Abstract We considered the kink oscillations of coronal magnetic loops, which form a coronal loop arcade with a magnetic shear. In this structure, the magnetic field consists of helical lines. A semicircular magnetic slab model was used, and the corresponding dispersion relation was derived. To study oscillations of an individual sigmoid loop, we focused on the quasi-perpendicular propagation limit. Two fast surface waves, denoted FSW + and FSW − , were found to couple with the Alfvén mode when the magnetic shear parameter α is nonzero. The FSW + mode corresponds to the vertical kink mode and its frequency is close to the kink frequency. In the propagating regime, the frequency of the forward wave increases with increasing magnetic shear, and that of the backward wave has more complex behavior. The real frequencies of the forward and backward waves in the FSW + mode exist up to certain values of the magnetic shear parameter. For a larger shear, the frequencies are complex values. The eigenfrequencies of the quasi-standing FSW + mode were found to increase slightly as the shear parameter increases, and the effect is most prominent for the fundamental mode. The obtained results are relevant in the context of seismological use of the propagating and standing kink waves in sigmoid coronal loops.
Igor Lopin (Mon,) studied this question.