Constructing stellarators with quasisymmetry to high order

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.

References in corpus (2)

• Direct construction of optimized stellarator shapes. III. Omnigenity near the magnetic axis
• Optimized quasisymmetric stellarators are consistent with the Garren-Boozer construction

Cited by in corpus (38)

• Magnetic fields with precise quasisymmetry for plasma confinement
• Mapping the space of quasisymmetric stellarators using optimized near-axis expansion
• Magnetic well and Mercier stability of stellarators near the magnetic axis
• Energetic particle loss mechanisms in reactor-scale equilibria close to quasisymmetry
• Single-Stage Stellarator Optimization: Combining Coils with Fixed Boundary Equilibria
• Measures of quasisymmetry for stellarators
• A single-field-period quasi-isodynamic stellarator
• Construction of Quasisymmetric Stellarators Using a Direct Coordinate Approach
• Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions: I. Generalised force balance
• Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry
• Phases and phase-transitions in quasisymmetric configuration space
• Constructing the space of quasisymmetric stellarators
• MHD stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators
• The Use of Near-Axis Magnetic Fields for Stellarator Turbulence Simulations
• Magnetic Fields with General Omnigenity
• Figures of merit for stellarators near the magnetic axis
• Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions. II. Circular axis stellarators
• Higher order theory of quasi-isodynamicity near the magnetic axis of stellarators
• Gradient-based optimization of 3D MHD equilibria
• Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1: Solutions near an axisymmetric surface
• Stellarator coil optimization supporting multiple magnetic configurations
• Ion-temperature-gradient stability near the magnetic axis of quasisymmetric stellarators
• Normal Forms and Near-Axis Expansions for Beltrami Magnetic Fields
• Collisionless zonal-flow dynamics in quasisymmetric stellarators
• Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation
• The On-Axis Magnetic Well and Mercier's Criterion for Arbitrary Stellarator Geometries
• Exact non-symmetric closed line vacuum magnetic fields in a topological torus
• Using Deep Learning to Design High Aspect Ratio Fusion Devices
• Connection between quasi-symmetric magnetic fields and anisotropic pressure equilibria in fusion plasmas
• Energetic Particle Tracing in Optimized Quasisymmetric Stellarator Equilibria
• The zonal-flow residual does not tend to zero in the limit of small mirror ratio
• The shear Alfvén continuum of quasisymmetric stellarators
• Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines
• Integrability, Normal Forms, and Magnetic Axis Coordinates
• Steady plasma flows in a periodic non-symmetric domain
• Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry
• Near-axis quasi-isodynamic database
• Application of Lagrangian techniques for calculating the on-axis rotational transform