MHD stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators

TL;DR

This paper investigates how the cross-sectional shape of magnetic confinement devices influences their MHD stability, revealing that positive triangularity benefits tokamaks but not necessarily quasisymmetric stellarators, with finite beta also playing a stabilizing role.

Contribution

It provides a near-axis theoretical analysis of the impact of shaping on MHD stability in both tokamaks and quasisymmetric stellarators, highlighting differences due to toroidal asymmetry.

Findings

Positive triangularity stabilizes vertically elongated tokamaks.

In quasisymmetric stellarators, shape does not always correlate with stability.

Finite beta can enhance stability even without magnetic shear.

Abstract

How much does the cross-section of a toroidal magnetic field configuration tell us about its MHD stability? It is generally believed that positive triangularity (typically leading to bean-shaped cross-sections with their indentation on the inboard side in stellarators) contributes positively to MHD stability. In this paper, we explore the basis of this statement within a near-axis description for axisymmetric and quasisymmetric magnetic configurations. In agreement with the existing literature, we show that positive triangularity stabilises vertically elongated tokamaks. In quasisymmetric stellarators, the toroidal asymmetry of flux surfaces modifies this relation. The behaviour of stellarator-symmetric, quasisymmetric stellarators can still be described in terms of the shape of one of their up-down symmetric cross-sections. However, we show that for a sample of quasisymmetric configurations, the positive-bean-shaped cross-sections do not contribute positively to stability. Unlike in the axisymmetric case, we also learn that finite $\beta$ can improve stability even without magnetic shear.