Design method of cylindrical coil systems for generating uniform magnetic field

In the field of precision measurement and aerospace, atomic gyroscope and atomic magnetometer have high requirements on the uniformity of magnetic field, while the uniformity of magnetic field generated by the traditional Helmholtz coil is not good enough for these applications. To obtain better field uniformity, a method to calculate the parameters of cylindrical coil systems is proposed based on the Taylor expansion of the axial magnetic field. The parameters of two-coil to nine-coil systems are computed, and the variation trends of magnetic field uniformity, coils' size, and coils' maximum ampere-turn ratio with coil number are analyzed. Numerical results demonstrate that the uniform region area of magnetic field increases almost linearly with the increasing of coil number, and the region area where the field uniformity is better than 0.01% in nine-coil system is about 30 times as large as that in Helmholtz coil. A method of rounding coil ampere-turn ratio is presented when integer coil turns and the same current in each coil turn are required, and the integer ampere-turn ratios of two-coil to nine-coil systems are given. Numerical results show that the uniformity of our coil systems is better than those in other papers. Finally, simulation analysis for the error caused by fabrication technique in practical five-coil system is conducted. Simulation results demonstrate that both the designed size and magnetic field of the coil meet the practical demand of atomic gyroscope and atomic magnetometer when error is taken into consideration.