Design of gradient coils based on the target field method in a high-permeability shield considering sidewall apertures

The combination of high-permeability ferrite and coils is often used to nullify ambient magnetic fields and is widely used in applications such as magnetic resonance imaging and high-sensitivity magnetic sensors. We propose the design method of transverse gradient coils based on the target field method in a high-permeability shield considering sidewall apertures (TFM-HPSCSA), which are installed in the ferrite shield to zero the residual magnetic field gradient. TFM-HPSCSA coils enable an innovative combination of magnetic field gradient linearity and structural luminescence. The coil current density distribution is set to avoid the central sidewall apertures. As a result, the contour distribution of the stream function under the optimized weight coefficients is calculated to obtain the wire alignments of the dB_y/dx, dB_y/dy and dB_y/dz gradient coils. The deviations of the experimentally measured values from the finite element simulations of the three types coils are 0.63%, 1.17% and 0.48%, respectively, which verified the validity and the accuracy of the proposed method. In comparison to the traditional saddle gradient coil designed under the free space condition, the proposed dB_y/dx coil produces a 30.5% improvement in the percentage range of regions with 5% magnetic field gradient nonlinearity. The increased linear range of the gradient magnetic field contributes to the improvement of the residual field nulling range in magnetic sensors and magnetic shielding systems in practical applications.