  Waves and shocks traveling through the solar chromospheric plasma are
influenced by its partial ionization and weak collisional coupling, and may
become susceptible to multi-fluid effects, similar to interstellar shock waves.
In this study, we consider fast magneto-acoustic shock wave formation and
propagation in a stratified medium, that is permeated by a horizontal magnetic
field, with properties similar to that of the solar chromosphere. The evolution
of plasma and neutrals is modeled using a two-fluid code that evolves a set of
coupled equations for two separate fluids. We observed that waves in neutrals
and plasma, initially coupled at the upper photosphere, become uncoupled at
higher heights in the chromosphere. This decoupling can be a consequence of
either the characteristic spatial scale at the shock front, that becomes
similar to the collisional scale, or the change in the relation between the
wave frequency, ion cyclotron frequency, and the collisional frequency with
height. The decoupling height is a sensitive function of the wave frequency,
wave amplitude, and the magnetic field strength. We observed that decoupling
causes damping of waves and an increase in the background temperature due to
the frictional heating. The comparison between analytical and numerical results
allows us to separate the role of the nonlinear effects from the linear ones on
the decoupling and damping of waves.
