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.

A fully nonlinear model is developed for the bump-on-tail instability including the effects of dynamical friction ͑drag͒ and velocity space diffusion on the energetic particles driving the wave. The results show that drag provides a destabilizing effect on the nonlinear evolution of waves. Specifically, in the early nonlinear phase of the instability, the drag facilitates the explosive scenario of the wave evolution, leading to the creation of phase space holes and clumps that move away from the original eigenfrequency. Later in time, the electric field associated with a hole is found to be enhanced by the drag, whereas for a clump it is reduced. This leads to an asymmetry of the frequency evolution between holes and clumps. The combined effect of drag and diffusion produces a diverse range of nonlinear behaviors including hooked frequency chirping, undulating, and steady state regimes. An analytical model is presented, which explains the aforementioned diversity. A continuous production of hole-clump pairs in the absence of collisions is also observed.

The developments of advanced tokamak scenarios as well as the employment of a new neutral beam injection (NBI) source with higher power and beam energy up to ≈65 keV have significantly broadened the frequency range and the variety of Alfvén eigenmodes (AEs) excited by the super-Alfvénic NBI on the spherical tokamak MAST. During recent experiments on MAST, several distinct classes of beam-driven AEs have been identified, with different modes being most unstable in different MAST scenarios. In MAST discharges with elevated monotonic q(r)-profiles and NBI power ⩾3 MW, chirping modes starting in the frequency range ⩽150 kHz decreased in frequency down to ≈20 kHz as q(0) decreased and then smoothly transformed to long-living modes with a weakly-varying frequency and a n = 1 kink-mode structure. The bolometer data suggest that the long-living modes can be responsible for fast ion losses on MAST, while the charge-exchange data show that a coupling between these modes and other low-frequency modes can cause a collapse of toroidal plasma rotation with a subsequent disruption. In MAST discharges with reversed magnetic shear, Alfvén cascade eigenmodes in the frequency range 40–180 kHz were observed at a moderate NBI power ⩽2 MW allowing an additional assessment of q(r)-profile evolution in time. A robust reproducible scenario was found on MAST, in which the instability of high-frequency modes in the range 0.4–3.8 MHz and typically with negative toroidal mode numbers was dominating the spectrum of beam-driven AEs. Since the highest frequency of such modes is close to the on-axis ion cyclotron frequency and the polarization study of these modes show a significant parallel perturbed magnetic field, these modes are identified as compressional Alfvén eigenmodes. For investigating the AE spectrum in plasmas with high β, an active AE antenna has been installed on MAST. First measurements of stable AE modes in MAST have been performed successfully and are described here.

Remarkable progress has been made in diagnosing energetic particle instabilities on presentday machines and in establishing a theoretical framework for describing them. This overview describes the much improved diagnostics of Alfvén instabilities and modelling tools developed world-wide, and discusses progress in interpreting the observed phenomena. A multi-machine comparison is presented giving information on the performance of both diagnostics and modelling tools for different plasma conditions outlining expectations for ITER based on our present knowledge.

A theoretical framework, built on the notion of nearly periodic fast particle orbits, is developed to describe long range frequency sweeping events in the 1D electrostatic bump-on-tail model with Krook collisions and dynamical friction (drag). Both the actual deviation from the linear mode frequency and the effect of particle trapping in the wave field due to an increasing wave amplitude affect the frequency sweeping rate. For upward sweeping holes, hooked and steady state frequency sweeping patterns are found as results of an interplay between Krook and drag collisions.