Linear and Nonlinear Properties of Geodesic Acoustic Mode and Beta-induced Alfvén Eigenmode

Global gyrokinetic toroidal code (GTC) is used to study the low-frequency modes in tokamaks including geodesic acoustic mode (GAM) and beta-induced Alfvén eigenmode (BAE). GAM and BAE have the same frequency due to the geodesic curvature and thermal particle compressibility in toroidal plasmas. Important new insights include: the collisionless damping rate of the GAM is greatly enhanced by trapped electrons in the high-q region of tokamak (q is the safety factor) due to the resonance of the GAM oscillation with the trapped electron bounce motion; nonlinear self-interactions of the GAM cannot efficiently generate the second harmonic due to a cancellation between the perpendicular convective nonlinearity and the parallel nonlinearity for the long wavelength GAM; the BAE is excited by antenna and energetic particles, the non-perturbative contributions by energetic particles modify the mode structure and reduce the frequency of the stable eigenmodes relative to the ideal magnetohydrodynamic (MHD) theory.