  There is ample evidence of twisted magnetic structures in the solar corona.
This motivates us to consider the magnetic twist as the cause of Alfven
frequency continuum in the coronal loops, which can support the resonant
absorption as a rapid damping mechanism for the observed coronal kink
magnetohydrodynamic (MHD) oscillations. We model a coronal loop with a straight
cylindrical magnetic flux tube which has constant but different densities in
the interior and exterior regions. The magnetic field is assumed to be constant
and aligned with the cylinder axis everywhere except a thin layer near the
boundary of the flux tube which has an additional small magnetic field twist.
Then, we investigate a number of possible instabilities that may arise in our
model. In the thin tube thin boundary approximation, we derive the dispersion
relation and solve it analytically to obtain the frequencies and damping rates
of the fundamental (l=1) and first/second overtone (l=2,3) kink (m=1) MHD
modes. We conclude that the resonant absorption by the magnetic twist can
justify the rapid damping of kink MHD waves observed in coronal loops.
Furthermore, the magnetic twist in the inhomogeneous layer can cause deviations
from P1/P2=2 and P1/P3=3 which are comparable with the observations.
