On the importance of high-m instabilities in line-tied coronal magnetic fields.

It is shown that for the determination of the magnetohydrodynamical (MHD) stability of coronal magnetic fields, where the photospheric line-tying effect is a basic element of the physical description, it is important to consider modes of both low and high angular wave number m. In particular, when the equilibrium deviates from the force-free state, modes with high m may have higher growth rates than the m=1 (kink) mode. It is then possible that high-m modes become unstable when the field line length increases in the evolution of the equilibrium, while the m=1 mode remains stable. This is important because the high-m modes intrinsically lead to strong dissipation. This contrasts to the case of the one-dimensional infinite (i.e. not line-tied) cylinder, where it is sufficient to prove stability of the m=1 mode to guarantee stability for all modes m>1 (Newcomb 1960). In the line-tied case however, there exists no prior reason to only consider m=1 instabilities in coronal magnetic fields.