Constructing stellarators with quasisymmetry to high order

TL;DR

This paper presents a fast, high-order method for designing quasisymmetric stellarator magnetic fields, enabling accurate configurations with strong shaping and minimal symmetry-breaking, advancing stellarator optimization techniques.

Contribution

It extends the near-axis expansion method to higher order, allowing rapid generation of highly accurate, strongly shaped quasisymmetric stellarator configurations without iterative MHD equilibrium calculations.

Findings

Achieved high-accuracy quasisymmetry with strong shaping.

Demonstrated ideal scaling of symmetry-breaking with inverse cube of aspect ratio.

Reported the smallest symmetry-breaking amplitudes ever observed in a nonaxisymmetric configuration.

Abstract

A method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a three-dimensional magnetohydrodynamic equilibrium code inside an optimization iteration. The method is based on direct solution of the equations of magnetohydrodynamic equilibrium and quasisymmetry using Garren and Boozer's expansion about the magnetic axis (Phys Fluids B 3, 2805 (1991)), and it is several orders of magnitude faster than the conventional optimization approach. The work here extends the method of Landreman, Sengupta and Plunk (J Plasma Phys 85, 905850103 (2019)), which was limited to flux surfaces with elliptical cross-section, to higher order in the aspect ratio expansion. As a result, configurations can be generated with strong shaping that achieve quasisymmetry to high accuracy. Using this construction, we give the first numerical demonstrations of Garren and Boozer's ideal scaling of quasisymmetry-breaking with the cube of inverse aspect ratio. We also demonstrate a strongly nonaxisymmetric configuration (vacuum $\iota > 0.4$) in which symmetry-breaking mode amplitudes throughout a finite volume are $< 2\times 10^{-7}$, the smallest ever reported. To generate boundary shapes of finite-minor-radius configurations, a careful analysis is given of the effect of substituting a finite minor radius into the near-axis expansion. The approach here can provide analytic insight into the space of possible quasisymmetric stellarator configurations, and it can be used to generate good initial conditions for conventional stellarator optimization.