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Context. One of the typical features shown by observations of solarprominence oscillations is that they are damped in time and that the values ofthe damping times are usually between one and three times the correspondingoscillatory period. However, the mechanism responsible for the attenuation isstill not well-known. Aims. Thermal conduction, optically thin or thickradiation and heating are taken into account in the energy equation, and theirrole on the attenuation of prominence oscillations is evaluated. Methods. Thedispersion relation for linear non-adiabatic magnetoacoustic waves is derivedconsidering an equilibrium made of a prominence plasma slab embedded in anunbounded corona. The magnetic field is orientated along the direction parallelto the slab axis and has the same strength in all regions. By solving thedispersion relation for a fixed wavenumber, a complex oscillatory frequency isobtained, and the period and the damping time are computed. Results. The effectof conduction and radiation losses is different for each magnetoacoustic modeand depends on the wavenumber. In the observed range of wavelengths theinternal slow mode is attenuated by radiation from the prominence plasma, thefast mode by the combination of prominence radiation and coronal conduction andthe external slow mode by coronal conduction. The consideration of the externalcorona is of paramount importance in the case of the fast and external slowmodes, whereas it does not affect the internal slow modes at all. Conclusions.Non-adiabatic effects are efficient damping mechanisms for magnetoacousticmodes, and the values of the obtained damping times are compatible with thoseobserved.

The effect of the solar corona on the attenuation of small-amplitude prominence oscillations. I. Longitudinal magnetic field