The nonlinear dispersion relation of geodesic acoustic modes

The interaction with the turbulence can raise the group velocity of the GAM from the order of the curvature drift velocity(~0.1 km/s, T ~ 100 eV, B ~ 1 T, R ~ 1 m) in the linear case [5, 6] to the order of the diamagnetic drift velocity(~ 1 km/s), which is the typical scale of turbulent motions. A global nonlinear eigenmode can be wide enough to form frequency plateaus as observed in ASDEX Upgrade [1]. The pulsed GAM activity reported here is not unlikely to play a role in the explanation of the pulsed GAM activity observed recently in ASDEX Upgrade [2]. It can also serve as an approach to the understanding of the quiet periods in NSTX [3] alternative to the direct modulation of the turbulence activity by GAMs. Since the curvature drift was directed towards the X-point in all of the discharges analyzed in [3], it would be interesting to investigate the changes related to an inversion of the curvature drift.