New approaches to stellarator optimization using expansion in aspect ratio

To achieve good orbit confinement, recent stellarators such as HSX and W7-X have been designed using optimization, with numerical calculation of a 3D MHD equilibrium at each objective function evaluation. Here we present new design methods which reduce the computational cost of each objective evaluation by orders of magnitude, while also providing new insights into the space of solutions [1-3]. These benefits are made possible by an expansion in large local aspect ratio [4]. The expansion enables a direct construction of stellarator shapes with quasisymmetry, a symmetry hidden in the field strength that provides good orbit confinement. This construction makes it possible to achieve quasisymmetry to much higher accuracy than reported before. The aspect ratio expansion also permits a precise understanding of how many unique quasisymmetric configurations are possible (close to the magnetic axis). Due to the reduction of the MHD equilibrium equations by the expansion, stellarator configurations can be evaluated far faster than in traditional optimization, enabling wide surveys over parameter space. Many figures of merit can be calculated directly from the near-axis solutions, including Mercier stability [5] and all the geometric quantities in the gyrokinetic equation [6-7]. This new approach to design can be used in concert with traditional stellarator optimization, the former providing initial conditions for the latter. The near-axis approach has also enabled the first simultaneous plasma-and-coil optimizations of quasisymmetric stellarators using analytic derivatives [8-9].

[1] Landreman, Sengupta, & Plunk, JPP (2019)

[2] Plunk, Landreman, & Helander, JPP (2019)

[3] Landreman & Sengupta, JPP (2019)

[4] Garren & Boozer, PFB (1991)

[5] Landreman & Jorge, JPP (2020)

[6] Jorge & Landreman, PPCF (2021a)

[7] Jorge & Landreman, PPCF (2021b)

[8] Giuliani et al, arXiv:2010.02033 (2020)

[9] Wechsung et al, arXiv:2106.12137 (2021)