Methods for the detection of Zonal Flows using one-point and two-point turbulence measurements

The sensitivity of two numerical methods for the detection of zonal flows, especially geodesic acoustic modes (GAMs), through the movement of turbulence eddies is studied. One of them is the widely used time delay estimation method which determines a propagation time delay between two measurement points. The second technique is based on analyzing movements of the minimum in the autocorrelation function of a single measurement signal (ACFM method). The applicability of both methods is analyzed in detail in terms of time resolution, signal-to-noise ratio (SNR) and velocity modulation amplitude. It is found that both methods exhibit a broadband noise spectrum in the calculated velocity from inherent statistical reasons and they also underestimate the RMS velocity modulation amplitude by at least a factor of two, even under noise-free conditions. Their sensitivity to GAMs ceases below an SNR of about 2. These methods are applied to measurement signals obtained in Ohmic plasmas using correlation reflectometry, lithium beam emission spectroscopy (Li-BES) and probe diagnostics on the TEXTOR tokamak. The equivalence of the two methods is shown under these conditions experimentally. The availability of both methods considerably widens the possibility to detect zonal flows therefore the phase relationship between velocity modulations, related to GAMs, can be determined at both poloidally and toroidally well separated locations. A toroidally and poloidally symmetric m=0, n=0 velocity modulation and a coherent π/2 out of phase electron density modulation is found with odd poloidal mode number, as predicted by theory.