AIP Digital Archive
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 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@B|/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. 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 10−2ωA , where ωA=vA/qR . Other types of global Alfvén waves are stable in deuterium–tritium (D–T) tokamaks due to toroidal coupling effects.
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