Based on nonlinear gyrokinetic theory, we analytically investigate the indirect nonlinear modification of drift wave instability by toroidal Alfvén eigenmodes (TAEs). In particular, using the ion temperature gradient (ITG) mode as a paradigm model, the present work contains two parts: (1) the modulation of TAE beat-driven zonal structures (ZSs) on the local stability of the ITG mode, and (2) the effects of beat-driven ZS on ITG radial propagation, with the individual contributions from zonal flows (ZFs), zonal currents (ZCs), and phase-space zonal structures (PSZSs) investigated separately. It is found that, while the contributions from ZC and PSZS are significantly larger than that from ZF for typical reactor parameter regimes, they cancel each other to a large extent. Consequently, the net effect of the ZS on both the local stability and non-local propagation of the ITG is weak, which contrasts with existing numerical results.
Fang et al. (Wed,) studied this question.