Design of uniform field coils coupled with a magnetic shield cylinder

Abstract

Active magnetic field coils and magnetic shields are widely employed to achieve uniform and low magnetic fields, and the coil generating magnetic field would be influenced as a result of the coupling with the shields. It turns out to increase the magnetic field strength and shrink the uniform area, which is detrimental to atomic devices. An analytical solution that takes into account the coupling effect of shields and coils is established by using the magnetic vector potential. Analyses for three different configurations are first performed, including mu-metals, 2K-MnZn ferrites and 10K-MnZn ferrites. Analytical calculations reveal that the optimal radii of the standard Lee-Whiting coils with high uniformity are all around 0.81 of shield radii. Additionally, adopting the Whale Optimization Algorithm (WOA), a modified coil with improved uniformity and comparable size is proposed. Experimental results show that a better uniformity of 2.68e−5 and a 34% longer uniform area is obtained when compared with the standard coil. The accuracy of the internal magnetic field distributions is compared and tested by simulations and experiments. Situations utilizing shields and coils will be facilitated by this effective application of WOA in uniform field coil design.