Abstract
An alternate form of the Energy Principle is derived, and used to produce a new criterion for pressure-driven interchange instabilities in MHD cylindrical columns. This criterion is not equivalent to Suydam's criterion and does not contain the magnetic shear. It is shown to reliably predict the actual growth-rates of a class of resonant eigenmodes, which are mostly transverse to the unperturbed magnetic field; the magnetic shear is shown to limit the radial extent of these eigenmodes, and not their growth-rates. It is also explained why the usual arguments about the stabilizing role of the magnetic shear are not valid for these modes. Furthermore, the conventional analysis based on the standard form of the Energy Principle evacuates from the onset the whole class of unstable modes discussed here, so that the presently derived criterion cannot be obtained from it. Conceptual and practical implications of this work are pointed out.
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