  Observations show that waves are ubiquitous in the solar atmosphere and may
play an important role for plasma heating. The study of waves in the solar
corona is usually based on linear ideal magnetohydrodynamics (MHD) for a fully
ionized plasma. However, the plasma in the photosphere and the chromosphere is
only partially ionized. Here we investigate theoretically the impact of partial
ionization on MHD wave propagation in cylindrical flux tubes in the two-fluid
model. We derive the general dispersion relation that takes into account the
effects of neutral-ion collisions and the neutral gas pressure. We take the
neutral-ion collision frequency as an arbitrary parameter. Particular results
for transverse kink modes and slow magnetoacoustic modes are shown. We find
that the wave frequencies only depend on the properties of the ionized fluid
when the neutral-ion collision frequency is much lower that the wave frequency.
For high collision frequencies realistic of the solar atmosphere ions and
neutrals behave as a single fluid with an effective density corresponding to
the sum of densities of both fluids and an effective sound velocity computed as
the average of the sound velocities of ions and neutrals. The MHD wave
frequencies are modified accordingly. The neutral gas pressure can be neglected
when studying transverse kink waves but it has to be taken into account for a
consistent description of slow magnetoacoustic waves. The MHD waves are damped
due to neutral-ion collisions. The damping is most efficient when the wave
frequency and the collision frequency are of the same order of magnitude. For
high collision frequencies slow magnetoacoustic waves are more efficiently
damped than transverse kink waves. In addition, we find the presence of
cut-offs for certain combinations of parameters that cause the waves to become
non-propagating.
