Topological stability of finite-length magnetic flux tubes

It has been suggested that the activity of cosmical magnetic fields is a consequence of a general topological nonequilibrium in the neighbourhood of magnetostatic equilibria. Evidence for this suggestion can be obtained from the Kolmogorov-Arnold-Moser theorem of classical mechanics, applied to the magnetic field line flow as a Hamiltonian system. A finite-length magnetic flux tube, however, always possesses two independent sets of flux surfaces - or, equivalently, the corresponding Hamiltonian system two independent first integrals - and is topologically stable if in the volume occupied by the tube there are no singular (null) points of the magnetic field and the normal field component does not change its sign on the end faces of the tube. Therefore, the concept of nonequilibrium due to flux surface destruction is not applicable to solar atmospheric loops with each end situated in the interior of one polarity of the photospheric normal field component. Further, it seems unlikely that the tearing-mode mechanism can play a role in such loops.