TAE instability and fast-ion losses

Nonlinear simulations of the fast-ion distribution function and the toroidicity-induced Alfven eigenmodes (TAE modes) have been carried out. Source and slowing-down of fast ions are considered in the drift kinetic equation. When the slowing-down time is comparable to the damping time of the TAE modes, the TAE modes reach steady saturation levels. On the other hand, when the slowing-down time is much longer than the damping time, the amplitudes of TAE modes are not at constant levels. Especially, when the fast-ion pressure is sufficiently high, all TAE modes show a coherent pulsating behavior. A five-dimensional Vlasov simulation code is also developed, and it is demonstrated that saturation of a TAE mode can be simulated soundly with this code.