Coronal Electric Currents and Kink Instability of Magnetic Flux Rope

Using the energy method and the thin magnetic flux tube approximation, we find the wave dispersion relation for magnetohydrodynamic kink oscillations of a force-free magnetic flux rope with uncompensated longitudinal electric current under solar coronal conditions. The eigenvectors are shown to impose restrictions on the conditions of the kink instability of a flux rope. The observed weak twist of coronal loops with a small (less than or similar to 1) number of turns of the magnetic field lines around the axis indicates the dominance of unshielded magnetic flux ropes in the corona of the Sun, in which the longitudinal electric currents do not exceed 10(11)-10(12) A. These restrictions can be associated with the absence of solar superflares. The period of kink oscillations of twisted coronal loops should decrease with decreasing longitudinal electric current, which can be used to study its dynamics in solar flares. No dependence of compact and eruptive solar flares on the twist of flux ropes can be explained by the coexistence of both shielded and unshielded electric currents in the corona.