Chinese Journal of Magnetic Resonance >
A Passive Shimming Method for Halbach Magnet Based on Numerical Optimization Algorithm
Received date: 2023-12-11
Online published: 2024-02-18
In recent years, Halbach magnet has been extensively used in miniaturized NMR spectrometers. However, the inhomogeneity of the magnetic field of permanent magnets poses a challenge to passive shimming method. In this paper, we conducted a passive shimming study of Halbach permanent magnet array structure which is mechanically adjustable. We modeled the relationship between the radial position of the magnetic blocks and magnetic field homogeneity. Then, an optimization algorithm combining the Levenberg-Marquardt method and quasi-Newton method was utilized to optimize the magnetic field homogeneity by adjusting the radial positions of the magnetic blocks. With this approach, the homogeneity of a 1.03 T Halbach magnet was improved from 7 391×10-6 to 154.23×10-6 in a sphere with a radius of 2.5 mm. This work provides a flexible and convenient passive shimming method for compact Halbach magnet, which has the potential to be applied in NMR spectrometers and other instruments that require high magnetic field homogeneity.
LI Zhengzhe , GUO Liang , REN Xuhu . A Passive Shimming Method for Halbach Magnet Based on Numerical Optimization Algorithm[J]. Chinese Journal of Magnetic Resonance, 2024 , 41(2) : 128 -138 . DOI: 10.11938/cjmr20233091
| [1] | EMSLEY J W, FEENEY J. Forty years of progress in nuclear magnetic resonance spectroscopy[J]. Prog Nucl Magn Reson Spectrosc, 2007, 50(4): 179-198. |
| [2] | ZAESSKIY S S, DANIELI E, BLüMICH B, et al. Miniaturization of NMR systems: Desktop spectrometers, microcoil spectroscopy, and ‘NMR on a chip’ for chemistry, biochemistry, and industry[J]. Chem Rev, 2014, 144(11): 5641-5694. |
| [3] | ZHANG X Y, YAO S Q, XU J C, et al. Magnetic field locking system based on fluxgate and time domain digital frequency discrimination[J]. Chinese J Magn Reson, 2022, 39(4): 448-458. |
| 张啸阳, 姚守权, 徐俊成, 等. 基于磁通门和时域数字鉴频的磁场锁定系统[J]. 波谱学杂志, 2022, 39(04): 448-458. | |
| [4] | SHI G H, XIAO L Z, LIAO G Z, et al. A new method and circuit of ringing suppression for low-field NMR instruments[J]. Chinese J Magn Reson, 2023, 40(1): 68-78. |
| 师光辉, 肖立志, 廖广志, 等. 低场核磁共振仪器振铃抑制新方法及其电路实现[J]. 波谱学杂志, 2023, 40(1): 68-78. | |
| [5] | GLOVERG P, MANSFIELD P. Limits to magnetic resonance microscopy[J]. Rep Prog Phys, 2002, 65(10): 1489-1511. |
| [6] | DENG D Y, LI C H. Exploration of the application of NMR technique in experimental teaching for undergraduates[J]. Res Explor Lab, 2021, 40(3):186-189. |
| 邓冬艳, 李成辉. 核磁共振技术应用于本科实验教学的探究[J]. 实验室研究与探索, 2021, 40(3): 186-189. | |
| [7] | AI H, GAO P F, LI X F. Application of nuclear magnetic resonance spectroscopy in open experiment teaching[J]. Res Explor Lab, 2022, 41(9): 186-189. |
| 艾惠, 高培峰, 李晓芳. 核磁共振波谱仪在开放实验教学中的应用[J]. 实验室研究与探索, 2022, 41(9): 186-189. | |
| [8] | HALBACH K. Design of permanent multipole magnets with oriented rare earth cobalt materials[J]. Nucl Instrum and Methods, 1980, 169(1): 1-10. |
| [9] | WU Z X, LU R S, JIANG X W, et al. An NMR relaxation method of characterizing hydrogen-bearing crystalline solid phases in hydrated cement paste[J]. IEEE Trans Instrum Meas, 2022, 71: 1-9. |
| [10] | TUREK K, LISZKOWSKI P. Magnetic field homogeneity perturbations in finite Halbach dipole magnets[J]. J Magn Reson, 2017, 238: 52-56. |
| [11] | WANG J N, JIANG X W, HU Z, et al. Design and shimming method of low length-to-interdiameter ratio Halbach magnet[J]. IEEE Trans Instrum Meas, 2022, 71: 1-10. |
| [12] | CHEN S S, XIA T, MIAO Z Y, et al. Active shimming method for a 21.3 MHz small-animal MRI magnet[J]. Meas Sci Technol, 2017, 28(5): 055902. |
| [13] | 李想. 高均匀度核磁共振Halbach磁体研究[D]. 重庆大学, 2019. |
| [14] | LI H Z, WU Y B, SUN W D, et al. Design and implementation of low-field NMR main magnet based on Halbach structure[J]. Chinese J Sci Instrum, 2022, 43(5): 46-56. |
| 励洪泽, 邬杨波, 孙伟达, 等. 基于Halbach结构的低场核磁共振主磁体的设计与实现[J]. 仪器仪表学报, 2022, 43(5): 46-56. | |
| [15] | WANG Y, XU Y J, WANG F, et al. A passive shimming method for Halbach magnet based on magnetic sheet arrays[J]. J Magn Reson, 2022, 339: 107210. |
| [16] | PARKER A J, ZIA W, REHORN C W G, et al. Shimming Halbach magnets utilizing genetic algorithms to profit from material imperfections[J]. J Magn Reson, 2016, 265: 83-89. |
| [17] | TEWARI S, O’REILLY T, WEBB A. Improving the field homogeneity of fixed-and variable-diameter discrete Halbach magnet arrays for MRI via optimization of the angular magnetization distribution[J]. J Magn Reson, 2021, 324: 106923. |
| [18] | DANIELI E, PERLO J, BLüMICH B, et al. Small magnets for portable NMR spectrometers[J]. Angew Chem Int Ed, 2010, 49(24): 4133-4135. |
| [19] | CHEN J Z, XU C Y. Design and analysis of the novel test tube magnet as a device for portable nuclear magnetic resonance[J]. IEEE Trans Magn, 2007, 43(9): 3555-3557. |
| [20] | 程艺苑. 小型永磁磁共振磁体的仿真设计与优化[D]. 浙江大学, 2015. |
| [21] | 李俊洲. 便携式核磁共振主磁体系统及射频线圈的结构设计[D]. 东北电力大学, 2023. |
/
| 〈 |
|
〉 |