The geodesic acoustic mode (GAM) has been observed for the first time in EAST H-mode operation using Doppler backscattering (DBS) systems. The poloidal and toroidal symmetries of the radial electric field (Er) fluctuation (m = 0 and n = 0) have also been demonstrated. Using the multichannel DBS system, the GAM frequencies at different radial locations have been investigated, with observations showing that H-mode GAM acts as a radial coherent eigenmode, rather than a continuum of frequencies in L-mode. The intermittency of GAM is observed in both L-mode and H-mode. The interplay between the background density fluctuations and the GAM intensity is revealed. The bicoherence analysis is also used to verify the presence of the nonlinear interaction between the GAM and background turbulence.
The correlation theory of turbulence suppression (Zhang and Mahajan 1993 Phys. Fluids B5 2000) by velocity shear was constructed by invoking the ansatz of potential vorticity conservation (PVC) that holds for relatively simple (slab) models of drift wave turbulence. It is, therefore, surprising that a detailed modern simulation of the H mode pedestal, using the gyrokinetic code GENE (Hatch et al 2018 Plasma Phys. Control. Fusion 60 084003), found ‘striking agreement’ with the predictions of the analytic model. To understand the reasons for this remarkable agreement, an extended theory that contains finite (magnetic) curvature, and which does not conserve potential vorticity, is developed and ‘solved’ by calculating an inhomogeneous Green function reflecting the fact that the new system has a potential vorticity source. It is, then, demonstrated that the effect of the broken PVC is insignificant for the normal operation parameters in tokamaks; the correction due to curvature is at the order of 2 L 0 / R , where L 0 is the scale length of the local gradient and R is the major radius. The excellent agreement between simulation and slab model 1993 theory is therefore not accidental; the latter can be applied with confidence to the tokamak pedestal.
To interpret the common symmetric peaks caused by the large-scale structure in the complex S(f) spectrum from the heterodyne Doppler reflectometry (DR) measurement in EAST, a 2D circular-shape O-mode full wave model based on the finite-difference time-domain method is built. The scattering characteristics and the influences on the DR signal from various scales are investigated. When the structure is located around the cut-off layer, a moving radial or poloidal large scale structure $k_\theta\lesssim k_{\theta,match}$ ($k_{\theta,match}$ is the theoretic wavenumber of Bragg scattering) could both generate an oscillation phase term called “phase modulation”, and symmetrical peaks in the complex S(f) spectrum. It was found that the image rejection ratio $A_{-1}/A_{+1}$ ($A_{\pm1}$ represent the amplitudes of $\pm1$ order modulation peaks) could be a feasible indicator for experiment comparison. In the case when the structure is near the cut-off layer same as experiment arrangement for the edge DR channel, the curve of $A_{-1}/A_{+1}$ versus to $k_\theta$ could be divided into three regions, weak asymmetrical range with $k_\theta/k_0\lesssim0.15$ ($k_0$ is the vacuum wavenumber), harmonics range with $0.15\lesssim k_\theta/k_0\lesssim0.4$, and Bragg scattering range $0.4\lesssim k_{\theta}/k_0\lesssim0.7$. In the case when the structure is located away from the cut-off layer, the final complex S(f) spectrum is the simple superimposing of modulation and Bragg scattering, and the modulation peaks have an amplitude response nearly proportional to the local density fluctuation, called the "propagation-route effect". Under the H-mode experiment arrangement for the core DR, a critical fluctuation amplitude $Amp(n_{e,Mod.@route})/Amp(n_{e,Tur.@MSA})\sim1.3-4.1$ ($Amp(n_{e,Mod.@route})$ refers to the pedestal large scale structure amplitude and $Amp(n_{e,Tur.@MSA})$ refers to turbulence amplitude at the main scattering area) is needed for the structure in the pedestal to be observed by the core DR measurement. The simulations are well consistent with the experimental results. These effects need to be carefully considered during the DR signal analyses as the injecting beam passing through the plasma region with large scale structures.
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