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The achievement of sustained nuclear fusion in magnetically confined plasmarelies on efficient confinement of high-energy ions produced by the fusionreaction. Such particles can excite Alfven Eigenmodes (AEs), whichsignificantly degrade their confinement and threatens the vacuum vessel offuture reactors. To develop diagnostics and control schemes, a betterunderstanding of linear and nonlinear features of resonant interactions betweenplasma waves and high-energy particles, is required. In the case of an isolatedsingle resonance, the problem is homothetic to the so-called Berk-Breizman (BB)problem, which is an extension of the classic bump-on-tail electrostaticproblem, including external damping to a thermal plasma, and collisions. Asemi-Lagrangian simulation code, COBBLES, is developed to solve theinitial-value BB problem. The nonlinear behavior of instabilities inexperimentally-relevant conditions is categorized into steady-state, periodic,chaotic, and frequency-sweeping (chirping) regimes. The chaotic regime is shownto extend into a linearly stable region, and a mechanism for such subcriticalinstabilities is proposed. Analytic and semi-empirical laws for nonlinearchirping characteristics, such as sweeping-rate, lifetime, and asymmetry, aredeveloped and validated. Long-time simulations demonstrate the existence of aquasi-periodic chirping regime. Collisional drag and diffusion are shown to beessential to reproduce the alternation between major chirping events andquiescent phases, which is observed in experiments. Based on these findings, afitting procedure between COBBLES simulations and chirping AE experiments isdevelopped. This procedure, which yields local linear drive and externaldamping rate, is applied to Toroidicity-induced AEs (TAEs) on JT-60U and MASTtokamaks. This suggests the existence of TAEs relatively far from marginalstability.

The Berk-Breizman Model as a Paradigm for Energetic Particle-driven Alfven Eigenmodes