Analysis and Design of Biplanar Coils Within Magnetic Shielding Room Considering Actual Ferromagnetic Boundaries

The target field is often distorted by coupling effects of the active magnetic compensation coil and magnetic shielding material in the magnetic shielding room (MSR). The permeability and thickness of the magnetic shielding layer are assumed infinite in existing image methods (IMs), which will generate large errors considering actual ferromagnetic boundaries. A novel method for designing high-uniformity biplane coil within MSR is presented. First, the effects of all image points are considered. A variable permeability and thickness IM (PT-IM) is proposed and an analytical model of the coil inside the ferromagnetic boundary is established. Second, a linear decreasing weight particle swarm optimization (LDW-PSO) algorithm is applied to optimize the coil parameters. The simulation results indicate that the proposed PT-IM and target field method (TFM) (PT-IM&TFM) lowers the maximum field deviations of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{\text {x}}$ </tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{\text {y}}$ </tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{\text {z}}$ </tex-math></inline-formula> uniform field coils by 30.82%, 37.86%, and 35% in the target region, respectively, compared to IM&TFM. The experimental results indicate that the actual maximum magnetic field deviation decreases by 40.01% and 32.48% for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{\text {x}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit {dB}_{\text {x}}/\textit {dz}$ </tex-math></inline-formula> coils, respectively. The results verify the effectiveness and practicality of this method in compensating for the residual magnetic field of MSR.