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We have further extended previously derived expressions for zonal electromagnetic fields (ZFs) beat driven by reversed shear Alfvén eigenmode (RSAE) [L. Chen et al., Nucl. Fusion 65 (2025) 016018] to the case of toroidal Alfvén eigenmode (TAE). It is found that the expression of zonal current (i.e., the zonal component of the parallel vector potential) remains robust. The expression of the zonal flow (i.e., the zonal component of the scalar potential including finite poloidal-harmonics coupling), however, could be quantitatively and qualitatively modified; depending on the relative time scales between thermal ions and zonal fields, as well as the ratio between the energetic-particle (EP) and thermal-ion pressures. In particular, while the energetic-particle polarization is always neoclassical; the thermal-ion polarization could be either neoclassical (for slow zonal time scale) or classical (for fast zonal time scale). In the case of Alfvén instabilities strongly excited by EPs, as in some current experiments and simulations, one has classical polarization for the thermal ions, and the resultant zonal flow could then, for typical parameters, be an order of magnitude larger than that given in [L. Chen et al., Nucl. Fusion 65 (2025) 016018]; which was derived under assumptions of thermal-ion neoclassical polarization and negligible EP contribution . Implications of the present results to the regime of burning plasmas will be discussed.