ABSTRACT
This chapter presents a simplified theory of ideal Alfven eigenmodes due to metric oscillations with a high mode number, n ≫ 1. It discusses starting equations for describing toroidicity-induced Alfven eigenmodes (TAE) and ellipticity-induced Alfven eigenmodes (EAE) modes. The chapter aims to calculate the eigenfunctions and eigenvalues of the TAE modes. It considers the energy of TAE modes, which is necessary for the subsequent analysis of the problem of interaction of these modes with the high-energy particles. Main attention in the literature has been devoted to the TAE modes. This is explained by the fact that they have eigenfrequencies smaller than those of EAE and NAE modes and thereby can more easily be driven by high-energy particles. Initially the TAE modes with n ≫ 1 were pointed out by Cheng et al using the ballooning representation.
