Uniform Field Coil Design Based on the Target-Field Method in Miniature Atomic Sensors

This paper presents the design of a uniform field coil based on the target-field method that offers an innovation in miniature atomic sensors. A selected uniform field cubical target region is located inside a cylinder with the surface comprised of coil windings. First, the current density was defined with unknown coefficients, and then a straightforward approach was used to obtain these coefficients via solving a matrix constructed by selecting field points in the target region. Subsequently, using the stream-function, the winding patterns of the coils are generated. Compared to the traditional coil design method, this method effectively solves the inconsistency between the uniform field areas and the sensor structures, by predefining the size of the coil surface before calculating the current distribution. It also avoids the cumbersome calculation process caused by the multi-order Taylor expansion based on the traditional method. Furthermore, a current density formula was expanded by trigonometric series that is particularly suitable for a cylindrical coil system with a uniform internal field. The theoretical accuracy can be greatly improved by choosing an optimal order of the trigonometric series. To prove its performance, a contrast with a Lee-Whiting coil is proposed. In addition, the utilized coil was manufactured by flexible printed circuit technology and magnetic field uniformities were verified by an actual test using a fluxgate magnetometer.