Optimal Design of Highly Uniform Magnetic Field Coils Under High-Permeability Magnetic Shields in Miniaturized NMR Sensors

Magnetic coils in the magnetic shield are combined to generate a precise and uniform magnetic field for nuclear magnetic resonance (NMR) sensors and shield against the disturbance of the external magnetic field. However, the effect of magnetic shields made of high-permeability materials on coil constants and magnetic field uniformity has become a significant issue for miniaturized NMR sensors. We proposed a novel optimal design method for the magnetic field coils based on the modified Green function of the ferromagnetic boundary and introduced an improved genetic algorithm (IGA) to improve the optimal efficiency. First, the coupling effect of the radius and height of the coil and the magnetic shield was analyzed. Then, a solenoid coil system in the cylindrical magnetic shield was designed and fabricated. In the experiment, compared with the traditional method, the coupling coefficient of the coil constant of the coil designed by the proposed method was reduced of 10.45%. The maximum magnetic field error in the target region reached a significant reduction by two orders of magnitude in calculations and experiments. Moreover, the optimized coils applied to the NMR sensor enhanced the transverse nuclear spin relaxation time of 129Xe by 44.32%, which has the potential to improve the sensor performance.