Abstract. The theory of turbulent transport of toroidal momentum is discussed in the context of the phenomenon of spontaneous/intrinsic rotation. We review the basic phenomenology and survey the fundamental theoretical concepts. We then proceed to an in-depth discussion of the radial flux of toroidal momentum, with special emphasis on the off-diagonal elements, namely the residual stress (the portion independent of V) and the pinch. A simple model is developed which unifies these effects in a single framework and which recovers many of the features of the Rice scaling trends for intrinsic rotation. We also discuss extensions to finite beta and the effect of SOL boundary conditions. Several issues for future consideration are identified.

Results from 3D global gyrokinetic particle simulations of ion temperature gradient driven microturbulence in a toroidal plasma show that the ion thermal transport level in the interior region exhibits significant dependence on the ion-ion collision frequency even in regimes where the instabilities are collisionless. This is identified as arising from the Coulomb collisional damping of turbulence-generated zonal flows.52.25. Fi, 52.35.Ra, 52.65.Tt Understanding the physical mechanism responsible for the turbulent transport observed in magnetized plasmas is crucial for developing techniques to improve confinement. In particular, ion thermal transport in the core region of a tokamak plasma is believed to arise from electrostatic pressure-gradient driven microinstabilities [1]. In most previous studies, ionion collisions have been assumed to have little or no effect on the microinstabilities most likely to be responsible for the ion thermal transport, such as ion-temperature-gradient (ITG) modes. This is because the temperature in present day major tokamak core plasmas is so high that the ion-ion collision frequency is much smaller than the characteristic frequency of the ITG mode (e.g., linear growth rate or nonlinear decorrelation rate, which is of the order of the ion diamagnetic frequency). Consequently, most theory based ion thermal diffusivities do not contain explicit dependence on the ion-ion collisionality [2,3].Current investigations indicate that ion-ion collisions can enhance turbulent transport via Coulomb collisional damping of turbulence-generated ¢ shear flows. These zonal flows [4], which are linearly stable ¼ modes, are nonlinearly driven by the flux-surface-averaged, radially local current modulations and are mainly in the poloidal direction for high aspect ratio devices. The shear decorrelation [5,6] by these small scale flows results in the reduction of turbulence and transport. Since the turbulence is regulated by zonal flows, the turbulent transport can depend on ion-ion collisions which damp poloidal flows through the "neoclassical" effects.In this letter, we report gyrokinetic particle simulation [7] results which show that the ion thermal transport from electrostatic ITG turbulence depends on ion-ion collisions for representative tokamak core plasma parameters using the global gyrokinetic toroidal code (GTC) [8]. The collisionalitydependence of the turbulent transport comes from the neoclassical damping of zonal flows. The fluctuations and transport exhibit bursting behavior with a period corresponding to the collisional damping time of poloidal flows. These results are contrary to the usual assumption that core ion transport is "collisionless". The fact that the change of the ion heat conductivity with collision frequency cannot be attributed to the change in the linear growth rate or mode spectrum places considerable limitations on the applicability of most of the existing transport models that are based on an oversimplified ¾ type mixing length rule.In the experiments, despite the di...

We study the simplest problem of turbulence spreading corresponding to the spatio-temporal propagation of a patch of turbulence from a region where it is locally excited to a region of weaker excitation, or even local damping. A single model equation for the local turbulence intensity Á´Ü ص includes the effects of local linear growth and damping, spatially local nonlinear coupling to dissipation and spatial scattering of turbulence energy induced by nonlinear coupling. In the absence of dissipation, the front propagation into the linearly stable zone occurs with the property of rapid progression at small t, followed by slower subdiffusive progression at late times. The turbulence radial spreading into the linearly stable zone reduces the turbulent intensity in the linearly unstable zone, and introduces an additional dependence on the £ to the turbulent intensity and the transport scaling. These are in broad, semi-quantitative agreements with a number of global gyrokinetic simulation results with zonal flows and without zonal flows. The front propagation stops when the radial flux of fluctuation energy from the linearly unstable region is balanced by local dissipation in the linearly stable region.