Constructing stellarators with quasisymmetry to high order

Journal Article · 14 November 2019 · Journal of Plasma Physics

DOI: https://doi.org/10.1017/S0022377819000783 · OSTI ID:1597688

Landreman, Matt  ^[1]; Sengupta, Wrick  ^[2]

---

1. Univ. of Maryland, College Park, MD (United States). Inst. for Research in Electronics and Applied Physics; University of Maryland
2. New York Univ. (NYU), NY (United States). Courant Inst. of Mathematical Sciences

Here, 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 & Boozer’s expansion about the magnetic axis (Phys Fluids B, vol. 3, 1991, p. 2805), and it is several orders of magnitude faster than the conventional optimization approach. The work here extends the method of Landremanet al. (J. Plasma Phys., vol. 85, 2019, 905850103), 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 the inverse aspect ratio. We also demonstrate a strongly non-axisymmetric configuration (vacuum rotational transform $$\unicode[STIX]{x1D704} >0.4$$) 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. In conclusion, 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.

• Research Organization: Univ. of Maryland, College Park, MD (United States)
• Sponsoring Organization: Simons Foundation; USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
• Grant/Contract Number: FG02-86ER53223; FG02-93ER54197
• OSTI ID: 1597688
• Journal Information: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 6 Vol. 85; ISSN 0022-3778
• Publisher: Cambridge University PressCopyright Statement
• Country of Publication: United States
• Language: English