The nonlinear evolution of waves excited by the resonant interaction with energetic particles, just above the instability threshold, is shown to depend on the type of relaxation process that restores the unstable distribution function. When dynamical friction dominates over diffusion in the phase space region surrounding the wave-particle resonance, an explosive evolution of the wave is found to be the only solution. This is in contrast with the case of dominant diffusion when the wave may exhibit steady-state, amplitude modulation, chaotic and explosive regimes near marginal stability. The experimentally observed differences between Alfvénic instabilities driven by neutral beam injection and those driven by ion-cyclotron resonance heating are interpreted.

• Received 4 December 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.195003