The turbulent flux of momentum - or Reynolds stress - is a mechanism responsible for the generation of sheared flow by turbulence. The structure of the flux-surface-averaged stress 〈ṽ rṽ ⊥〉 is investigated in the edge region of an L-mode tokamak plasma. The stress induced by the perpendicular tilting of ballooning modes is considered. In addition to the tilting by the E × B flow shear, which is a negative viscosity effect, a magnetic-shear-induced Reynolds stress - called ŝ-residual stress - arises as a consequence of a residual spatial tilting of ballooning modes by the magnetic shear in a poloidally up-down asymmetric magnetic geometry. A model is derived in the weak flow shear regime under the approximation of circular flux surfaces. The amplitude of this residual stress is of the order of the square of the radial velocity fluctuations in the scrape-off layer (SOL), and in the immediate radial vicinity of the separatrix if an X-point exists. Its amplitude drops rapidly to zero towards the plasma core, thus appearing as a source of transverse rotation at the interface. Its non-linear dependence on the electric shear is discussed in the context of the weak electric shear effect on the poloidal shape of the ballooning envelope. The local ŝ-residual stress is non-uniform poloidally and changes sign according to the up/down position of SOL end-plates with respect to the ∇B × B direction. The electric- and magnetic-shear-induced stresses are then included in a flux-surface-averaged 1D model of mean flow conservation at the plasma edge, including the SOL volume. In L-mode weak shear regimes, it is shown that changing the plasma geometry from ∇B × B away from the divertor to ∇B × B towards the divertor approximately doubles the electric shear strength inside the separatrix, as reported in experiments. This shearinduced stress also enters the toroidal momentum balance, where it appears as a significant source of momentum in the immediate vicinity of the separatrix. Balanced by the toroidal viscosity only, it can sustain toroidal flow gradients of the order of a km s -1 cm -1 at the separatrix, with a sign also dependent on the plasma geometry. These momentum sources arising from symmetry breaking at the boundary of the confined region may explain why low to high mode power thresholds are lower in favourable than unfavourable configurations, and may be important for the issue of optimal plasma shapes with respect to edge intrinsic shear. © 2012 IAEA, Vienna.

The dynamical interaction between eddies and shear flow is investigated through a simplified model of vorticity conservation with tilted eddies. Energy is transferred either to the flow or to eddies, depending on the eddy tilt with respect to the flow shear. When eddies are tilted in the shear direction, the system is favorable to shear increase: tilt instability (TI) or the negative viscosity phenomenon. When eddies are tilted in the opposite direction, the shear flow is damped via a Kelvin-Helmholtz (KH) process. The TI generally dominates the interaction on the largest radial scale, but a fraction of the energy cascades to smaller radial scales through the alternation of tilting and KH dynamics. Within this eddy description, we show that the symmetry breaking required to generate a net residual stress is set by the intrinsic eddy tilt. We recall that magnetic shear can provide an intrinsic tilt to ballooning modes at the edge of tokamak plasmas, with an orientation which depends on flux surface geometry. In L-mode weak shear regimes, this residual stress can dominate the Reynolds stress. Coupled to momentum sources acting in the scrape-off layer, it can induce a significant difference of the edge radial electric field between lower single null and upper single null geometries. A comparison with experimental profiles measured across the edge of Tore Supra L-mode plasmas is discussed. © 2013 IOP Publishing Ltd.

The kinetic energy transfer between shear flows and the ambient turbulence is investigated in the Experimental Advanced Superconducting Tokamak during the L-H transition. As the rate of energy transfer from the turbulence into the shear flow becomes comparable to the energy input rate into the turbulence, the transition into the H-mode occurs. As the observed behavior exhibits several predicted features of zonal flows, the results show the key role that zonal flows play in mediating the transition into H-mode. © 2012 American Institute of Physics.

Velocity fields and density fluctuations of edge turbulence are studied in I-mode [F. Ryter, Plasma Phys. Controlled Fusion 40, 725 (1998)] plasmas of the Alcator C-Mod [I. H. Hutchinson, Phys. Plasmas 1, 1511 (1994)] tokamak, which are characterized by a strong thermal transport barrier in the edge while providing little or no barrier to the transport of both bulk and impurity particles. Although previous work showed no clear geodesic-acoustic modes (GAM) on C-Mod, using a newly implemented, gas-puff-imaging based time-delay-estimate velocity inference algorithm, GAM are now shown to be ubiquitous in all I-mode discharges examined to date, with the time histories of the GAM and the I-mode specific [D. Whyte, Nucl. Fusion 50, 105005 (2010)] Weakly Coherent Mode (WCM, f = 100-300 kHz, Δ f / f ≈ 0.5, and kθ ≈ 1.3 cm -1) closely following each other through the entire duration of the regime. Thus, the I-mode presents an example of a plasma state in which zero frequency zonal flows and GAM continuously coexist. Using two-field (density-velocity and radial-poloidal velocity) bispectral methods, the GAM are shown to be coupled to the WCM and to be responsible for its broad frequency structure. The effective nonlinear growth rate of the GAM is estimated, and its comparison to the collisional damping rate seems to suggest a new view on I-mode threshold physics. © 2013 AIP Publishing LLC.

Experiments on HL-2A, DIII-D and EAST show that turbulence just inside the last closed flux surface acts to reinforce existing sheared E × B flows in this region. This flow drive gets stronger as heating power is increased in L-mode, and leads to the development of a strong oscillating shear flow which can transition into the H-mode regime when the rate of energy transfer from the turbulence to the shear flow exceeds a threshold. These effects become compressed in time during an L-H transition, but the key role of turbulent flow drive during the transition is still observed. The results compare favourably with a reduced predator-prey type model. © 2013 IAEA, Vienna.

The turbulence and flows at the plasma edge during the L-I-H, L-I-L and single-step L-H transitions have been measured directly using two reciprocating Langmuir probe systems at the outer midplane with several newly designed probe arrays in the EAST superconducting tokamak. The E× B velocity, turbulence level and turbulent Reynolds stress at ∼1cm inside the separatrix ramp-up in the last ∼20ms preceding the single-step L-H transition, but remain nearly constant near the separatrix, indicating an increase in the radial gradients at the plasma edge. The kinetic energy transfer rate from the edge turbulence to the E×B flows is significantly enhanced only in the last ∼10ms and peaks just prior to the L-H transition. The E×B velocity measured inside the separatrix, which is typically in the electron diamagnetic drift direction in the L-mode, decays towards the ion diamagnetic drift direction in response to fluctuation suppression at the onset of the single-step L-H, L-I-L as well as L-I-H transitions. One important distinction between the L-I-H and the L-I-L transitions has been observed, with respect to the evolution of the edge pressure gradient and mean E×B flow during the I-phase. Both of them ramp up gradually during the L-I-H transition, but change little during the L-I-L transition, which may indicate that a gradual buildup of the edge pedestal and mean E×B flow during the I-phase leads to the final transition into the H-mode. In addition, the transition data in EAST strongly suggest that the divertor pumping capability is an important ingredient in determining the transition behaviour and power threshold.

The absolute rate of nonlinear energy transfer among broadband turbulence, low-frequency zonal flows (ZFs) and geodesic acoustic modes (GAMs) was measured for the first time in fusion-grade plasmas using two independent methods across a range of heating powers. The results show that turbulent kinetic energy from intermediate frequencies (20-80 kHz) was transferred into ZFs and GAMs, as well as into fluctuations at higher frequencies (>80  kHz). As the heating power was increased, the energy transfer from turbulence into GAMs and the GAM amplitudes increased, peaked and then decreased, while the energy transfer into the ZFs and the ZFs themselves increased monotonically with heating power. Thus there exists a competition between ZFs and GAMs for the transfer of turbulent energy, and the transfer into ZFs becomes dominant as the heating power is increased. The poloidal-radial Reynolds stress and the mean radial electric field profiles were also measured at different heating powers and found to be consistent with the energy transfer measurement. The results suggest that ZFs play an important role in the low-to-high (L-H) plasma confinement transition.

The intermediate oscillatory phase during the L-H transition, termed the I-phase, is studied in the EAST superconducting tokamak using a newly developed dual gas puff imaging (GPI) system near the L-H transition power threshold. The experimental observations suggest that the oscillatory behaviour appearing at the L-H transition could be induced by the synergistic effect of the two components of the sheared m, n = 0 E × B flow, i.e. the turbulence-driven zonal flow (ZF) and the equilibrium flow. The latter arises from the equilibrium, and is, to leading order, balanced by the ion diamagnetic term in the radial force balance equation. A slow increase in the poloidal flow and its shear at the plasma edge are observed tens of milliseconds prior to the I-phase. During the I-phase, the turbulence recovery appears to originate from the vicinity of the separatrix with clear wave fronts propagating both outwards into the far scrape-off layer (SOL) and inwards into the core plasma. The turbulence Reynolds stress is directly measured using the GPI system during the I-phase, providing direct evidence of kinetic energy transfer from turbulence to ZFs at the plasma edge. The GPI observations strongly suggest that the SOL transport physics and the evolution of pressure gradient near the separatrix play an important role in the L-I-H transition dynamics. To highlight these new physics, the previous predator-prey model is extended to include a new equation for the SOL physics. The model successfully reproduces the L-I-H transition process with several features comparing favourably with GPI observations. © 2014 IAEA, Vienna.