Analysis of coil constant of triaxial uniform coils in Mn–Zn ferrite magnetic shields

Triaxial uniform coils housed in magnetic shields are extensively used in atomic sensors. The coil constant can be affected by the magnetic shield that imposes a ferromagnetic boundary. This study numerically and experimentally analyzes the coil constant dependence on the Mn–Zn ferrite magnetic shield thickness, aspect ratio, air gaps between the magnetic annuli, and the distance from the coils. Results show that the radial coil constant (saddle-shaped coil) only depends upon the distance between the coil and the magnetic shield. The axial coil constant (Lee–Whiting coil) depends on the aspect ratio, distance between the coil and the magnetic shield, and air gap width between the magnetic annuli. The axial coil constant is linearly related to the air gap. When the thickness of the magnetic shield is greater than 2 mm, the radial and axial coil constants are independent of the shield thickness. The difference between the simulated and measured values is only 3.9%. The numerical calculation accuracy was verified by experimental measurements. This study can aid in the design and research of coils in the ferrite magnetic shield in atomic sensors.