Simple tests for the ideal MHD stability of line-tied coronal magnetic fields

Methods for the study of the ideal magnetohydrodynamic stability of line-tied cylindrically-symmetric magnetic fields are discussed and are applied to four different classes of equilibria for the cases of both arcade and loop geometries. The energy method is combined with a modification of the perturbed potential energy integral in order to obtain simple tests that predict either stability to general coronal disturbances or instability to localized modes, both satisfying photospheric line tying. These test are used to estimate the maximum amount of magnetic energy that can be stored in the coronal magnetic field prior to an instability.