Arbitrary mode number boundary-layer theory for nonideal toroidal Alfvén modes

Abstract

The theory of toroidicity-induced Alfvén eigenmodes (TAE) and kinetic TAE (KTAE) is generalized to arbitrary mode numbers for a large aspect ratio low-beta circular tokamak. The interaction between nearest neighbors is described by a three-term recursion relation that combines elements from an outer region, described by the ideal magnetohydrodynamic equations of a cylinder, and an inner region, which includes the toroidicity and the nonideal effects of finite ion Larmor radius, electron inertia, and collisions. By the use of quadratic forms, it is proven that the roots of the recursion relation are stable and it is shown how perturbation theory can be applied to include frequency shifts due to other kinetic effects. Analytic forms are derived which display the competition between the resistive and radiative damping, where the radiation is carried by kinetic Alfvén waves. When the nonideal parameter is small, the KTAE modes appear in pairs. When this parameter is large, previously found scaling for the single gap case is reproduced analytically.