Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with MA ∝ βN, although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with βN = 2.6, an intrinsic rotation Alfven Mach number of MA ≃ 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input.
Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E ×B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.
Direction reversals of intrinsic toroidal rotation have been observed in Alcator CMod Ohmic L-mode plasmas following modest electron density or toroidal magnetic field ramps. The reversal process occurs in the plasma interior, inside of the q = 3/2 surface. For low density plasmas, the rotation is in the co-current direction, and can reverse to the counter-current direction following an increase in the electron density above a certain threshold. Reversals from the co-to counter-current direction are correlated with a sharp decrease in density fluctuations with k R ≥2 cm −1 and with frequencies above 70 kHz. The density at which the rotation reverses increases linearly with plasma current, and decreases with increasing magnetic field. There is a strong correlation between the reversal density and the density at which the global Ohmic L-mode energy confinement changes from the linear to the saturated regime.
Bulk plasma toroidal rotation is observed to invert spontaneously from counter to cocurrent direction in TCV (Tokamak à Configuration Variable) Ohmically heated discharges, in low confinement mode, without momentum input. The inversion occurs in high current discharges, when the plasma electron density exceeds a well-defined threshold. The transition between the two rotational regimes has been studied by means of density ramps. The results provide evidence of a change of the balance of nondiffusive momentum fluxes in the core of a plasma without an external drive.
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