Theory of shear Alfvén waves in toroidal plasmas

Fundamental wave and stability properties of shear Alfvén waves in nonuniform axisymmetric toroidal plasmas are reviewed. Using a slab model with nonuniform density, concepts such as continuous spectrum, resonant absorption, and linear mode conversion to kinetic Alfvén wave are first discussed. We then analyze the formation of frequency gaps in the continuous spectrum due to the finite toroidicity-induced coupling between the poloidal harmonics in an axisymmetric torus. Existence of discrete eigenmodes both inside the frequency gap and the continuous spectra are further demonstrated. Kinetic excitations of collective toroidal shear Alfvén instabilities via resonances with energetic particles are also reviewed; first in the one-dimensional radially local limit and then with a full two-dimensional global analysis. Effects due to the non-perturbative nature of the energetic-particle drive and the global extent of the eigenmodes are emphasized.