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The standing magnetohydrodynamic (MHD) modes in a cylindrical incompressible magnetic flux tube modelled as a straight core surrounded by a magnetically twisted annulus, both embedded in a straight ambient external field, are considered. The dispersion relation for the MHD waves is derived and solved numerically to obtain the frequencies of both the kink  ( m = 1)  and fluting  ( m = 2, 3)  waves. Damping rates due to both viscous and resistive dissipations in the presence of the twisted magnetic field are derived and solved numerically for both the kink and fluting waves.

The effects of twisted magnetic field on coronal loop oscillations and dissipation