The computation of 3-D magnetic fields is a demanding task in the analysis of electrical machines and other electromagnetic devices. In this context, integral field calculation provides a smooth solution, high precision and resolution, “on-demand”-calculation, and an origin-based formulation of the magnetic field and the magnetic vector potential. However, conventional elliptic methods lead to huge parallelizable computing efforts and significant errors. In this article, a 3-D generic current-carrying arc segment with rectangular cross section is studied. A new analytic formulation is proposed to speed up the computation of magnetic fields and reduce the error by more than three orders of magnitude. In addition, the proposed magnetic vector potential expression has a similar accuracy as numerical integration. In fact, a significant reduction of the error level has been showcased clearly with respect to the existing approaches. This article is promising for improving the design methodology and optimization of large superconducting dipole magnets or arched end-winding geometries of large electrical machines.

中文翻译：

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具有矩形截面的载流有限弧段的快速 3-D 磁积分场计算

在电机和其他电磁设备的分析中，3-D 磁场的计算是一项艰巨的任务。在这种情况下，积分场计算提供了平滑的解决方案、高精度和分辨率、“按需”计算以及磁场和磁矢量势的基于原点的公式。然而，传统的椭圆方法会导致巨大的可并行计算工作量和重大错误。在本文中，研究了具有矩形横截面的 3-D 通用载流弧段。提出了一种新的解析公式来加速磁场的计算并将误差减少三个数量级以上。此外，所提出的磁矢量势表达式具有与数值积分相似的精度。实际上，与现有方法相比，已经清楚地展示了错误水平的显着降低。本文有望改进大型超导偶极磁铁或大型电机的拱形端部绕组几何结构的设计方法和优化。