Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

This article is a tutorial review of the interaction between energetic particles and Alfvén eigenmodes (AEs) which is one of the important research issues for fusion burning plasmas. The destabilization mechanism of AEs is a kind of inverse Landau damping through the resonant interaction with energetic particles. The important properties of the AE instability, such as resonance condition, conserved variable during the interaction, and particle trapping by the AE, are explained. The time evolution of AEs is classified into various types, steady state, frequency splitting, frequency chirping, and recurrent bursts. Berk and Breizman presented both a one-dimensional weakly nonlinear theory for marginal stability and a reduced simulation model that qualitatively explain the various types of time evolution. Berk–Breizman’s theory and reduced simulation model are introduced, and their limitations and the future works are discussed in this article. In addition, energetic particle transport by AEs is illustrated with surface-of-section plots. The particle trapping by the AE creates phase space islands and leads to the local flattening of the energetic particle spatial profile. The resonance overlap of multiple AEs and the overlap of higher-order resonances of a single AE lead to the emergence of stochasticity in phase space and the global transport of energetic particles.