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.

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.

Progress in thermonuclear fusion energy research based on deuterium plasmas magnetically confi ned in toroidal tokamak devices requires the development of effi cient current drive methods. Previous experiments have shown that plasma current can be driven effectively by externally launched radio frequency power coupled to lower hybrid plasma waves. However, at the high plasma densities required for fusion power plants, the coupled radio frequency power does not penetrate into the plasma core, possibly because of strong wave interactions with the plasma edge. Here we show experiments performed on FTU (Frascati Tokamak Upgrade) based on theoretical predictions that nonlinear interactions diminish when the peripheral plasma electron temperature is high, allowing signifi cant wave penetration at high density. The results show that the coupled radio frequency power can penetrate into high-density plasmas due to weaker plasma edge effects, thus extending the effective range of lower hybrid current drive towards the domain relevant for fusion reactors.

Some of the crucial physics aspects of burning plasmas magnetically confined in toroidal systems are presented from the viewpoint of nonlinear dynamics. Most of the discussions specifically refer to tokamaks, but they can be readily extended to other toroidal confinement devices. Particular emphasis is devoted to fluctuation induced transport processes of mega electron volts energetic ions and charged fusion products as well as to energy and particle transports of the thermal plasma. Long time scale behaviours due to the interplay of fast ion induced collective effects and plasma turbulence are addressed in the framework of burning plasmas as complex self-organized systems. The crucial roles of mutual positive feedbacks between theory, numerical simulation and experiment are shown to be the necessary premise for reliable extrapolations from present day laboratory to burning plasmas. Examples of the broader applications of fundamental problems to other fields of plasma physics and beyond are also given.