Optimized Cylindrical Uniform Magnetic Field Coils for Accurate Magnetic Compensation in Magnetically Shielded Cylinders

This article presents a modified design method of a cylindrical uniform magnetic field (CUMF) coil inside a closed magnetically shielded cylinder (MSC) with finite permeability and thickness. Combining the traditional target field method (TFM) with the image method (IM), the structure of the CUMF coil can be determined, and the magnetic field distortion resulting from the interaction between the high magnetic permeability material and the coil itself is effectively avoided. To further improve the uniformity of the magnetic field in the target region, a hybrid algorithm combining the grey wolf optimizer and cuckoo search (GWOCS) is firstly introduced to optimize the parameters of the CUMF coil. The simulation results indicate that the absolute maximum uniformity error in the target region can be optimized from 1.2×10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> to 6.49×10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> comparing with the traditional TFM coil. After GWOCS optimization, the absolute maximum uniformity error is further optimized to 5.71×10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup>, and the volume proportion of absolute uniformity error less than 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> is increased to 19.14%. The experimental results of the magnetic field generated by the optimized coil show a good agreement with the simulation ones, indicating the effectiveness of the design method. The design method presented in this article has important significance for accurate magnetic compensation.