Stability of the toroidicity-induced Alfvén eigenmode in axisymmetric toroidal equilibria

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Abstract
The stability of toroidicity‐induced Alfvén eigenmodes (TAE) is investigated in general tokamak equilibria with finite aspect ratio and finite plasma beta. The finite orbit width of the hot particles and the collisional damping of the trapped electrons are included. For the trapped hot particles, the finite orbit width is found to be stabilizing. For the circulating hot particles, the finite orbit width effect is stabilizing for larger values of vh/vA (≳1) and destabilizing for smaller values of vh/vA (vh is the hot particle speed and vA is the Alfvén speed. The collisional damping of the trapped electrons is found to have a much weaker dependence on the collision frequency than the previous analytic results. The contribution of the curvature term to the trapped electron collisional damping is negligible compared to that of the parallel electric field term for typical parameters. The calculated critical hot particle beta values for the TAE instability are consistent with the experimental measurements.