Numerical study of the nonlinear evolution of toroidicity-induced Alfvén eigenmodes

A simulation code for the nonlinear evolution of the toroidicity-induced Alfvén eigenmodes (TAE) is implemented based on a collisional $δf$ simulation method [Phys. Plasmas 4, 3591 (1997)] and a Hamiltonian formulation of the guiding-center motion [Phys. Fluids 27, 2455 (1984)]. The nonlinear behavior of TAE in the regime of weak damping is studied numerically and compared with the predictions of theoretical analysis. The theoretical prediction for the scaling of the saturation amplitude with the linear growth rate and the collision rate is well confirmed. The enhancement of the saturation level due to resonance overlapping when there are multiple modes is observed and analyzed. The simulation code is applied to the alpha-driven TAE’s in the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Fusion 26, 11 (1984)]. An estimate of the background damping rate is obtained from the simulation result.