  A ray-theoretic phase space description of linear waves in a two-fluid
(charges and neutrals) magnetized plasma is used to calculate analytic decay
rates and mode transmission and conversion coefficients between fast and slow
waves in two dimensions due to finite ion-neutral collision frequencies at
arbitrary ionization fraction. This is relevant to partially ionized
astrophysical plasmas, in particular solar and stellar atmospheres. The most
important parameter governing collisional effects is the ratio of the wave
frequency to the neutral-charges collision frequency,
$\epsilon=\omega/\nu_{nc}$, with secondary dependence on ionization fraction
and wave attack angle. Comparison is made to the one-fluid magnetohydrodynamic
(MHD) case, and it is found that acoustic-to-acoustic and magnetic-to-magnetic
transmission through the Alfv\'en-acoustic equipartition layer is decreased by
a term of $\mathcal{O}(\epsilon^2)$ relative to one-fluid (infinite collision
frequency), and correspondingly acoustic-to-magnetic and magnetic-to-acoustic
conversion is increased. The neutral acoustic mode is shown to dissipate
rapidly as $\nu_{nc}\to\infty$. Away from the mode conversion region,
dissipative decay along the remaining magneto-acoustic rays scales as
$\mathcal{O}(\epsilon)$ and is found to be much more effective on magnetically
dominated rays compared to acoustically dominated rays. This produces a steep
jump in dissipation in mode conversion regions, where the rays change
character, and can produce localized heating there and beyond. Applications to
the solar chromosphere are discussed.
