Electromagnetic effects on geodesic acoustic and beta-induced Alfvén eigenmodes

The local kinetic theory of geodesic acoustic modes and beta-induced Alfvén eigenmodes is developed. The local dispersion relations are derived in two opposite limits: and , where k 0 = (m − nq)/qR, m and n are poloidal and toroidal mode numbers, and is the electron thermal velocity. It is shown that the nature of the (m ± 1, n) sideband oscillations depends on the radial modes width. The localized modes are mostly electrostatic, while the meso-scale modes of the radial width larger than c/(ωpi q) have a strong electromagnetic component. It is shown that the dispersion relations are remarkably similar provided the radial mode width of the principal (m, n) harmonic is sufficiently small.