Wave propagation in a zero-beta magnetic flux tube with a discontinuous Alfv`en speed at its surface is considered. The problem is reduced to solving a wave equation for the projection of the magnetic perturbation along the axis of the cylinder. The mathematical formalism is identical with that for the propagation of electromagnetic waves in optical fibers with a varying index of refraction in the cross section of the fiber. The dispersion relation is solved in its full generality and three wave numbers are assigned to the normal modes of the cylinder. There is a lower cuto for the longitudinal wave number along the cylinder axis and an upper cuto for the radial wave number. Eigenfrequencies and eigenfields (i.e. the magnetic and velocity fields of modes) are calculated. Resistive and viscous dissipation rates have mathematically identical forms, di ering only in their being inversely proportional to the Lundquist and Reynolds numbers, respectively. These rates as well as the energy densities are obtained for each mode and are commented on.
