Abstract
Based on linear magnetohydrodynamic equations and an energy principle we analyze the ideal kink instability of a twisted force-free coronal loop (flux rope) surrounded by an outer potential magnetic field by using the sharp-boundary approximation at the surface. Unlike Tsap et al., a magnetic flux rope with nonneutralized (uncompensated) electric current is considered. We have shown that the twist angle of magnetic field lines is closely related to coronal mass ejections and solar flares. The kink instability condition does not depend on the radial profile of the magnetic field inside a flux rope in the long-wavelength limit but depends strongly on the reverse electric currents at the surface. The total critical twist angle of magnetic field lines, which determines the kink instability threshold, can be much greater than π radians due to reverse azimuthal surface current. This agrees with observations and illustrates the importance of the role of reverse currents for stabilization of a flux rope. Additional arguments in favor of the energy release models based on the uncompensated electric currents are presented.
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