This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis Nucl. Fusion 39 2137 in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvénic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfvén eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfvén eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfvén eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions.

A general theoretical framework for investigating the nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or comparable to the wave-particle trapping period. In this limit, both theoretical and numerical simulation studies show that nonadiabatic frequency chirping and phase locking could lead to secular resonant particle transport on meso-or macro-scales. The interplay between mode structures and resonant particles then provides the crucial ingredient to properly understand and analyze the nonlinear dynamics of Alfvén wave instabilities excited by nonperturbative energetic particles in burning fusion plasmas. Analogies with autoresonance in nonlinear dynamics and with superradiance in free-electron lasers are also briefly discussed.

Resonant energetic particles play a major role in determining the stability of toroidal Alfvén eigenmodes (TAE’s) by yielding the well-known driving mechanism for the instability and by producing an effective dissipation, which removes the singular character of local oscillations of the shear-Alfvén continuum and gives discrete kinetic Alfvén waves (KAW’s). Toroidal coupling of two counterpropagating KAW’s generates the kinetic analog of the TAE, the KTAE (kinetic TAE). The nonperturbative character of this phenomenon and of the coupling between TAE and KAW’s, and the relevance of finite drift-orbit effects limit the effectiveness of the analytical approach to asymptotic regimes, which are difficult to compare with realistic situations. A three-dimensional hybrid fluid-particle initial-value code for the numerical simulation of the linear and nonlinear evolution of toroidal modes of the Alfvén branch has been developed. It is shown that for typical parameters the KTAE is, indeed, more unstable than the TAE.

The change in nonlinear energetic particle mode (EPM) dynamics that accompanies the transition from weak to strong energetic ion transport is discussed in this work. It is demonstrated that the nonlinear threshold in fast ion energy density for the onset of strong convective transport occurring in avalanches is close to the linear EPM excitation threshold. This phenomenology is strictly related to the resonant character of the modes, which tend to be radially localized where the drive is strongest. After the convective loss phase, during which nonlinear EPM mode structure is displaced outwards, fast ion transport continues owing to diffusive processes. Theoretical analyses, presented here, are the basis for consistency analyses of operation scenarios in proposed burning plasma experiments. Comparisons between theoretical predictions and both simulation and experimental results are also briefly discussed.

The role of energetic particles (EPs) in fusion plasmas is unique as they could act as mediators of cross-scale couplings. More specifically, EPs can drive instabilities on the macro-and meso-scales and intermediate between the microscopic thermal ion Larmor radius and the macroscopic plasma equilibrium scale lengths. On one hand, EP driven shear Alfvén waves (SAWs) could provide a nonlinear feedback onto the macro-scale system via the interplay of plasma equilibrium and fusion reactivity profiles. On the other hand, EP-driven instabilities could also excite singular radial mode structures at SAW continuum resonances, which, by mode conversion, yield microscopic fluctuations that may propagate and be absorbed elsewhere, inducing nonlocal behaviors. The above observations thus suggest that a theoretical approach based on advanced kinetic treatment of both EPs and thermal plasma is more appropriate for burning fusion plasmas. Energetic particles, furthermore, may linearly and nonlinearly (via SAWs) excite zonal structures, acting, thereby, as generators of nonlinear equilibria that generally evolve on the same time scale of the underlying fluctuations. These issues are presented within a general theoretical framework, discussing evidence from both numerical simulation results and experimental observations. Analogies of fusion plasmas dynamics with problems in condensed matter physics, nonlinear dynamics, and accelerator physics are also emphasized.