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