Advanced stellarators are typically optimized in two stages. The plasma equilibrium is optimized first, followed by the design of coils/permanent magnets. However, the coils/permanent magnets in the second stage may become too complex to achieve the desired equilibrium. To address this problem, single-stage optimization methods have been proposed. In this paper, we introduce a novel single-stage optimization method for designing permanent magnet (PM) stellarators. This approach combines straightforward PM metrics to penalize the maximum required PM thickness and the mismatch between the fixed-boundary equilibrium and the free-boundary one, along with typical physical targets. We apply this single-stage optimization method to find a new quasi-axisymmetric PM design. The new design starts from MUSE, which was initially designed using a two-stage optimization approach. The resulting design, MUSE++, exhibits an order of magnitude lower quasi-symmetric error and a one-order reduction in normal field error. We show that MUSE++ has approximately 30% fewer magnets compared to a proxy model MUSE-0 that uses the same FAMUS optimization without the benefit of a single-stage equilibrium optimization. These results demonstrate that the new single-stage optimization method can concurrently improve plasma properties and simplify permanent magnet complexity.
Comment: 18 pages, 14 figures