Optimal Design of a Bi-planar coil with a High-uniformity Magnetic Field

This paper presents a method for analyzing and optimizing bi-planar coil structures that generate a high-uniformity magnetic field within a limited installation space. As an alternative to finding a numerical solution to the equations, this method uses the particle swarm algorithm to directly adjust the position distribution and current in the current loop to minimize the relative error of the magnetic field in the target area. Compared with the traditional method of eliminating higher even-order derivatives of the Taylor expansion terms, the advantage of this method is that the coil size is predetermined before calculation, which results in a better magnetic field uniformity and overcomes the size constraints. Theoretical calculations showed that the uniformity of the designed coil could be improved about 1.2 times compared with the Helmholtz coil, and the occupied volume could be reduced by 3.3 times in a cylinder with a radius and half-height of 0.25 d in the center area. The magnetic field generated by the uniform coil we designed and constructed using 3D printing technology matched the theoretical simulations.