Damping of coronal loop kink oscillations due to mode conversion

The damping of kink oscillations of a thin magnetic tube due to mode conversion, also called resonant absorption, is studied. The tube consists of a homogeneous core region and an inhomogeneous annulus, where the density monotonically decreases from its value in the core region to the value in the surrounding plasma. The annulus is assumed to be thin, so the study is carried out in the thin tube thin boundary approximation. The equation governing the amplitude variation of kink oscillations is derived. The initial value problem for this equation is solved to study the resonant damping. This means that, in particular, we study the transient state before the loop oscillates with the stationary or nearly stationary state. The results are compared with those of the direct numerical modelling, and the agreement is found to be fairly good. On the basis of the solution to the initial value problem for the governing equation, the damping time is calculated and compared with that given by the classical theory of resonant absorption. It is found that the classical theory underestimates the damping time, with the error increasing with the increase of the annulus thickness. However, the error is not large, so the damping time given by the classical theory of resonant absorption can be taken as a sufficiently good approximation.