Frequency scaling and localization of geodesic acoustic modes in ASDEX Upgrade

The frequency behaviour and localization of the geodesic acoustic mode (GAM), believed to be a coherent plasma turbulence-generated Er × B zonal flow (ZF) oscillation, is studied in the ASDEX Upgrade tokamak using Doppler reflectometry. In typical elongated (1.4 < κ < 1.75) plasmas with an X-point divertor configuration the GAM is observed only in the edge density gradient region 0.95 < ρpol < 1.0 between the density pedestal top and the flux surface boundary. The GAM frequency (5–25 kHz) is found to scale linearly as ω = G cs/Ro (sound speed over major radius) but with an inverse dependence on the plasma elongation κ and a weak direct dependence on the safety factor q. The lower the GAM frequency the more important it is expected to become in moderating the turbulence via shear decorrelation. A heuristic scaling law for the frequency scale factor involving κ and finite aspect ratio terms has been obtained from dedicated parameter scans. For circular plasmas κ ~ 1 touching the limiter the density pedestal is weakened and the GAM is seen to reach in radially as far as ρpol ~ 0.75, depending on the q profile, with a frequency scale consistent with theoretical predictions. Radially the GAM frequency is not a smooth function but displays a series of plateaus a few centimetres wide coinciding with peaks in the GAM amplitude, suggesting several ZF layers. At the plateau edges the GAM spectral peak splits into two frequency branches.