The paper investigates the stability of coronal magnetic loops, with the influence of the dense photosphere (line-tying) taken into account. The stability method, based on the finite Fourier series method developed by Einaudi and Van Hoven (1981, 1983), is applied to two different equilibria, and the approximate critical conditions for the onset of different azimuthal instabilities are investigated. It is shown that, for nearly force-free loops, the extended Suydam criterion obtained by De Bruyne and Hood (1989) for localized modes predicts the existence of a global kink instability when a localized mode is just destabilized. For loops with substantial gas pressure gradients, it is the localized modes that are destabilized first of all, and the extended Suydam criterion gives the necessary and sufficient conditions for an instability. In the latter case, the instability threshold for the kink mode is quite close to the localized mode threshold. It is shown that the growth times of the instabilities are comparable to the Alfven travel times along the loop when the extended Suydam criterion is violated.
- Coronal Loops
- Magnetohydrodynamic Stability
- Solar Magnetic Field