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Observations have shown that magnetohydrodynamic waves over a large frequencyrange are ubiquitous in solar prominences. The waves are probably driven byphotospheric motions and may transport energy up to prominences suspended inthe corona. Dissipation of wave energy can lead to heating of the coolprominence plasma, so contributing to the local energy balance within theprominence. Here we discuss the role of Alfv\'en wave dissipation as a heatingmechanism for the prominence plasma. We consider a slab-like quiescentprominence model with a transverse magnetic field embedded in the solar corona.The prominence medium is modelled as a partially ionized plasma composed of acharged ion-electron single fluid and two separate neutral fluids correspondingto neutral hydrogen and neutral helium. Friction between the three fluids actsas a dissipative mechanism for the waves. The heating caused byexternally-driven Alfv\'en waves incident on the prominence slab isanalytically explored. We find that the dense prominence slab acts as aresonant cavity for the waves. The fraction of incident wave energy that ischannelled into the slab strongly depends upon the wave period, $P$. Usingtypical prominence conditions, we obtain that wave energy trapping andassociated heating are negligible when $P \gtrsim 100$ s, so that it isunlikely that those waves have a relevant influence on prominence energetics.When $1$ s $\lesssim P \lesssim 100$ s the energy absorption into the slabshows several sharp and narrow peaks, that can reach up to 100%, when theincident wave frequency matches a cavity resonance of the slab. Wave heating isenhanced at those resonant frequencies. Conversely, when $P \lesssim 1$ scavity resonances are absent, but the waves are heavily damped by the strongdissipation. We estimate that wave heating may compensate for about 10% ofradiative losses of the prominence plasma.

The role of Alfv\'en wave heating in solar prominences