Figure 4
From: Characteristics and FEA verification of the attraction between like magnetic poles
The Bz distributions of the center-aligned D16 × 2 and D32 × 2 pair with various distances show that the smaller the distance is, the stronger the LD and the EE (edge effect) are. The LDL is defined as the ratio of \(\Delta {\int }_{{x}_{1}}^{{x}_{2}}{B}_{z}dx\) at the distance d over the \({\int }_{{x}_{1}}^{{x}_{2}}{B}_{z}dx\) of a standalone D32 × 2, calculated using Eq. (1), with the details for this case shown here: \(LDL=\frac{\Delta {\int }_{{x}_{1}}^{{x}_{2}}{B}_{z@d}dx}{{\int }_{{x}_{1}}^{{x}_{2}}{B}_{z@\mathrm{standalone}}dx}=\frac{{\int }_{{x}_{1}}^{{x}_{2}}{B}_{z@\mathrm{distance}\_d}dx-{\int }_{{x}_{1}}^{{x}_{2}}{B}_{z\_D32x2\_\mathrm{standalone}}dx}{{\int }_{{x}_{1}}^{{x}_{2}}{B}_{z\_D32x2\_\mathrm{standalone}}dx}\), where x1 and x2 are the positions where the LD starts and ends. Plots for the center aligned pairs have \({x}_{1}=-8\mathrm{mm}\) and \({x}_{2}=8\mathrm{mm}\) (a), and for the edge aligned pairs have \({x}_{1}=0\mathrm{mm}\) and \({x}_{2}=16\mathrm{mm}\) (b). The |LDL| of the center-aligned pairs is as large as 243% at d = 0.2 mm, and the center-aligned pairs have much larger |LDL| than the edge-aligned pairs. The ratios of |LDL|center/|LDL|edge range from 1.43 to 1.92 for d = 0.2 to 18 mm (c). The 2D Bz maps at the cross-section through a diameter for both center- and edge-aligned with d = 0.2 and 50 mm are displayed in (d), showing the LD and the EEs.
