= Localized interchange criterion for a magnetized atmosphere
{title2=$-\frac{d\ln\rho}{dz}<\frac{\rho g}{\gamma p+B^2/\mu_0}$}
For disturbances constant along the horizontal <magnetic field>, the minimized energy <density> is $\rho g[-(\ln\rho)'-\rho g/(\gamma p+C)]|\xi_z|^2$. If its coefficient is nonnegative everywhere, the full energy is nonnegative. If it is strictly negative at a point of a smooth equilibrium, a compactly supported vertical displacement in a neighbouring interval gives negative energy. These interchange motions compress gas and <magnetic pressure> together.
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