Alpha particle destabilization of the toroidicity-induced Alfvén eigenmodes

The high-frequency, low mode number toroidicity-induced Alfvén eigenmodes (TAE) [Phys. Fluids 29, 3695 (1986)] are shown to be driven unstable by the circulating and/or trapped α particles through the wave-particle resonances. Satisfying the resonance condition requires that the α-particle birth speed υ_α ≥ υ_A/ 2|m - nq|, where υ_A is the Alfvén speed, m is the poloidal mode number, and n is the toroidal mode number. To destabilize TAE modes, the inverse Landau damping associated with the α-particle pressure gradient free energy must overcome the velocity space Landau damping due to both the α particles and the core electrons and ions. The growth rate was studied analytically with a perturbative formula derived from the quadratic dispersion relation, and numerically with the aid of the NOVA-K code. Stability criteria in terms of the α-particle beta β_α, α-particle pressure parameter (ω _*/ω_A) (ω_* is the α-particle diamagnetic drift frequency), and (υ_α/ υ_A) parameters will be presented for the Tokamak Fusion Test Reactor (TFTR) [Proceedings of the Thirteenth International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Crystal City, VA, 1990 (International Atomic Energy Agency, Vienna, in press)], Compact Ignition Tokamak (CIT) [Phys. Scr. T16, 89 (1987)], and the International Thermonuclear Experimental Reactor (ITER) [ITER Documentation Series, No. 21 (International Atomic Energy Agency, Vienna, 1991)]. The volume-averaged α-particle beta threshold for TAE instability also depends sensitively on the core electron and ion temperature. Typically the volume-averaged α-particle beta threshold is in the order of 10^-4. Typical growth rates of the n = 1 TAE mode can be in the order of 10^-2ω_A, where ω_A = υ_A/qR. Other types of global Alfvén waves are stable in deuterium-tritium (D-T) tokamaks due to toroidal coupling effects.