A Combination Solving Method for Multiple Square Coils to Generate Large Uniform Magnetic Field Region for Atomic Magnetometers

Atomic magnetometers have been widely used for the measurement of ultra-weak magnetic signals, while the high-uniformity magnetic fields are required to maintain the stable working environment. The present study proposes a combination solving method (CSM) for the design of multiple square coils (MSCs) to generate uniform magnetic field in confined spaces. Cooperative particle swarm optimization (PSO) algorithm is applied to design the coils with two pairs through five pairs via solving the optimal coil currents and distances. Each additional pair in the designed-coils expands the uniform regions with relative error less than 1% by approximately 6%. The MSCs with three pairs (Pairs-3) achieves excellent uniformity performance with a simple configuration, making it well suited for atomic magnetometers. The maximum relative error in center region is 0.54%, less than Merritt coil (1.39%), Rubens coil (2.18%), and 3-TE coil (2.63%). In addition, numerical simulation and experimental results confirm the validity of the CSM. The new method is of significant importance for designing high-uniformity coils that meet spatial constraints of atomic magnetometers.