Long-wavelength torsional modes of solar coronal plasma structures

Aims. We consider the effects of the magnetic twist and plasma rotation on the propagation of torsional m = 0 perturbations of cylindrical plasma structures (straight magnetic flux tubes) in the case when the wavelength is much longer than the cylinder diameter. Methods. The second order thin flux tube approximation is used to derive dispersion relations and phase relations in linear longwavelength axisymmetric magnetohydrodynamic waves in uniformly twisted and rotating plasma structures. Results. Asymptotic dispersion relations linking phase speeds with the plasma parameters are derived. When twist and rotation are both present, the phase speed of torsional waves depends upon the direction of the wave propagation, and also the waves are compressible. The phase relations show that in a torsional wave the density and azimuthal magnetic field perturbations are in phase with the axial magnetic field perturbations and anti-phase with tube cross-section perturbations. In a zero-β non-rotating plasma cylinder confined by the equilibrium twist, the density perturbation is found to be about 66 percent of the amplitude of the twist perturbation in torsional waves.