Context. Observations have shown that twisted magnetic fields naturally occur, and indeed are omnipresent in the Sun’s atmosphere. Itudis therefore of great theoretical interest in solar atmospheric waves research to investigate the types of magnetohydrodynamic (MHD)udwave modes that can propagate along twisted magnetic flux tubes.udAims. Within the framework of ideal MHD, the main aim of this work is to investigate small amplitude incompressible wave modesudof twisted magnetic flux tubes with m ≥ 1. The axial magnetic field strength inside and outside the tube will be allowed to vary, toudensure the results will not be restricted to only cold plasma equilibria conditions.udMethods. The dispersion equation for these incompressible linear MHD wave modes was derived analytically by implementing theudlong wavelength approximation.udResults. It is shown, in the long wavelength limit, that both the frequency and radial velocity profile of the m = 1 kink mode areudcompletely unaffected by the choice of internal background magnetic twist. However, fluting modes with m ≥ 2 are sensitive to theudparticular radial profile of magnetic twist chosen. Furthermore, due to background twist, a low frequency cut-off is introduced forudfluting modes that is not present for kink modes. From an observational point of view, although magnetic twist does not affect theudpropagation of long wavelength kink modes, for fluting modes it will either work for or against the propagation, depending on theuddirection of wave travel relative to the sign of the background twist.ud
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