A scalable design framework for single-sided permanent magnet arrays (PMAs)

Designing single-sided permanent magnet arrays (PMAs) requires exploring a high-degree-of-freedom configuration space, whereas conventional Halbach and C/H-shaped geometries fix structural patterns. To address this limitation, we introduce a scalable design framework that decomposes the discretized design space into symmetry-defined modules, enabling their independent optimization through magnetic-field superposition. This modular strategy enables efficient exploration of large design spaces while maintaining computational tractability. A prototype PMA containing 400 N52 magnets was designed and fabricated to demonstrate the framework. It generates a 49mT magnetic field at a depth of 65 mm with uniform distribution over an 80mm×20 mm field of view (FoV), within which a monotonic built-in gradient is present for slice selection. The measured field maps showed similar spatial patterns to simulation, together with a consistent global magnitude offset that was supported by independently measured deviations in the batch-mean equivalent remanence of the magnets. Compared with genetic-algorithm-based approaches, the proposed method achieves higher field strength under the same magnet count and maintains stable field direction. The framework provides a compact and efficient pathway for designing single-sided PMAs and enables scalable exploration of high-dimensional configurations for portable MRI and other open-geometry imaging systems.