The potential benefits of frustum-shaped magnets over cuboidal magnets have been seldom studied. This article compares these magnet shapes by optimizing frustum geometry for both a single magnet and a multi-magnet planar Halbach array to produce a desirable field. This field is compared to the equivalent field for optimized cuboidal magnets and differences quantified. A single magnet is considered, where the field strength above the center of a magnet is maximized. If the field is measured close to the magnet surface, an optimized frustum magnet can produce a field stronger than an optimized cuboidal magnet. If the field is measured further from the magnet, there is little benefit in using a frustum magnet over a cuboid. In addition, a planar magnet array is considered, in which the field strength and how closely the field resembled a sinusoidal profile are maximized. In this case, no significant benefit is observed using frustum magnets over cuboidal magnets.

中文翻译：

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针对单磁体和平面 Halbach 阵列配置的平截头永磁体产生的磁场的优化


截头锥体磁体相对于立方体磁体的潜在优势很少被研究。本文通过优化单磁体和多磁体平面 Halbach 阵列的平截头体几何形状来比较这些磁体形状，以产生所需的磁场。将该磁场与优化的立方体磁体的等效磁场进行比较，并对差异进行量化。考虑单个磁体，其中磁体中心上方的场强最大化。如果在靠近磁体表面的位置测量磁场，则优化的截锥体磁体可以产生比优化的立方体磁体更强的磁场。如果测量距离磁铁较远的磁场，则使用截头锥体磁铁比使用长方体磁铁几乎没有什么好处。此外，还考虑了平面磁体阵列，其中场强以及场与正弦曲线的相似程度被最大化。在这种情况下，与立方体磁体相比，使用截头体磁体没有观察到明显的好处。