Stellarator optimization for nested magnetic surfaces at finite β and toroidal current

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Journal Article
Good magnetic surfaces, as opposed to magnetic islands and chaotic field lines, are generally desirable for stellarators. In previous work, Landreman et al. [Phys. of Plasmas 28, 092505 (2021)] showed that equilibria computed by the Stepped-Pressure Equilibrium Code (SPEC) [Hudson et al., Phys. Plasmas 19, 112502 (2012)] could be optimized for good magnetic surfaces in vacuum. In this paper, we build upon their work to show the first finite-β, fixed-, and free-boundary optimization of SPEC equilibria for good magnetic surfaces. The objective function is constructed with the Greene s residue of selected rational surfaces, and the optimization is driven by the SIMSOPT framework [Landreman et al., J. Open Source Software 6, 3525 (2021)]. We show that the size of magnetic islands and the consequent regions occupied by chaotic field lines can be minimized in a classical stellarator geometry (rotating ellipse) by optimizing either the injected toroidal current profile, the shape of a perfectly conducting wall surrounding the plasma (fixed-boundary case), or the vacuum field produced by the coils (free-boundary case). This work shows that SPEC can be used as an equilibrium code both in a two-step or single-step stellarator optimization loop.
Physics of Plasmas