Stable Design of High-Uniformity Magnetic Compensation Coils for SERF Atomic Magnetometers

High-uniformity magnetic compensation coils are essential for establishing a near-zero and spatially stable magnetic-field environment in spin-exchange relaxation-free (SERF) atomic magnetometers. However, conventional Taylor-expansion-based coil objectives mainly suppress local high-order field terms near the centre and do not directly constrain the usable uniform-field length, regional field error or configuration repeatability. This paper presents a stable design method for circular magnetic compensation coils by combining a two-stage gated objective function with a gated multi-archive reliability-guided success-history adaptive differential evolution algorithm. The gated objective first enforces the basic central-field uniformity through a Taylor residual criterion and then optimizes the axial uniform-field length, root-mean-square relative error and geometric regularity. The optimization algorithm adaptively coordinates exploration and refinement using population-state gating, archive-assisted search and reliability-guided strategy selection. Finite-element simulations and prototype magnetic-field measurements are used to evaluate the designed coil. The results show that the proposed design achieves an effective uniform region of ±0.8R under a relative-uniformity threshold of 0.01, with a root-mean-square relative error on the order of 10−3. Repeated optimization tests further show that the gated objective reduces the axial uniform-region fluctuation by approximately one order of magnitude and the configuration dispersion by more than two orders of magnitude. The method provides a reproducible optimization route for compact high-uniformity compensation coils in weak magnetic-field measurement systems.