Flexible Control of Magnetic Fields by Shaped-Optimized Three-Dimensional Coil Arrays

The synthesis of desired low-frequency magnetic fields is of high importance in electromagnetic design. The use of coil arrays (CAs) is among the most effective methods for realizing a desired field. However, in designing CAs, researchers are faced with a lack of design parameters. At low frequencies, the design parameters are usually limited to the size and phase of the source and the size and position of the coils. In this letter, with the help of three-dimensional (3-D) coils, the spatial current distribution, i.e., the shape of coils, is added to the design parameters of the CA problem. This novel 3-D coil array creates a high degree of freedom for the synthesis of the desired magnetic field which cannot be achieved by ordinary coil arrays or a single 3-D coil. The technological advances in the field of 3-D printing helps in the fabrication of these 3-D structures with high precision, low cost, and fast prototyping. In the design process, dyadic Green's functions are used to analytically calculate the magnetic field. Then, in order to define the shape of the 3-D coils, these shapes are extended based on the proper basis functions. By determining the coefficients of these basis functions by means of optimization methods, the shape of each 3-D coil in the array is obtained. This method is used to realize an arbitrary magnetic field along a line by means of a single-source array that includes three 3-D coils. The designed array is implemented with the use of fused-deposition-modeling 3-D printing. The design results, numerical simulations, and experimental tests demonstrate a high degree of accuracy in the fabrication process and the ability of 3-D arrays to synthesize magnetic fields.