General nonlinear equations describing reversed shear Alfvén eigenmode (RSAE) self-modulation via zero-frequency zonal structure (ZFZS) generation are derived using nonlinear gyrokinetic theory, which are then applied to study the spontaneous ZFZS excitation as well as RSAE nonlinear saturation. It is found that both electrostatic zonal flow and electromagnetic zonal current can be preferentially excited by finite-amplitude RSAE, depending on specific plasma parameters. The modification to local shear Alfvén wave continuum is evaluated using the derived saturation level of zonal current, which is shown to play a comparable role in saturating RSAE with the ZFZS scattering.

The two-field equations that govern fully nonlinear dynamics of the drift wave (DW) and geodesic acoustic mode (GAM) interaction in toroidal geometry are derived within the nonlinear gyrokinetic framework. Two stages with distinctive features are identified and analyzed using both analytical and numerical approaches. In the ‘linear’ growth stage, the derived set of nonlinear equations can be reduced to the intensively studied parametric decay instability, accounting for the spontaneous resonant excitation of GAM by the DW. The main results of previous works on spontaneous GAM excitation, e.g. the greatly enhanced GAM group velocity and the nonlinear growth rate of GAM, are reproduced from the numerical solution of the two-field equations. In the fully nonlinear stage, soliton structures are observed to form due to the balancing of the self-trapping effect by the spontaneously excited GAM and kinetic dispersiveness of the DW. The soliton structures enhance turbulence spreading from the DW linearly unstable region to the stable region, exhibiting convective propagation instead of a typical linear dispersive process, and are thus expected to induce core-edge interaction and nonlocal transport.

Two novel nonlinear mode coupling processes for reversed shear Alfvén eigenmode (RSAE) nonlinear saturation are proposed and investigated. In the first process, the RSAE nonlinearly couples to a co-propagating toroidal Alfvén eigenmode (TAE) with the same toroidal and poloidal mode numbers, and generates a geodesic acoustic mode. In the second process, the RSAE couples to a counter-propagating TAE and generates an ion acoustic wave quasi-mode. The condition for the two processes to occur is favored during current ramp. Both the processes contribute to effectively saturate the Alfvénic instabilities, as well as nonlinearly transfer of energy from energetic fusion alpha particles to fuel ions in burning plasmas.

Nonlinear generation of high frequency mode (HFM) by toroidal Alfvén eigenmode (TAE) observed in HL-2A tokamak is analyzed using nonlinear gyrokinetic theory. It is found that, the HFM can be dominated by |nq − m| = 1 perturbations with predominantly ideal magnetohydrodynamic if the two primary TAEs are co-propagating; while the HFM can be characterized by nq − m = 0 electrostatic perturbations if the two primary TAEs are counter-propagating. Here, n and m are respectively the toroidal and poloidal mode numbers, and q is the safety factor. The nonlinear process is sensitive to the equilibrium magnetic geometry of the device.

The local stability of ion-temperature gradient driven mode (ITG) in the presence of a given radial electric field is investigated using gyrokinetic theory and ballooning mode formalism with toroidal effect accounted for. It is found that zero frequency radial electric field-induced poloidal rotation can significantly stabilize ITG, while the associated density perturbation has little effect on ITG stability due to the modification of finite-orbit-width effect. However, the parallel mode structure is slightly affected due to the evenly symmetric density modulation associated with the zero-frequency radial electric field.