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An analytical theory of toroidicity-induced shear-Alfv\'en eigenmodes (TAE) is presented. The full two-dimensional problem is treated using a variational approach and the radial eigenmode structure is analyzed. We show that TAE suffer a significant damping due to the strong absorption occurring at the resonances with the shear-Alfv\'en continouus spectrum. The resonant damping is shown to be larger than the electron Landau damping and therefore constitutes an important dissipation mechanism in determining the threshold for TAE instabilities driven by alpha and energetic particles in tokamak experiments.
Zonca et al. (1992) studied this question.