Zonal flows (ZFs) and associated geodesic oscillations are turbulence-generated time-varying E r × B T rigid poloidal plasma flows with finite radial extent. They are of major interest for tokamak confinement since they are thought to moderate drift-wave turbulence and hence edge transport. However, detection of ZFs (believed to be driven by Reynolds stress) and Geodesic acoustic modes (GAMs) (linked with poloidal pressure asymmetries) is challenging since they appear predominantly as low frequency (few kilohertz) potential or radial electric field E r fluctuations. Presented here are measurements of GAM/ZF properties in ohmic, L-mode and H-mode ASDEX Upgrade tokamak discharges using a new Doppler reflectometry technique to measure E r fluctuations directly.

A transcollisional, electromagnetic fluid model, incorporating the parallel heat flux as a dependent variable, is constructed to treat electron drift turbulence in the regime of tokamak edge plasmas at the L-H transition. The resulting turbulence is very sensitive to the plasma beta throughout this regime, with the scaling with rising beta produced by the effect of magnetic induction to slow the Alfvénic parallel electron dynamics and thereby leave the turbulence in a more robust, non-adiabatic state. Magnetic flutter and curvature have a minor qualitative effect on the turbulence mode structure and on the beta scaling, even when their quantitative effect is strong. Transport by magnetic flutter is small compared to that by the E × B flow eddies. Fluctuation statistics show that while the turbulence shows no coherent structure, it is coupled strongly enough so that neither density nor temperature fluctuations behave as passive scalars. Both profile gradients drive the turbulence, with the total thermal energy transport varying only weakly with the gradient ratio, d log T /d log n. Scaling with magnetic shear is pronounced, with stronger shear leading to lower drive levels. Scaling with either collision frequency or magnetic curvature is weak, consistent with their weak qualitative effect. The result is that electron drift turbulence at L-H transition edge parameters is drift Alfvén turbulence, with both ballooning and resistivity in a clear secondary role. The contents of the drift Alfvén model will form a significant part of any useful first-principles computation of tokamak edge turbulence.

Doppler reflectometry is characterized by a finite tilt angle of the probing microwave beam with respect to the normal onto the cutoff surface. According to the Bragg condition the diagnostic selects density perturbations with wave number K ⊥ in the reflecting layer. From the Doppler shift of the returning microwave the propagation velocity of these perturbations v ⊥ can be obtained directly. The signal intensity contains information about the perturbation amplitude. The diagnostic potential of Doppler reflectometry is demonstrated both numerically by the use of two-dimensional full-wave codes and experimentally by an antenna system with variable tilt angle installed at the W7-AS stellarator. During stationary plasma conditions the measured profile of the propagation velocity v ⊥ (r) is dominated by the E × B velocity of the plasma, which is obtained from passive spectroscopy. Transient states of the plasma can be followed with a temporal resolution of less than 50 µs. Thus, Doppler reflectometry allows us to investigate the interdependence of sheared flow and turbulence on that timescale.

The competition between drift wave and interchange physics in general E-cross-B drift turbulence is studied with computations in three dimensional tokamak flux tube geometry. For a given set of background scales, the parameter space can be covered by the plasma beta and drift wave collisionality. At large enough plasma beta the turbulence breaks out into ideal ballooning modes and saturates only by depleting the free energy in the background pressure gradient. At high collisionality it finds a more gradual transition to resistive ballooning. At moderate beta and collisionality it retains drift wave character, qualitatively identical to simple two dimensional slab models. The underlying cause is the nonlinear vorticity advection through which the self sustained drift wave turbulence supersedes the linear instabilities, scattering them apart before they can grow, imposing its own physical character on the dynamics. This vorticity advection catalyses the gradient drive, while saturation occurs solely through turbulent mixing of pressure disturbances. This situation persists in the whole of tokamak edge parameter space. Both simplified isothermal models and complete warm ion models are treated.