  The standing slow magneto-acoustic oscillations in cooling coronal loops are
investigated. There are two damping mechanisms which are considered to generate
the standing acoustic modes in coronal magnetic loops namely thermal conduction
and radiation. The background temperature is assumed to change temporally due
to optically thin radiation. In particular, the background plasma is assumed to
be radiatively cooling. The effects of cooling on longitudinal slow MHD modes
is analytically evaluated by choosing a simple form of radiative function that
ensures the temperature evolution of the background plasma due to radiation
coincides with the observed cooling profile of coronal loops. The assumption of
low-beta plasma leads to neglect the magnetic field perturbation and eventually
reduces the MHD equations to a 1D system modelling longitudinal MHD
oscillations in a cooling coronal loop. The cooling is assumed to occur on a
characteristic time scale much larger than the oscillation period that
subsequently enables using the WKB theory to study the properties of standing
wave. The governing equation describing the time-dependent amplitude of waves
is obtained and solved analytically. The analytically derived solutions are
numerically evaluated to give further insight into the evolution of the
standing acoustic waves. We find that the plasma cooling gives rise to a
decrease in the amplitude of oscillations. In spite of the reduction in damping
rate caused by rising the cooling, the damping scenario of slow standing MHD
waves strongly increases in hot coronal loops.
