Excitation of energetic-particle (EP)-induced geodesic acoustic modes (EGAMs) by velocity space anisotropy is investigated taking into account the coupling to the GAM continuous spectrum. The response of EPs is studied nonperturbatively and both local and nonlocal dispersion relations of EGAM are derived assuming a single pitch angle slowing-down energetic ion equilibrium distribution function. For a sharply localized EP source, it is shown that the mode is self-trapped where the EP drive is strongest, with an exponentially small damping due to the tunneling coupling to the GAM continuous spectrum.

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.

Collisionless damping of geodesic acoustic mode (GAM) excited in the large safety factor (q) region of a tokamak plasma is investigated taking into account the effects of finite ion Larmor radius and guiding-center drift orbit width as well as parallel electric field contributions. A corresponding analytical expression for the damping rate including higher-order harmonics of ion transit resonances is systematically derived and agrees well with numerical results in its validity regime.

Generation of zonal flow (ZF) by energetic particle (EP) driven toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, nonlinear resonant EP contribution dominates over the usual Reynolds and Maxwell stresses due to thermal plasma nonlinear response. ZF can be forced driven in the linear growth stage of TAE, with the growth rate being twice the TAE growth rate. The ZF generation mechanism is shown to be related to polarization induced by resonant EP nonlinearity. The generated ZF has both the usual meso-scale and microscale radial structures. Possible consequences of this forced driven ZF on the nonlinear dynamics of TAE are also discussed.Understanding the nonlinear dynamics of shear Alfvén waves (SAW) is of crucial importance to future burning plasmas with energetic particle (EP) population such as fusion-αs significantly contributing to the overall plasma energy density [1]. With frequency comparable to the characteristic frequencies of EPs, and group velocities mainly along magnetic field lines, SAWs are expected to be driven unstable by resonant EPs [2-5]; leading to EP transport and degradation of overall confinement, as reviewed in Ref. 1. Toroidal Alfvén eigenmode (TAE) [6,7], excited inside the toroidicity-induced SAW continuum gap to minimize continuum damping, is one of most dangerous candidates for effectively scattering EPs.There are two routes for the nonlinear saturation of TAEs, i.e., nonlinear wave-particle and nonlinear wavewave interactions [8]. Wave-particle phase space nonlinearity [9], e.g., wave-particle trapping, describes the nonlinear distortion of the EP distribution function; and leads to SAW saturation as the wave-particle trapping frequency, proportional to square root of the mode amplitude, is comparable with linear growth rate [10][11][12][13]. On the other hand, wave-wave coupling accounts for the transfer of TAE wave energy away from the most unstable modes. Among various wave-wave nonlinearities, generation of zonal structures (ZS) is of particular importance. Chen et al [14] investigated the nonlinear excitation of zero frequency zonal structure (ZFZS) by TAE with a prescribed amplitude, and found that finite amplitude TAE can excite ZFZS via modulational instability at a rate proportional to the amplitude of the pump TAE. Meanwhile, zonal current with lower excitation threshold could be preferentially excited in specific plasma equilibria, which, however, do not reflect typical experimental tokamak plasmas [14]. Numerical simulations of nonlinear dynamics of EP driven TAE are carried out by both hybrid code [15] and PIC code [16], and found that zonal flow (ZF) is excited by forced driven process, with the ZF growth rate being twice of TAE growth rate. In this paper, we will clarify the "discrepancies" between analytical theory and simulation, with emphasis on the important role played by EPs [1,17]. Our results indicate that there is no conflict between analytical theory [14] and numerical simulations [15,16]; in fact, they desc...