Nonideal theory of toroidal Alfvén eigenmodes

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Abstract
Ambiguities in the ideal magnetohydrodynamic (MHD) analysis of toroidal Alfvén eigenmodes (TAE) are resolved by incorporating nonideal effects (finite electron conductivity and ion gyroradius) into the MHD model of Rosenbluth et al. [Phys. Fluids B 4, 1806 (1992)]. The previous ideal theory yields a dielectric function containing branch points in the complex frequency plane, but provides no specification of the corresponding branch lines. The kinetic model represents a singular perturbation of the ideal theory, and specifies precisely the location of branch cuts in the ideal limit. Moreover, the analytic structure of the complex frequency plane for the kinetic model shows a countably infinite set of poles in place of a branch cut—with a new kinetic‐type TAE mode near each pole. It has also been verified that the ideal frequency root is in most cases close to one of the kinetic roots. The damping and mode structure is determined numerically within the framework of the high‐mode‐number, small inverse aspect ratio, low beta, small gyroradius model. Finally, an analytic form for the damping is obtained including both continuum and nonideal effects, and agrees well with the numerical results.