The stability of line-tied coronal loops and an extended Suydam criterion

The initiation of prominence eruptions and solar flares can be described in terms of an MHD instability. When the footpoint of a coronal magnetic structure is anchored in the dense photosphere, magnetic energy is slowly built up until critical conditions are exceeded and an instability is triggered. The significance of an extended Suydam criterion for testing line-tied magnetic fields is illustrated by comparing with numerical instability thresholds for a variety of different modes. It is shown that when the extended Suydam criterion predicts an instability, for a nearly force free field, then there exists a global instability with a lower threshold. When the gas pressure is significant localised modes are destabilised slightly before a global mode.