Measurements of the Spatial Structure of Geodesic Acoustic Modes in DIII-D

Geodesic acoustic modes (GAMs) are linearly stable, turbulence driven modes exhibiting oscillating axisymmetric ($m=0$, $n=0$) $E\times B$ flows. They potentially play an important role in establishing the saturated level of turbulence in fusion plasmas. Two Doppler backscattering (DBS) systems at locations separated toroidally by 180$^{\circ}$ are aligned to make simultaneous measurements at the same radial location ($\rho\approx 0.8$) and wavenumber ($k_\perp\sim 4\,$cm$^{-1}$, $k_\perp\rho_s\sim 1$) in a beam-heated L-mode DIII-D plasma. Flow oscillations, which agree with the predicted GAM frequency scaling, correlate toroidally between the two DBS systems with an ensemble averaged cross-coherency of $\gamma\approx 0.6$ over 600 ms. The cross-phase between pairs of the DBS signals is consistent with the expected GAM structure. The radial variation in cross-phase agrees with descriptions of the GAM eigenmode as having an Airy function character with outward radial propagation; the measured radial wavelength is $\lambda_r\approx 2.8\,$cm and the calculated GAM characteristic length scale is $L_{GAM}=\rho_i^{2/3}L_T^{1/3}\approx 1.2\,$cm.