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 ι > 0.4) in which symmetry-breaking mode amplitudes throughout a finite volume are < 2 × 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. †

Magnetic well and Mercier stability of stellarators near the magnetic axis

“…Colour indicates the magnetic field strength, and black curves indicate field lines.

Figure 2.Verification of the magnetic well calculation. The five colours indicate the five quasisymmetric configurations detailed in § 5 of Landreman & Sengupta (2019), also shown in figure 1. Triangles show evaluated from (3.7).

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“…The result is a set of equations at each order in . These equations are displayed in Garren & Boozer (1991 a ) and appendix A of Landreman & Sengupta (2019).…”

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Figure 1.The five magnetic configurations considered in this paper. Section numbers refer to Landreman & Sengupta (2019), where the axis shape and other parameters of each configuration are detailed. Colour indicates the magnetic field strength, and black curves indicate field lines.

Figure 2.Verification of the magnetic well calculation.

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“…Such an expansion is accurate in the core of any stellarator, even those for which the aspect ratio of the boundary is low (Landreman 2019). We have argued recently (Landreman & Sengupta 2019; Landreman, Sengupta & Plunk 2019; Jorge, Sengupta & Landreman 2020 a ) that this asymptotic approach deserves further attention, as it complements numerical optimization. The asymptotic approach allows equilibria to be evaluated orders of magnitude faster, and it provides a practical way to generate new initial conditions for numerical optimization (Landreman & Sengupta 2019; Landreman et al.…”

“…The direct and indirect expansions each have advantages and disadvantages. Here we focus on Garren & Boozer's expansion because interchange stability has not previously been analysed in this approach, and because it is convenient for obtaining configurations with omnigenity and high-order quasisymmetry (Landreman & Sengupta 2019; Plunk et al. 2019).…”