Linear Properties and Nonlinear Frequency Chirping of Energetic Particle Driven Geodesic Acoustic Mode in LHD

Linear Properties and nonlinear frequency chirping of energetic particle driven geodesic acoustic mode (EGAM) is investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic fluid. It is found that the EGAM is a global mode with the spatially uniform oscillation frequency. The poloidal mode numbers of poloidal velocity fluctuation, plasma density fluctuation, and magnetic fluctuation are m = 0, 1 and 2, respectively. It is demonstrated in the simulation result that both frequency chirping up and chirping down take place in the nonlinear evolution of EGAM. It is also found that two hole-clump pairs are formed in the energetic particle distribution function in 2-dimensional velocity space of pitch angle variable and energy. One pair is formed in the phase space region that destabilizes the instability, while the other in the stabilizing region. The transit frequency of the hole (clump) in the destabilizing region chirps up (down), while in the stabilizing region the hole (clump) chirps down (up). The transit frequencies of the holes and clumps are in good agreement with the chirping EGAM frequency indicating that the particles comprising the hole and clump are kept resonant with the EGAM during the nonlinear frequency chirping. Continuous energy transfer takes place from the destabilizing phase space region to the stabilizing region during the spontaneous frequency chirping of the wave.