Alpha particle destabilization of the toroidicity-induced Alfvén eigenmodes

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Abstract
The high‐frequency, low mode number toroidicity‐induced Alfvén eigenmodes (TAE) [Phys. Fluids 2 9, 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 vα≥vA/2‖m−nq‖, where vA 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 βα, α‐particle pressure parameter (ω*/ωA) (ω* is the α‐particle diamagnetic drift frequency), and (vα/vA) 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. T 1 6, 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 10−2ωA , where ωA=vA/qR . Other types of global Alfvén waves are stable in deuterium–tritium (D–T) tokamaks due to toroidal coupling effects.