion. Equality is marginal and global escape requires additional information.