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Abstract:

Rotation is favorable for confinement, but a stellarator can rotate at high speeds if and only if it is sufficiently close to quasisymmetry. This article investigates how close it needs to be. For a magnetic field $\mathbf{B} = \mathbf{B}_0 + \alpha \mathbf{B}_1$, where $\mathbf{B}_0$ is quasisymmetric, $\alpha\mathbf{B}_1$ is a deviation from quasisymmetry, and $\alpha\ll 1$, the stellarator can rotate at high velocities if $\alpha < \epsilon^{1/2}$, with $\epsilon$ the ion Larmor radius over the characteristic variation length of $\mathbf{B}_0$. The cases in which this result may break down are discussed. If the stellarator is sufficiently quasisymmetric in the above sense, the rotation profile, and equivalently, the long-wavelength radial electric field, are not set neoclassically; instead, they can be affected by turbulent transport. Their computation requires the $O(\epsilon^2)$ pieces of both the turbulent and the long-wavelength components of the distribution function. This article contains the first step towards a formulation to calculate the rotation profile by providing the equations determining the long-wavelength components of the $O(\epsilon^2)$ pieces.

Abstract:

The effect of small deviations from a Maxwellian equilibrium on turbulent momentum transport in tokamak plasmas is considered. These non-Maxwellian features, arising from diamagnetic effects, introduce a strong dependence of the radial flux of co-current toroidal angular momentum on collisionality: As the plasma goes from nearly collisionless to weakly collisional, the flux reverses direction from radially inward to outward. This indicates a collisionality-dependent transition from peaked to hollow rotation profiles, consistent with experimental observations of intrinsic rotation.

Abstract:

We consider the effects of a finite radial electric field on ion orbits in a subsonic pedestal. Using a procedure that makes a clear distinction between a transit average and a flux surface average we are able to solve the kinetic equation to retain the modifications due to finite E→ × B→ drift orbit departures from flux surfaces. Our approach properly determines the velocity space localized, as well as the nonlocal, portion of the ion distribution function in the banana and plateau regimes in the small aspect ratio limit. The rapid variation of the poloidal ion flow coefficient and the electrostatic potential in the total energy modify previous banana regime evaluations of the ion flow, the bootstrap current, and the radial ion heat flux in a subsonic pedestal. In the plateau regime, the rapid variation of the poloidal flow coefficient alters earlier results for the ion flow and bootstrap current, while leaving the ion heat flux unchanged since the rapid poloidal variation of the total energy was properly retained. © 2013 IOP Publishing Ltd.

Abstract:

The ion toroidal rotation in a tokamak consists of an $E\times B$ flow due to the radial electric field and a diamagnetic flow due to the radial pressure gradient. The turbulent pinch of toroidal angular momentum due to the Coriolis force studied in previous work is only applicable to the $E\times B$ flow. In this Letter, the momentum pinch for the rotation generated by the radial pressure gradient is calculated and is compared with the Coriolis pinch. This distinction is important for subsonic flows or the flow in the pedestal where the two types of flows are similar in size and opposite in direction. In the edge, the different pinches due to the opposite rotations can result in intrinsic momentum transport that gives significant rotation peaking.