  The chromosphere is a partially ionized layer of the solar atmosphere, the
transition between the photosphere where the gas motion is determined by the
gas pressure and the corona dominated by the magnetic field. We study the
effect of partial ionization for 2D wave propagation in a gravitationally
stratified, magnetized atmosphere with properties similar to the solar
chromosphere. We adopt an oblique uniform magnetic field in the plane of
propagation with strength suitable for a quiet sun region. The theoretical
model used is a single fluid magnetohydrodynamic approximation, where
ion-neutral interaction is modeled by the ambipolar diffusion term. Magnetic
energy can be converted into internal energy through the dissipation of the
electric current produced by the drift between ions and neutrals. We use
numerical simulations where we continuously drive fast waves at the bottom of
the atmosphere. The collisional coupling between ions and neutrals decreases
with the decrease of the density and the ambipolar effect becomes important.
Fast waves excited at the base of the atmosphere reach the equipartition layer
and reflect or transmit as slow waves. While the waves propagate through the
atmosphere and the density drops, the waves steepen into shocks. The main
effect of ambipolar diffusion is damping of the waves. We find that for the
parameters chosen in this work, the ambipolar diffusion affects the fast wave
before it is reflected, with damping being more pronounced for waves which are
launched in a direction perpendicular to the magnetic field. Slow waves are
less affected by ambipolar effects. The damping increases for shorter periods
and larger magnetic field strengths. Small scales produced by the nonlinear
effects and the superposition of different types of waves created at the
equipartition height are efficiently damped by ambipolar diffusion.
