Optimal Design of a Bipolar Ultra-Low-Field Magnetic Resonance Imaging Magnet Using Third-Order Bézier Radial Parameterization and a Dual-Material Architecture

XUAN Liang; XU Xianfeng

doi:10.7652/xjtuxb202609002

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Optimal Design of a Bipolar Ultra-Low-Field Magnetic Resonance Imaging Magnet Using Third-Order Bézier Radial Parameterization and a Dual-Material Architecture

更新时间：2026-09-04

- Optimal Design of a Bipolar Ultra-Low-Field Magnetic Resonance Imaging Magnet Using Third-Order Bézier Radial Parameterization and a Dual-Material Architecture
- Journal of Xi'an Jiaotong University Vol. 60, Issue 9, Pages: 9-18(2026)
- 作者机构：
  
  长安大学交通新能源开发、应用与汽车节能技术陕西省重点实验室，710018，西安
  长安大学能源与电气工程学院，710018，西安
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202609002
  CLC： TM15
- Received：22 December 2025，
  
  Online First：25 May 2026，
  
  Published：10 September 2026
- 稿件说明：
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XUAN Liang, XU Xianfeng. Optimal Design of a Bipolar Ultra-Low-Field Magnetic Resonance Imaging Magnet Using Third-Order Bézier Radial Parameterization and a Dual-Material Architecture[J]. Journal of Xi'an Jiaotong University,2026,60 (9):9-18. https://doi.org/10.7652/xjtuxb202609002.
DOI：

XUAN Liang, XU Xianfeng. Optimal Design of a Bipolar Ultra-Low-Field Magnetic Resonance Imaging Magnet Using Third-Order Bézier Radial Parameterization and a Dual-Material Architecture[J]. Journal of Xi'an Jiaotong University,2026,60 (9):9-18. https://doi.org/10.7652/xjtuxb202609002. DOI：

摘要

针对超低场磁共振成像系统中双极型永磁体磁场均匀性受限且材料成本较高的问题，提出一种采用三阶贝塞尔径向参数化的磁体几何优化方法。该方法将传统圆盘磁体的单一半径参数拓展为4个径向自由度，在保持轮廓平滑性与制造可行性的同时显著扩大结构优化空间。基于遗传算法与有限元方法耦合计算，对磁体、极靴及铁轭等关键部件的几何参数进行联合仿真优化，获得磁场强度均值为59.2 mT、磁场不均匀度为1272×10

-6

的钐钴永磁体系统，相较传统圆盘结构不均匀度降低了21%。在此基础上，引入钐钴-钕铁硼（SmCo-NdFeB）双材料复合磁体架构，并在新几何范式下开展整数-贝塞尔复合优化，最终得到磁场强度均值为58.5 mT

、不均匀度为556×10

-6

的双材料磁体系统，不均匀度较传统方案降低66%。研究结果表明，基于三阶贝塞尔径向参数化的几何范式能够有效提升双极型超低场永磁体的磁场均匀性，并为双材料磁体的协同优化提供可行路径。

Abstract

To address the limited magnetic field homogeneity and high material cost of bipolar permanent magnet systems for ultra-low-field magnetic resonance imaging

a geometric optimization method using third-order Bézier radial parameterization is proposed.The single radius parameter of a conventional disk-shaped magnet is extended to four radial degrees of freedom

thereby significantly expanding the structural optimization space while maintaining profile smoothness and manufacturing feasibility.Coupled calculations using a genetic algorithm and the finite element method are performed to jointly optimize the geometric parameters of key components

including the magnets

pole pieces

and yoke.A SmCo permanent magnet system with an average magnetic field of 59.2 mT and a field inhomogeneity of 1272×10

-6

is obtained

with the inhomogeneity reduced by 21% compared with that of the conventional disk structure.On this basis

an SmCoNdFeB dual-material composite magnet architecture is introduced

and integer-Bézier composite optimization is performed under the new geometric framework.A dual-material magnet system with an average magnetic field of 58.5 mT and an inhomogeneity of 556×10

-6

is finally obtained

with the inhomogeneity reduced by 66% compared with that of the conventional design.It is shown that the geometric framework based on third-order Bézier radial parameterization effectively improves the magnetic field homogeneity of bipolar ultra-low-field permanent magnets and provides a feasible approach for the coordinated optimization of dual-material magnets.

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