Abstract Solar prominences are partially ionized plasma structures embedded in the solar corona. Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences, which have been interpreted in terms of standing or propagating MHD waves. Some of these observations suggest that slow magnetoacoustic waves could be responsible for these oscillations and have provided us with evidence about their damping/amplification with very small ratios between damping/amplifying times and periods, which have been difficult to explain from a theoretical point of view. Here we investigate the temporal behavior of non-adiabatic, slow, magnetoacoustic waves when a heating–cooling misbalance is present. The influence of optically thin losses and of a general heating term, in which density and temperature dependence can be modified, as well as the effect of partial ionization have been considered. Furthermore, a tentative example of how, using observational data, the observed ratio between damping/amplifying times and periods could be matched with those theoretically obtained is shown. In summary, different combinations of radiative losses, heating mechanisms, and typical wavenumbers, together with the effect of partial ionization, could provide a theoretical tool able to reproduce observational results on small-amplitude oscillations in prominences.
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