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

Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK

Corresponding author: M.S.Ruderman@sheffield.ac.uk

Received: 16 April 2003
Accepted: 7 July 2003

Abstract

Motivated by recent Transition Region and Coronal Explorer (TRACE) observations of damped oscillations in coronal loops, Ruderman & Roberts ([CITE]), 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, and , . The eigenfrequencies and correspond to modes with nodes at the tube boundary. In particular, and 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 is monotonically growing and monotonically decreasing, and they both tend to  as , where is the frequency of the kink mode of tubes with circular cross-sections. In particular, . 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.