Role of the geodesic acoustic mode shearing feedback loop in transport bifurcations and turbulence spreading

A theory of the effect of the geodesic acoustic mode !GAM" on turbulence is presented. Two synergistic issues are elucidated: namely, the physics of the zonal flow modulation and its role in the L-H transition, and the role of the GAM wave group propagation in turbulence spreading. Using a wavekinetic modulational analysis, the response of the turbulence intensity field to the GAM is calculated. This analysis differs from previous studies of zero-frequency zonal flows since it accounts for resonance between the drift wave group speed and the GAM strain field, which induces secularity. This mechanism is referred to as secular stochastic shearing. Finite real frequency and radial group velocity are intrinsic to the GAM, so its propagation can induce nonlocal phenomena at the edge and pedestal regions. To understand the effect of the GAM on turbulence and transition dynamics, a predator-prey model incorporating the dynamics of both turbulence and the GAMs is constructed and analyzed for stability around fixed points. Three possible states are identified, namely, an L-modelike stationary state, a reduced turbulence state, and a GAM limit-cycle state. The system is attracted to the state with the minimum turbulence level. © 2010 American Institute of Physics. #doi:10.1063/1.3353037$