产生匀强磁场的圆柱形线圈组设计方法

在精密测量和航空航天领域，原子陀螺仪、原子磁强计等对线圈产生磁场的均匀度有很高的要求，而传统的亥姆霍兹线圈磁场均匀度较差，难以满足应用需求。为了设计产生高均匀度磁场的线圈组，基于线圈轴向磁场的泰勒展开式，提出了任意线圈数的圆柱形线圈组参数的计算方法，并给出了9线圈以内的线圈参数，分析了磁场均匀度、线圈尺寸、线圈最大安匝比随线圈个数的变化趋势。结果表明随着线圈个数的增加，均匀区面积几乎线性增大，9线圈组磁场均匀度优于0.01%的区域面积约为亥姆霍兹线圈的30倍。在要求各个线圈由整数匝线圈组成且各匝线圈电流相同的情况下，提出了一种线圈安匝比取整的方法，并给出2~9线圈组的安匝比取整结果，计算结果表明相同线圈个数下设计的线圈组产生磁场的均匀度优于已有文献。以5线圈组为例，对实际线圈组制作工艺产生的误差进行了仿真分析，仿真结果表明，考虑误差的情况下，设计的尺寸和磁场也满足原子陀螺仪、原子磁强计等的实际要求。

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 ampereturn 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.