Spectral features of the geodesic acoustic mode and its interaction with turbulence in a tokamak plasma

The three-dimensional wavenumber and frequency spectrum for the geodesic acoustic mode (GAM) has been measured in the HuanLiuqi-2A tokamak for the first time. The spectrum provides definite evidence for the GAM, which is characterized by k_θ=k_φ=0 and k_rρ_i≅0.04-0.09 with the full width at half-maximum Δk_rρ_i≅0.03-0.07. The localized GAM packet is observed to propagate outward in the radial direction with nearly the same phase and group velocity. The envelopes of the radial electric field and density fluctuations are observed to be modulated by the GAM. By comparing the experimental result with that of the envelope analysis using model signals, the mechanism of the envelope modulation has been identified. The results strongly suggest that the envelope modulation of the E-tilde_r fluctuations is dominantly caused by the direct regulation of the GAM during the GAM generation in the energy-conserving triad interaction, and the envelope modulation of the density fluctuations is induced by the GAM shearing effect, which transfers the fluctuation energy from low to high frequencies. In addition, the cross- and auto-bicoherences for interactions between the GAM and turbulent fluctuations show a similar peaked feature that may reflect the resonant property in the nonlinear coupling between the GAM and turbulent fluctuations