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
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.
Key words: magnethohydrodynamics (MHD) / plasmas / Sun: corona / waves
© ESO, 2003