Numerical Simulation and Additive Manufacturing Technology Research on Complex Curved Surface Permanent Magnets for Stellarators

MENG Xiaowei; HE Ketai; DONG Hao; DU Yangwei

doi:10.7512/j.issn.1001-2303.2026.04.11

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Numerical Simulation and Additive Manufacturing Technology Research on Complex Curved Surface Permanent Magnets for Stellarators
Vol. 56, Issue 4, Pages: 87-97(2026)
Received：11 December 2025，

Revised：2026-01-30，

Published：20 April 2026
DOI： 10.7512/j.issn.1001-2303.2026.04.11
稿件说明：

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孟晓伟，贺可太，董浩，等.仿星器复杂曲面永磁体的数值仿真与增材制造技术研究［J］.电焊机，2026，56（4）：87-97. DOI： 10.7512/j.issn.1001-2303.2026.04.11.

MENG Xiaowei, HE Ketai, DONG Hao, et al.Numerical Simulation and Additive Manufacturing Technology Research on Complex Curved Surface Permanent Magnets for Stellarators[J].Electric Welding Machine, 2026, 56(4): 87-97. DOI： 10.7512/j.issn.1001-2303.2026.04.11.

摘要

为解决仿星器磁约束聚变装置中复杂三维磁场位形的精确控制问题，突破传统线圈磁体系统在空间布局和运行维护方面的技术瓶颈，系统研究了复杂曲面永磁体的有限元数值仿真方法与增材制造技术方案。采用REGCOIL_PM电流势优化方法获得仿星器永磁体结构的三维形状，该方法基于Tikhonov正则化策略在等离子体表面磁场精度与永磁体复杂度之间实现优化平衡。针对永磁体具有空间扭曲轨迹和连续变化截面的几何特征，开发了基于MATLAB的STL网格自动生成程序，实现了复杂几何的精确数字化表征。建立了COMSOL三维静磁场有限元模型，通过插值函数技术实现了磁化强度和磁化方向在三维空间的连续变化配置。对NCSX构型仿星器开展的三维仿真分析表明，永磁体系统在等离子体表面产生的法向磁场呈现明显的非轴对称分布特征，磁场强度的空间变化范围覆盖正负极性区域。仿真结果与REGCOIL_PM计算结果磁场的归一化均方根误差低于5%，与理想等离子体约束磁场分布的最大相对偏差同样控制在5%以内，满足磁约束聚变对磁场精度的工程要求。磁场分布成功再现了仿星器构型的多重周期性特征。误差空间分布分析揭示，磁场梯度剧烈变化区域和等离子体边界高曲率位置的误差相对较大，主要源于几何离散化偏差、磁化向量插值误差和有限元网格分辨率的综合影响。在增材制造方案方面，提出采用激光选区熔化等增材制造工艺直接成型钕铁硼或铝镍钴永磁体。针对空间变化磁化方向的技术难题，设计了多自由度程控充磁系统，采用迭代充磁与全场测量相结合的闭环控制方法，补偿充磁过程的交叉耦合效应。本研究建立了仿星器复杂曲面永磁体从优化设计、数值仿真到增材制造的完整技术体系，验证了永磁体替代线圈磁体的技术可行性，为磁约束聚变装置提供了新型永磁体技术方案。

Abstract

To address the challenge of precise control over complex three-dimensional magnetic field configurations in stellarator magnetic confinement fusion devices and overcome technical bottlenecks of conventional coil magnet systems in spatial arrangement and operational maintenance

this study systematically investigated finite element numerical simulation methods and additive manufacturing technology schemes for complex curved surface permanent magnets. The REGCOIL_PM current potential optimization method was employed to obtain the three-dimensional geometry of stellarator permanent magnet structures

which achieved an optimized balance between plasma surface magnetic field accuracy and permanent magnet complexity based on the Tikhonov regularization strategy. Considering the geometric characteristics of permanent magnets featuring spatially twisted trajectories and continuously varying cross-sections

a MATLAB-based automatic STL mesh generation program was developed to achieve precise digital characterization of complex geometries. A three-dimensional magnetostatic finite element model was established in COMSOL

where the continuous spatial variation of magnetization intensity and direction was configured through interpolation function techniques. Three-dimensional simulation analysis conducted on the NCSX-configuration stellarator demonstrated that the permanent magnet system generated normal magnetic field distributions on the plasma surface exhibiting pronounced non-axisymmetric characteristics

with spatial variation ranges spanning both positive and negative polarity regions. The normalized root mean square error between simulation results and REGCOIL_PM calculations remained below 5%

while the maximum relative deviation from the ideal plasma confinement magnetic field distribution was similarly controlled within 5%

meeting the engineering requirements for magnetic field accuracy in magnetic confinement fusion. The magnetic field distribution successfully reproduced the multiple periodicity features characteristic of stellarator configurations. Spatial error distribution analysis revealed that regions with dramatic magnetic field gradient variations and high-curvature locations at the plasma boundary exhibited relatively larger errors

primarily attributed to the combined effects of geometric discretization deviations

magnetization vector interpolation errors

and finite element mesh resolution. Regarding the additive manufacturing scheme

laser powder bed fusion and other additive manufacturing processes were proposed for direct fabrication of neodymium-iron-boron or aluminum-nickel-cobalt permanent magnets. To address the technical challenge of spatially varying magnetization directions

a multi-degree-of-freedom programmable magnetization system was designed

employing a closed-loop control method combining iterative magnetization with full-field measurement to compensate for cross-coupling effects during the magnetization process. This research established a complete technical framework for complex curved surface permanent magnets in stellarators

spanning from optimization design and numerical simulation to additive manufacturing

validated the technical feasibility of replacing coil magnets with permanent magnets

and provided a novel permanent magnet technology solution for magnetic confinement fusion devices.

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Keywords

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