  In this paper we study the role of radiative cooling in a two-fluid model
consisting of coupled neutrals and charged particles. We first analyze the
linearized two-fluid equations where we include radiative losses in the energy
equation for the charged particles. In a 1D geometry for parallel propagation
and in the limiting cases of weak and strong coupling, it can be shown
analytically that the instability conditions for the thermal mode and the sound
waves, the isobaric and isentropic criteria, respectively, remain unchanged
with respect to one-fluid radiative plasmas. For the parameters considered in
this paper, representative for the solar corona, the radiative cooling produces
growth of the thermal mode and damping of the sound waves. When neutrals are
included and are sufficiently coupled to the charges, the thermal mode growth
rate and the wave damping both reduce by the same factor, which depends on the
ionization fraction only. For a heating function which is constant in time, we
find that the growth of the thermal mode and the damping of the sound waves are
slightly larger. The numerical calculation of the eigenvalues of the general
system of equations in a 3D geometry confirm the analytic results. We then run
2D fully nonlinear simulations which give consistent results: a higher
ionization fraction or lower coupling will increase the growth rate. The
magnetic field contribution is negligible in the linear phase.
Ionization-recombination effects might play an important role because the
radiative cooling produces a large range of temperatures in the system. In the
numerical simulation, after the first condensation phase, when the minimum
temperature is reached, the fraction of neutrals increases four orders of
magnitude because of the recombination.
