Fig. 1. Schematic illustration of permanent magnet and equivalent magnetic dipole: (a) Permanent magnet; (b) equivalent magnetic dipole.永磁体和等效磁偶极子坐标示意图　(a) 永磁体; (b) 电流环(磁偶极子)

Fig. 2. Variation of |B_z| versus distance (rectangular permanent magnet and ideal magnetic dipole): (a) y = 0, z = 0, along x-axis; (b) x = 0, z = 160 mm, along y-axis; (c) x = 0, y = 0, along z-axis; (d) x = 0, y = 180 mm, along z-axis. |B_z|随距离的变化(矩形永磁体和理想磁偶极子)　(a) y = 0, z = 0, 沿x轴变化; (b) x = 0, z = 160 mm, 沿y轴变化; (c) x = 0, y = 0, 沿z轴变化; (d) x = 0, y = 180 mm, 沿z轴变化

Fig. 3. Schematic illustration of the equivalence between spinning permanent magnet and spinning magnetic dipole: (a) Spinning permanent magnet; (b) spinning magnetic dipole.旋转永磁体与旋转磁偶极子的等效　(a) 旋转永磁体; (b) 旋转磁偶极子

Fig. 4. Schematic illustration of the equivalence between spinning magnet dipole and orthogonal magnetic dipoles: (a) Spinning magnet dipole; (b) orthogonal magnetic dipoles; (c) orthogonal magnetic currents旋转磁偶极子与正交磁流元的等效关系　(a) 旋转磁偶极子; (b) 正交磁偶极子; (c) 正交磁流元

Fig. 5. Coordinate system of the orthogonal electric dipoles.正交电偶极子的坐标系

Fig. 6. Results comparison between the proposed method and the formula in Ref. [13] (along x-axis, the spherical coordinate parameters: , ). 两种计算方法的结果对比(沿x轴, 球坐标变量为 , )

Fig. 7. Simulated magnetic flux density versus distance: (a) Air; (b) seawater. 旋转永磁体的磁感应强度 随距离的变化　(a) 空气; (b) 海水

Fig. 8. Variation of simulated magnetic flux density with material and frequency: (a) 160 Hz; (b) seawater. 旋转永磁体磁感应强度的一般变化规律　(a) 160 Hz; (b) 海水

Fig. 9. Spinning permanent magnets array with two elements.旋转永磁体二元阵列

Fig. 10. Performance comparison between spinning magnet array and single spinning magnet: (a) Along x-axis, the spherical coordinate parameters , ; (b) magnetic near field pattern at the horizontal plane (d = 50 m, r = 1000m, ) 二元旋转永磁体和单个旋转永磁体的场强对比　(a) 沿x轴, 球坐标变量为 , ; (b) 近场水平面方向图(d = 50 m, r = 1000 m, )

Fig. 11. Simulated magnetic flux density in the elevation plane. 二元阵列俯仰面磁场分布

Fig. 12. Simulated magnetic flux density of the spinning magnet array with two elements: (a) r = 1000 m; (b) r = 2000 m. 改变初始旋转角, 二元阵列的水平面磁场方向图(a) r = 1000 m; (b) r = 2000 m