Bennett et al. (1999) considered the collective MHD modes of a straight uniformly twisted magnetic cylinder in the incompressible limit, and concluded that the twist leads to the appearance of body modes with phase speeds about the “longitudinal” Alfvén speed (calculated with the use of the longitudinal component of the field only). As well as in the untwisted case, there is a surface mode with the phase speed about the kink speed.
An alternative approach to the modelling of twisted and curved coronal loops was suggested by Cargill et al. (1994), which allowed the authors to take into account the hoop force - the feature missing from the straight cylinder model. The force is connected with both the loop twist and the curvature. The presence of the new restoring force was shown to give rise to a new oscillation mode manifested as the periodic change of the loop major radius and the loop density, whose frequency could be independent of the loop length. Oscillations of the loop minor radius were also found. The oscillation frequencies obtained were significantly different from the frequencies of straight cylinder eigenmodes. This approach certainly requires attention and further development.
Also, oscillations of current carrying loops can be described in terms of the LCR-model, see Section 3.5.
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