Nonlinear excitation of finite-radial-scale zonal structures by toroidal Alfvén eigenmode

The set of equations describing nonlinear evolution of a single toroidal Alfvén eigenmode are derived, including both zero frequency zonal structure (ZFZS) generation and wave-particle phase space nonlinearities. The simplified case of neglecting wave-particle phase space nonlinearity is then investigated to focus on different roles of energetic particles and bulk plasmas on ZFZS generation. It is shown that energetic particles and bulk plasma play dominant roles in ZFZS generation in different nonlinear stages, and the corresponding processes are qualitatively different. Several properties of ZFZS generation, e.g. fine- versus meso-scale, forced driven versus spontaneous excitation, are clarified by the present analysis. (paper)