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.
An overview of the physics of intrinsic torque is presented, with special emphasis on the phenomenology of intrinsic toroidal rotation in tokamaks, its theoretical understanding, and the variety of momentum transport bifurcation dynamics. Ohmic reversals and ECH-driven counter torque are discussed in some detail. Symmetry breaking by LSN vs. USN asymmetry is related to the origin of intrinsic torque at the separatrix.
We identify an isotopic dependence of residual zonal flows from an analytic calculation. While the well-known Rosenbluth–Hinton residual zonal flows with radial scale greater than the magnetically trapped ion radial width ρbi have no isotopic dependence (Rosenbluth and Hinton 1998 Phys. Rev. Lett. 80 724), we find that shorter radial scale (shorter than ρbi, but larger than the magnetically trapped electron radial width ρbe) residual zonal flows (Wang and Hahm 2009 Phys. Plasmas 16 062309) exhibit isotopic dependence. These finer scale zonal flows in deuterium (D) plasmas can be stronger than those of hydrogen (H) plasmas, and possibly lead to lower turbulence and transport and better confinement in qualitative agreement with experimental results.
Modulation of turbulent electron temperature fluctuations () and density fluctuations () by an m/n = 1/1 tearing mode island was observed in the core plasma region of the HL-2A tokamak. High spatiotemporal resolution two-dimensional images of show the first evidence that the turbulence modulation occurs only when the island width exceeds a certain threshold value ( cm) and the modulation is localized merely in the inner area of the island due to significant alteration of local profiles and turbulence drives. Evidence also reveals that for large islands turbulence spreading takes place across the island region. The results are generally consistent with theories and simulations.
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