The nonlinear saturation of beam-driven instabilities: Theory and experiment

Intense fast-ion populations created by neutral-beam injection into a tokamak can destabilize toroidicity-induced Alfvén eigenmodes (TAE modes) or internal kink modes. Experimentally, these modes stabilize when fast ions are ejected from the plasma, producing a cycle of relaxation oscillations about the marginal stability point. A pair of coupled differential equations describes this cycle. This simple theoretical formalism successfully describes the cycles observed during TAE experiments in DIII-D [Plasma Physics Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159].