Mode structure and continuum damping of high-n toroidal Alfvén eigenmodes*

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Abstract
An asymptotic theory is described for calculating the mode structure and continuum damping of short‐wavelength toroidal Alfvén eigenmodes (TAE). The formalism somewhat resembles the treatment used for describing low‐frequency toroidal modes with singular structure at a rational surface, where an inner solution, which for the TAE mode has toroidal coupling, is matched to an outer toroidally uncoupled solution. A three‐term recursion relation among coupled poloidal harmonic amplitudes is obtained, whose solution gives the structure of the global wave function and the complex eigenfrequency, including continuum damping. Both analytic and numerical solutions are presented. The magnitude of the damping is essential for determining the thresholds for instability driven by the spatial gradients of energetic particles (e.g., neutral‐beam‐injected ions or fusion‐product alpha particles) contained in a tokamak plasma.