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| Design and Optimization of a Multi-Coil Structure for Dual-Zone Uniform Magnetic Fields |
| Liu Xufei1, Fu Jiqing2, Peng Lisha1, Huang Songling1,3 |
1. Department of Electrical Engineering Tsinghua University Beijing 100084 China;
2. National Institute of Metrology Beijing 100029 China;
3. State Key Laboratory of Power System Operation and Control Beijing 100084 China |
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Abstract This study presents a novel coil design and optimization approach for generating high-uniformity magnetic fields in two spatially separated regions, addressing the limitations of conventional coil systems in compact, multi-sensor calibration scenarios. Traditional Helmholtz and modified multi-coil configurations often require large physical dimensions to maintain field uniformity over extended volumes. When scaled down, they tend to suffer from performance degradation and electromagnetic crosstalk, particularly when used for simultaneous calibration of multiple magnetometers. To resolve these issues, we propose a dual-zone magnetic field system based on a coaxial seven-segment coil structure, specifically optimized to generate two discrete yet highly uniform magnetic field regions with minimized interference and reduced footprint.
The optimization method combines a continuous nonlinear solver with a mixed-integer programming strategy. By jointly adjusting the axial positions and relative number of turns in each coil segment, the system minimizes high-order magnetic field nonuniformity in the target regions. The optimization is guided by a Taylor-series-based field analysis that focuses on reducing spatial derivatives of the magnetic field near the center, thereby directly improving uniformity. A continuous optimization is first performed under physical constraints such as coil spacing, overall length, and region separation. The resulting fractional solutions are then discretized into feasible integer turns, followed by local adjustment to refine uniformity.
Simulation results demonstrate the effectiveness of the proposed method across varying coil segment counts, with seven segments offering the best tradeoff between design complexity and field performance. The dual-zone system achieves comparable or slightly lower field uniformity than an optimized single-zone six-coil system, but it uniquely enables two 60 mm-long uniform zones spaced more than 70 cm apart. This dual-region capability is particularly advantageous for calibrating multiple sensors simultaneously, minimizing crosstalk and enabling more efficient workflows.
Finite-element simulation using Ansys Maxwell confirms the analytical optimization results, validating the coil positions and field distribution. The designed system maintains field uniformity within 4.8×10-5 across each 60 mm zone. Sensitivity analysis further indicates that axial coil placement tolerances within ±0.01 mm are essential for preserving high uniformity, while deviations of ±0.1 mm can degrade performance by an order of magnitude, highlighting the critical importance of precise mechanical fabrication.
To validate the design experimentally, a physical prototype was fabricated by the National Institute of Metrology. The device, measuring approximately 1.3 m by 0.6 m, was constructed with axial placement precision better than 10 µm. Field measurements show a uniformity of 9×10-6 over a 6 cm scanning range in both regions, closely aligning with simulation predictions and confirming the effectiveness of the dual-zone design under real-world conditions.
In summary, the proposed method provides a practical and effective solution for dual-zone uniform magnetic field generation in compact devices. The combination of structured coil segmentation and hybrid optimization achieves field performance previously limited to larger systems, with potential applications in multi-sensor calibration, low-field magnetic experiments, and portable magnetic measurement platforms. Future work will explore alternative winding geometries and global optimization techniques to further enhance robustness and manufacturing flexibility.
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Received: 27 March 2025
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2026, Vol. 41 
