Dynamics of shear Alfvén waves and energetic particles are crucial to the performance of burning fusion plasmas. This article reviews linear as well as nonlinear physics of shear Alfvén waves and their self-consistent interaction with energetic particles in tokamak fusion devices. More specifically, the review on the linear physics deals with wave spectral properties and collective excitations by energetic particles via wave-particle resonances. The nonlinear physics deals with nonlinear wave-wave interactions as well as nonlinear wave-energetic particle interactions. Both linear as well as nonlinear physics demonstrate the qualitatively important roles played by realistic equilibrium nonuniformities, magnetic field geometries, and the specific radial mode structures in determining the instability evolution, saturation, and, ultimately, energetic-particle transport. These topics are presented within a single unified theoretical framework, where experimental observations and numerical simulation results are referred to elucidate concepts and physics processes.

An analytical theory of toroidicity-induced shear-Alfvén 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-Alfvén 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.