Gyrokinetic theory of toroidal Alfvén 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 Alfvén 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 Alfvénic 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 Alfvén 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.