Figures of merit for stellarators near the magnetic axis

Abstract

A new paradigm for rapid stellarator configuration design has been recently demonstrated, in which the shapes of quasisymmetric or omnigenous flux surfaces are computed directly using an expansion in small distance from the magnetic axis. To further develop this approach, here we derive several other quantities of interest that can be rapidly computed from this near-axis expansion. First, the $\nabla \vec{B}$ and $\nabla \nabla \vec{B}$ tensors are computed, which can be used for direct derivative-based optimization of electromagnetic coil shapes to achieve the desired magnetic configuration. Moreover, if the norm of these tensors is large compared to the field strength for a given magnetic field, the field must have a short length scale, suggesting it may be hard to produce with coils that are suitably far away. Second, we evaluate the minor radius at which the flux surface shapes would become singular, providing a lower bound on the achievable aspect ratio. This bound is also shown to be related to an equilibrium beta limit. Finally, for configurations that are constructed to achieve a desired magnetic field strength to first order in the expansion, we compute the error field that arises due to second order terms.

References in corpus (4)

• An improved current potential method for fast computation of stellarator coil shapes
• Near-Axis Expansion of Stellarator Equilibrium at Arbitrary Order in the Distance to the Axis
• The Use of Near-Axis Magnetic Fields for Stellarator Turbulence Simulations
• Optimized quasisymmetric stellarators are consistent with the Garren-Boozer construction

Cited by in corpus (7)

• Mapping the space of quasisymmetric stellarators using optimized near-axis expansion
• A single-field-period quasi-isodynamic stellarator
• Constructing the space of quasisymmetric stellarators
• MHD stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators
• Gradient-based optimization of 3D MHD equilibria
• Using Deep Learning to Design High Aspect Ratio Fusion Devices
• Near-axis quasi-isodynamic database