Ram. Vanderlinden et Aw. Hood, ON THE IMPORTANCE OF HIGH-M INSTABILITIES IN LINE-TIED CORONAL MAGNETIC-FIELDS, Astronomy and astrophysics, 299(3), 1995, pp. 912-920
It is shown that for the determination of the magnetohydrodynamical (M
HD) stability of coronal magnetic fields, where the photospheric line-
tying effect is a basic element of the physical description, it is imp
ortant to consider modes of both low and high angular wave number m. I
n 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 f
ield line length increases in the evolution of the equilibrium, while
the m = 1 mode remains stable. This is important because the high-m mo
des intrinsically lead to strong dissipation. This contrasts to the ca
se of the one-dimensional infinite (i.e. not line-tied) cylinder, wher
e it is sufficient to prove stability of the m = 1 mode to guarantee s
tability for all modes m > 1 (Newcomb 1960). In the line-tied case how
ever, there exists no prior reason to only consider m = 1 instabilitie
s in coronal magnetic fields.