Stellarators close to quasisymmetry

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.

59 pages, 2 figures. arXiv admin note: text overlap with arXiv:1204.1509

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