Wave propagation in incompressible MHD wave guides: the twisted magnetic Annulus

Solar Physics & upper-Atmosphere Research Group, Department of Applied Mathematics, University of Sheffield, The Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK e-mail: [robertus;b.carter]@sheffield.ac.uk

Received: 27 January 2006
Accepted: 2 May 2006

Abstract

The propagation of MHD waves in a structured magnetic flux tube embedded within a straight vertical magnetic environment is studied analytically. The motivation of this analysis comes from the observations of damped loop oscillations showing that possibly only part of the loop is homogeneous in the radial direction. The general dispersion relation of longitudinal wave propagation is derived for a fully magnetically twisted configuration consisting of a core, annulus and external region each with magnetic field of uniform, yet distinct, twist. Next, a simplified case representing coronal loops is analysed in detail considering magnetic twist just in the annulus, the internal and external regions having straight magnetic field. Modes of oscillations are examined from the general dispersion relation that is suitable for obtaining information on not just oscillations but also on some instability properties of this complex tube structure. It is shown that there are purely surface (i.e. evanescent) and hybrid (spatially oscillatory in the twisted annulus, otherwise evanescent) modes. Except for small wavenumbers, the surface waves show little dispersion; a property making them more suitable for observations. The hybrid modes show a more complex character. Though the frequency range seems to be rather limited, there is a continuum band of frequencies for a given wavenumber. Both short and long wavelength approximations are considered for the symmetrical (sausage) mode and with small twist in particular.