Design and Optimization Method of Hybrid Biplanar Coils for Suppressing Uniform and Gradient Residual Magnetic Field

To achieve a nearly zero-field environment in a magnetically shielded room (MSR), compensation for both uniform and gradient magnetic fields is crucial. However, conventional strategies employing six pairs of coils face challenges of complex construction and coupling effects with ferromagnetic boundaries. To address this issue, a design and optimization method of hybrid bi-planar coils for suppressing uniform and gradient residual magnetic field for the MSR is proposed. By applying the symmetry of uniform and gradient coils, this method can substantially improve the integration of the system. Meanwhile, the coupling effect between the magnetic shielding material and compensation field is effectively reduced by incorporating the influence of ferromagnetic coupling on the coil magnetic fields. Numerical simulations and experimental verifications demonstrate that the designed coils exhibit superior uniformity in both uniform and gradient magnetic fields, which can be applied to achieve a remarkable zero-magnetic environment during measurements. The sensors sensitivity is significantly improved, from 2596.0 fT/Hz<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> to 121.4 fT/Hz<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> at 1 Hz, and reduced magnetic field fluctuations, from 1269.6 pT to 52.8 pT.