A perturbation method has been developed to find the structure of the mode in a cylindrical waveguide filled with a cold, uniform plasma with vacuum layer between the plasma and conducting wall when the magnetic field in the waveguide is a superposition of a uniform and an inhomogeneous field created by l=2 helical windings. The influence of the magnetic field nonuniformity on the wave mode structure is treated as a perturbation. The wave structure of a modified m=+1 fast Alfvén wave in the vicinity of the ion cyclotron frequency is examined numerically for a collisionless plasma. It is shown that the m=−1 harmonic of the modified m=+1 fast Alfvén wave is left-hand polarized in the central part of the plasma. This can be considered as a coupling between the m=+1 fast (right-hand polarized) wave and m=−1 slow (left-hand polarized) wave which is due to the inhomogeneity of the l=2 fields. The coupling efficiency is examined numerically for different parameters of the waveguide.

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