ABSTRACT
This chapter presents the magnetohydrodynamic approach to studying the Kinetic Toroidicity-Induced Alfven Eigenmodes (KTAE) modes. This approach is based on using the parallel Ohm law allowing for the term with the electron pressure gradient and the expression for the perpendicular current allowing for the ion collisionless viscosity tensor. The chapter provides the starting equations for KTAE modes, outlines the eigenfunctions and dispersion relations for these modes, and considers their energy. It discusses the localization region of the modes into two regions: the inner layer and the outer region. The dimensionless eigenfrequency shift of odd KTAE modes is close to the eigenvalues for the odd states of the harmonic oscillator.
