Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas*

Nonlinear evolution of multiple toroidal Alfvén eigenmodes (TAEs) driven by fast ions is self-consistently investigated by kinetic simulations in toroidal plasmas. To clearly identify the effect of nonlinear coupling on the beam ion loss, simulations over single-n modes are also carried out and compared with those over multiple-n modes, and the wave-particle resonance and particle trajectory of lost ions in phase space are analyzed in detail. It is found that in the multiple-n case, the resonance overlap occurs so that the fast ion loss level is rather higher than the sum loss level that represents the summation of loss over all single-n modes in the single-n case. Moreover, increasing fast ion beta β h can not only significantly increase the loss level in the multiple-n case but also significantly increase the loss level increment between the single-n and multiple-n cases. For example, the loss level in the multiple-n case for β h = 6.0% can even reach 13% of the beam ions and is 44% higher than the sum loss level calculated from all individual single-n modes in the single-n case. On the other hand, when the closely spaced resonance overlap occurs in the multiple-n case, the release of mode energy is increased so that the widely spaced resonances can also take place. In addition, phase space characterization is obtained in both single-n and multiple-n cases.