Resonant damping of kink oscillations of thin expanding magnetic tubes

¹ Solar Physics and Space Plasma Research Centre (SP 2RC), University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
e-mail: m.s.ruderman@sheffield.ac.uk
² ITMO University, Kronverkskii ave 49, 197101 Saint-Petersburg, Russia
³ Space Research Institute (IKI) Russian Academy of Sciences, Moscow, Russia

Received: 1 December 2017
Accepted: 20 February 2018

Abstract

We study the resonant damping of kink oscillations of thin expanding magnetic flux tubes. The tube consists of a core region and a thin transitional region at the tube boundary. The resonance occurs in this transitional layer where the oscillation frequency coincides with the local Alfvén frequency. Our investigation is based on the system of equations that we previously derived. This system is not closed because it contains the jumps of the magnetic pressure perturbation and plasma displacement across the transitional layer. We calculate these jumps and thus close the system. We then use it to determine the decrements of oscillation eigenmodes. We introduce the notion of homogeneous stratification. In accordance with this condition the ratio of densities in the tube core and outside the tube does not vary along the tube, while the density in the transitional layer can be factorised and written as a product of two function, one depending on the variable along the tube and the other on the magnetic flux function. Our main result is that, under the condition of homogeneous stratification, the ratio of the decrement to the oscillation frequency is independent of a particular form of the density variation along the tube. This ratio is also the same for all oscillation eigenmodes.