Density fluctuation of GAM zonal flows on the HL-2A tokamak

Although Zonal Flow (ZF) characteristics have been reviewed theoretically and experimentally due to its suppression effect on turbulent transport, there are some unclear issues necessary to be elucidated. Especially, there is little understanding for the mode structures of zero frequency ZF and the density fluctuation of the Geodesic Acoustic Mode (GAM) ZF, on which the recent experimental study in HL-2A is focused. The poloidal and toroidal mode numbers of the density fluctuation for the GAMZF are identified in HL-2A for the first time. Recently, a novel design combined rake probes with three-step Langmuir probes is used to measure the GAM density fluctuation in HL-2A. Each tip as single probe measures the saturation ion current (I_s). The relative density fluctuation is replaced by the relative I_s fluctuation because the relative temperature fluctuation contributes less than 10% of the I_s fluctuation. The zonal flow on density fluctuation in shot 8847 has the GAM frequency f = 9.8 kHz, full width (∼ 3.9 kHz) at half magnitude (FWHM) and lifetime ∼ 0.3 ms. The relative I_s fluctuation within the FWHM at the GAM frequency is 4.1%, corresponding to the relative density fluctuation, which is much higher than the value predicted by the ZF theory (0.03%). The phase difference of the signals between tips is used to estimate the poloidal or toroidal mode number, respectively. The poloidal mode number at the GAM frequency is m = 1.3 in shot 8847, while the corresponding toroidal mode number is n = 0.04 . Both are in agreement with the theoretical prediction mode numbers (m = 1/n = 0). Statistic analysis results in different discharges also indicate that the poloidal mode numbers approach unit. The radial wave vector at the GAM frequency is estimated as 0.9 cm^-1 in a similar discharge. The squared auto-bicoherence of the ion saturation current fluctuation has a spectral peak at the GAM frequency, indicating that the GAM density fluctuation may be driven by nonlinear three-wave coupling of ambient turbulence. In addition, the poloidal and toroidal mode numbers (m = 0/n = 0) of the GAM potential fluctuation predicted by the ZF theory are simultaneously confirmed as well within experimental error bars (m < 0.3, n < 0.1). (author)