  A fluid theory has been developed by taking account of gyro-viscosity to
study wave propagation characteristics in a homogeneous pair-ion magnetized
plasma with a cylindrical symmetry. The exact dispersion relations derived by
the Hankel-Fourier transformation are shown comparable with those observed in
the experiment by Oohara and co-workers. The gyro-viscosity is responsible for
the change in propagation characteristics of the ion cyclotron wave from
forward to backward by suppressing the effect of the thermal pressure which
normally causes the forward nature of dispersion. Although the experiment has
been already explained by a kinetic theory by the present authors, the kinetic
derivations are so involved because of exact particle orbits in phase space,
finite Larmor radius effects, and higher order ion cyclotron resonances. The
present fluid theory provides a simple and transparent structure to the
dispersion relations since the gyro-viscosity is renormalized into the ion
cyclotron frequency which itself indicates the backward nature of dispersion.
The usual disadvantage of a fluid theory, which treats only fundamental modes
of eigen-waves excited in a system and is not able to describe higher harmonics
that a kinetic theory does, is compensated by simple derivations and clear
picture based on the renormalization of the gyro-viscosity.
