The resonant damping of oscillations of coronal loops with elliptic cross-sections

Motivated by recent Transition Region and Coronal Explorer (TRACE) observations of damped oscillations in coronal loops, Ruderman & Roberts (2002), studied resonant damping of kink oscillations of thin straight magnetic tubes in a cold plasma. In their analysis, Ruderman & Roberts considered magnetic tubes with circular cross-sections. We extend their analysis for magnetic tubes with elliptic cross-sections. We find that there are two infinite sequences of the eigenfrequencies of the tube oscillations, {omega(nc)} and {omega(ns)}, n = 1,2,.... The eigenfrequencies {omega(nc)} and {omega(ns)} correspond to modes with 2n nodes at the tube boundary. In particular, omega(1c) and omega(1s) correspond to two kink modes. These modes are linearly polarized in the direction of the large and small axis of the tube elliptic cross-section respectively. The sequence {omega(nc)} is monotonically growing and {omega(ns)} monotonically decreasing, and they both tend to omega(k) as n --> infinity, where omega(k) is the frequency of the kink mode of tubes with circular cross-sections. In particular, omega(1c) < omega(k) < omega(1s). We calculate the decrements of the two kink modes and show that they are of the order of decrement of the kink mode of a tube with a circular cross-section.