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(Received 3 June 1992; accepted 20 July 1992)
The^{ }stability of highn toroidicityinduced shear Alfvén eigenmodes (TAE) in the^{ }presence of fusion alpha particles or energetic ions in tokamaks^{ }is investigated. The TAE modes are discrete in nature, and^{ }thus can easily tap the free energy associated with energetic^{ }particle pressure gradient through wave particle resonant interaction. A quadratic^{ }form is derived for the highn TAE modes using gyrokinetic^{ }equation. The kinetic effects of energetic particles are calculated perturbatively^{ }using the ideal magnetohydrodynamic (MHD) solution as the lowestorder eigenfunction.^{ }The finite Larmor radius (FLR) effects and the finite drift^{ }orbit width (FDW) effects are included for both circulating and^{ }trapped energetic particles. It is shown that, for circulating particles,^{ }FLR and FDW effects have two opposite influences on the^{ }stability of the highn TAE modes. First, they have the^{ }usual stabilizing effects by reducing the wave particle interaction strength.^{ }Second, they also have destabilizing effects by allowing more particles^{ }to resonate with the TAE modes. It is found that^{ }the growth rate induced by the circulating alpha particles increases^{ }linearly with the toroidal mode number n for small k_{}_{},^{ }and decreases as 1/n for k_{}_{}1. The maximum growth rate^{ }is obtained at k_{}_{} on the order of unity, and^{ }is nearly constant for the range of 0.7v_{}/v_{A}2.5. On the^{ }other hand, the trapped particle response is dominated by the^{ }precessional drift resonance. The bounce resonant contribution is negligible. The^{ }growth rate peaks sharply at the value of k_{}_{}, such^{ }that the precessional drift resonance occurs for the most energetic^{ }trapped particles. The maximum growth rate due to the energetic^{ }trapped particles is comparable to that of circulating particles. Finally,^{ }the effect of the twodimensional wave structure of TAE modes^{ }is considered by using the Wentzel–Kramers–Brillouin (WKB) method. Physics of Fluids B: Plasma Physics is copyrighted by The American Institute of Physics. ^{ }
DOI: 10.1063/1.860328
PACS:
52.35.Bj, 52.55.Fa
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