Transverse oscillations of non-planar coronal loops

School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
e-mail: m.s.ruderman@sheffield.ac.uk

Received: 19 November 2010
Accepted: 22 February 2011

Abstract

We suggested a simple model of a non-planar coronal loop (i.e. a loop with torsion). In this model the loop axis is a part of a helical line. Using curvilinear coordinates where the loop axis is a coordinate line and the loop boundary is a coordinate surface we derived the governing equation for the loop kink oscillations. When doing so we have used asymptotic method with the ratio of the loop cross-section radius to the loop curvature radius as a small parameter. The governing equation is exactly the same as one obtained for kink oscillations of a thin straight magnetic tube with the density varying along the tube. This implies that neither the loop curvature nor the loop torsion can directly affect the eigenfrequencies of the loop kink oscillations. They can affect these eigenfrequencies only indirectly through modifying the dependence of the density on the distance along the loop. The main effect of the loop torsion is on the polarization of the loop oscillations. We found that, when we are moving along the loop, the polarization direction is rotating together with the principal normal to the loop axis due to the loop torsion. The application of the obtained results to the interpretation of observations of the loop kink oscillations with a node is discussed.