Gyrokinetic theory of toroidal Alfvn eigenmode saturation via nonlinear wave-wave coupling

Nonlinear wave-wave coupling constitutes an important route for the turbulence spectrum evolution in both space and laboratory plasmas. For example, in a reactor relevant fusion plasma, a rich spectrum of symmetry-breaking shear Alfven wave (SAW) instabilities is expected to be excited by energetic fusion alpha particles, and self-consistently determines the anomalous alpha particle transport rate by the saturated electromagnetic perturbations. In this work, we will show that the nonlinear gyrokinetic theory is a necessary and powerful tool in qualitatively and quantitatively investigating the nonlinear wave-wave coupling processes. More specifically, one needs to employ the gyrokinetic approach to account for the breaking of the "pure Alfvenic state" in the short-wavelength kinetic regime, due to the short-wavelength structures associated with nonuniformity intrinsic to magnetically confined plasmas. Using well-known toroidal Alfven eigenmode (TAE) as a paradigm case, three nonlinear wave-wave coupling channels expected to significantly influence the TAE nonlinear dynamics are investigated to demonstrate the strength and necessity of nonlinear gyrokinetic theory in predicting crucial processes in a future reactor burning plasma. These are: 1. the nonlinear excitation of meso-scale zonal field structures via modulational instability and TAE scattering into short-wavelength stable domain; 2. the TAE frequency cascading due to nonlinear ion-induced scattering and the resulting saturated TAE spectrum; and 3. the cross-scale coupling of TAE with micro-scale ambient drift wave turbulence and its effect on TAE regulation and anomalous electron heating.