On nonlinear saturation of toroidal Alfv\'en eigenmode due to thermal plasma nonlinearities
The nonlinear saturation of toroidal Alfven eigenmode (TAE) due to thermal plasma nonlinearities is investigated using gyrokinetic particle-in-cell simulations and theoretical analysis. In the single toroidal mode number simulations with zonal fields filtered out, we find that the saturation level of TAE is governed by thermal plasma nonlinearities for gamma_L/omega_n > 0.47%, which has weak dependence on the linear drive gamma_L, i.e., "stiffness" in saturation level. We find that the frequency of TAE decreases as the amplitude of it increases, which is induced by the phase-space zonal structure (PSZS) of thermal plasmas universally existed in particle-in-cell simulations. The saturation of TAE can be finally reached when the mode merges into the continuum. Following this process, the separation of neighboring poloidal harmonics and mode transition to energetic particle modes can be observed. In simulations with zonal fields, zonal fields can essentially counteract the effects of PSZS of thermal plasmas, leading to roughly a factor of 2 enhancement of the TAE saturation level compared to the single toroidal mode number simulation, implying the necessity of including zonal modes in evaluating the saturation level of TAE.