Position Tolerance of Permanent Magnets and Reduction of Magnetic Islands in the Stellarator MUSE

We adapt techniques developed for coil optimization to the design of permanent magnet stellarators. Permanent magnets were recently proposed to address the challenge of building optimized stellarators by simplifying complex modular coils. MUSE is a table-top stellarator experiment using permanent magnets and will be built at Princeton Plasma Physics Laboratory. The permanent magnets for MUSE are designed by using the FAMUS code.\footnote{Zhu et al. arXiv:2005.05504 (2020).} We are adapting the shape-gradient method\footnote{Landreman & Paul, \textit{Nuclear Fusion} \textbf{58}(7), 076023 (2018).} and the Hessian matrix method\footnote{Zhu et al. \textit{Plasma Physics and Controlled Fusion}, \textbf{60}(5), 054016 (2018).} to calculate the position tolerance of permanent magnets in MUSE. The target figures of merit that we are going to evaluate are the normal field error on the target plasma boundary, the quasi-symmetry of the produced magnetic field and the magnetic island width. In doing so, we can help construct MUSE to an acceptable precision and reduce the magnetic islands for MUSE.