Design of Highly Uniform Three Dimensional Spherical Magnetic Field Coils for Atomic Sensors

In this paper, three dimensional spherical magnetic field coils are proposed and optimized for atomic sensors that require highly uniform magnetic field coils within a limited volume. The design objective of the uniform coil is transformed into a nonlinear optimization model with constraints, which is solved by combining with the particle swarm optimization algorithm. Compared with the traditional cylindrical tri-axial magnetic field coil system whose volume is limited by the aspect ratio of the coil structure, the three dimensional spherical coils not only effectively reduce the volume but also provide consistent magnetic field performance in the three coordinate axis directions. It is of great significance to the miniaturization of atomic sensors. The theoretical calculation shows that the uniformity of spherical coil is improved by about 2 to 3 orders of magnitude compared with the Lee-Whiting coil and the saddle coil. The measurements show that the magnetic field uniformity of our design reached $1.5\times 10^{-4}$ along the ${z}$ -axis within a range of $\pm 0.25{R}$ . The actual magnetic field distribution is basically consistent with the theory. However, due to the limited processing and experimental conditions, the actual magnetic field uniformity is 1 to 2 orders of magnitude lower than the theory.