Optimizing stellarators for large flows

TL;DR

This paper investigates how deviations from quasisymmetry in stellarators affect plasma flow damping, providing rigorous bounds on the impact of large-gradient perturbations and refining previous heuristic estimates.

Contribution

It rigorously analyzes the effects of large-gradient perturbations on stellarator symmetry, improving understanding of flow damping and correcting earlier heuristic predictions.

Findings

Large-gradient perturbations cause at most linear deviations from quasisymmetry at low collisionality.

Quadratic scaling of radial electric current with perturbation size is valid only for small gradients.

Heuristic estimates of deviation magnitude were previously overestimated, now corrected to linear order.

Abstract

Plasma flow is damped in stellarators because they are not intrinsically ambipolar, unlike tokamaks, in which the flux-surface averaged radial electric current vanishes for any value of the radial electric field. Only quasisymmetric stellarators are intrinsically ambipolar, but exact quasisymmetry is impossible to achieve in non-axisymmetric toroidal configurations. By calculating the violation of intrinsic ambipolarity due to deviations from quasisymmetry, one can derive criteria to assess when a stellarator can be considered quasisymmetric in practice, i.e. when the flow damping is weak enough. Let us denote by $\alpha$ a small parameter that controls the size of a perturbation to an exactly quasisymmetric magnetic field. Recently, it has been shown that if the gradient of the perturbation is sufficiently small, the flux-surface averaged radial electric current scales as $\alpha^2$ for any value of the collisionality. It was also argued that when the gradient of the perturbation is large, the quadratic scaling is replaced by a more unfavorable one. In this paper, perturbations with large gradients are rigorously treated. In particular, it is proven that for low collisionality a perturbation with large gradient yields, at best, an $O(|\alpha|)$ deviation from quasisymmetry. Heuristic estimations in the literature incorrectly predicted an $O(|\alpha|^{3/2})$ deviation.