A Study on the Excitation and Resonant Absorption of Coronal Loop Kink Oscillations

We study theoretically the issue of externally driven excitations of standing kink waves and their resonant absorption into torsionally polarized m=1 waves in the coronal loops in pressureless plasmas. We use the ideal MHD equations, for which we develop an invariant imbedding method available in cylindrical geometry. We assume a sinusoidal density profile at the loop boundary where the density inside the loop is lower than the outside and vice versa. We present field distributions for these two cases and find that they have similar behaviors. We compare the results for the overdense loops, which describe the usual coronal loops, with the analytical solutions of Soler et al. obtained using the Frobenius method. Our results show some similarity for thin nonuniform layers but deviate a lot for thick nonuniform layers. For the first case, which describes the wave train propagation in funnels, we find that resonant absorption depends crucially on the thickness of the nonuniform boundary, loop length, and density contrast. The resonant absorption of the kink mode is dominant when the loop length is sufficiently larger compared with its radius (thin loop). The behavior of the far-field pattern of the scattered wave by the coronal loop is closely related to that of the resonant absorption. For the mode conversion phenomena in inhomogeneous plasmas, a certain universal behavior of the resonant absorption is found for the first time. We expect that the main feature may also apply to the overdense loops and discuss its relation to the damping rate.