On resonant destabilization of toroidal Alfvén eigenmodes by circulating and trapped energetic ions/alpha particles in tokamaks

Toroidal Alfvén eigenmodes are shown to be resonantly destabilized by both circulating and trapped energetic ions/alpha particles. In particular, the energetic circulating ions are shown to resonate with the mode not only at the Alfvén speed (vA), but also at one-third of this speed, while for trapped ions, the dominant instability mechanism is shown to be due to the resonance between the precessional magnetic drift and the wave. Implications of the theory for present and future tokamaks are discussed.