  There is observational evidence of the presence of small-amplitude transverse
magnetohydrodynamic (MHD) waves with a wide range of frequencies in the threads
of solar prominences. It is believed that the waves are driven at the
photosphere and propagate along the magnetic field lines up to prominences
suspended in the corona. The dissipation of MHD wave energy in the partially
ionized prominence plasma is a heating mechanism whose relevance needs to be
explored. Here we consider a simple 1D model for a non-uniform thin thread and
investigate the heating associated with dissipation of Alfven waves. The model
assumes an ad hoc density profile and a uniform pressure, while the temperature
and ionization degree are self-consistently computed considering either LTE or
non-LTE approximations for the hydrogen ionization. A broadband driver for
Alfven waves is placed at one end of the magnetic field line, representing
photospheric excitation. The Alfvenic perturbations along the thread are
obtained by solving the linearized MHD equations for a partially ionized plasma
in the single-fluid approximation.We find that wave heating in the partially
ionized part of the thread is significant enough to compensate for energy
losses due to radiative cooling. A greater amount of heating is found in the
LTE case because the ionization degree for core prominence temperatures is
lower than that in the non-LTE approximation. This results in a greater level
of dissipation due to ambipolar diffusion in the LTE case. Conversely, in the
hot coronal part of the model, the plasma is fully ionized and wave heating is
negligible. The results of this simple model suggest that MHD wave heating can
be relevant for the energy balance in prominences. Further studies based on
more elaborate models are required.
