Analysis and Design of Biplanar Coils Within Magnetic Shielding Room Considering Actual Ferromagnetic Boundaries
Extremely weak magnetic field conditions are essential for the study of spin-exchange-free relaxing atomic magnetometers, magnetoencephalography, and fundamental physics experiments. A magnetic shielding room (MSR) is usually combined with an active magnetic compensation coil to achieve better shielding performance. However, the coupling between the ferromagnetic material and the coil alters the magnetic field. It affects the residual magnetic compensation.
The mirror method is commonly used to solve the problem of coupling a magnetic shielding room to a coil. Most existing studies consider the magnetic shielding room as an ideal magnetic conductor with infinite permeability and thickness. However, this assumption ignores the fact that the internal magnetic field is affected by permeability and thickness. The method will generate large errors when the shield thickness is small. Even though a few studies have considered the effects of permeability and thickness, the analytical models presented are limited to studying simple axial toroidal coils and do not cover coils of other complex structures.
This paper proposes a magnetic field coupling model with finite permeability and thickness, which considers the effect of permeability and thickness of ferromagnetic materials on the coupling of magnetically compensated coils. The method first considers the effects of all reflection points. The effects of magnetic permeability and thickness of ferromagnetic materials are considered by applying the multiple reflection theory.
In the conventional target field method, magnetic field bias occurs due to the use of discrete conductors to approximate the continuous current density. To reduce this error, a linearly decreasing inertia weight particle swarm optimization algorithm is introduced for parameter optimization. Thus, the determination of the stream function is transformed into a hybrid optimization problem. Uniform field coils and proposed coils are designed based on the proposed method.
The simulation results indicate that the proposed method lowers the maximum field deviations of the Bx, By, and Bz uniform field coils by 30.82%, 37.86%, and 35% in the target region, respectively, compared to the traditional method. For the gradient coils and in the same condition, the gradient deviations of the dBx/dz, dBy/dz, dBz/dz, and dBx/dy coils can also be reduced by 36.8%, 30.35%, 55%, and 74.85%, respectively.
The experimental results also verify the effectiveness and practicality of this design method in compensating for the residual magnetic field of the magnetic shielding room. The method proposed in this study is of great significance for realizing a near-zero magnetic field environment.
The proposed analytical model is verified by comparing it with the experimental results. The design of the biplane compensation coil inside the magnetic shielding room, based on the proposed method, further improves the uniformity and compensates for the residual magnetic field. It provides the weak magnetic field environment required to operate the spin-exchange-free relaxing atomic magnetometers. This study provides theoretical support for calculating coil magnetic fields and designing uniform and gradient coils inside the magnetic shielding room.