Symmetric wave modes in coronal flux tubes with magnetically twisted layer

Abstract

ABSTRACT The properties of axisymmetric magnetohydrodynamic wave modes are studied for the model of coronal magnetic tube, consisting of a central cord with homogeneous axial magnetic field, surrounded by an annulus with twisted magnetic field. This model mimics the coronal loops with radially localized magnetic twist. The derived dispersion relation is solved numerically. A number of limiting cases are examined analytically. The two families of axisymmetric modes are found to exist in the model. The first one includes an infinite number of fast-sausage modes (FSMs), modified by the twist and the second one is a set of modes with frequencies, lying in a narrow band, closed to Alfvén frequency of a twisted layer ωA0. The fundamental FSM (the mode of the lowest radial order) exists as a trapped mode for the entire range of axial wavenumbers. Its phase speed is always below the Alfvén speed of a magnetically twisted layer. This mode has a weak dispersion in the range of long and intermediate wavelengths. The higher radial order FSMs were found to be less sensitive to the presence of the magnetic twist. Both the fundamental FSM in the case of a weak magnetic twist and a set of symmetric modes for arbitrary twist have very similar frequencies, which are nearly equal to ωA0. This property implies that aforementioned wave modes behave like Alfvén torsional modes in the twisted annulus and like the radial modes in the untwisted core and environment, moreover they are strongly coupled. The main results of the study are discussed in the framework of their applications to coronal seismology.