基于数值优化方法的Halbach磁体无源匀场方法研究

doi:10.11938/cjmr20233091

波谱学杂志 ›› 2024, Vol. 41 ›› Issue (2): 128-138.doi: 10.11938/cjmr20233091

基于数值优化方法的Halbach磁体无源匀场方法研究

李正喆¹, 郭亮¹^,^*(), 任旭虎²^,^#()

1.中国石油大学（华东），控制科学与工程学院，山东青岛 266580
2.中国石油大学（华东），海洋空间与信息学院，山东青岛 266580

收稿日期:2023-12-11 出版日期:2024-06-05 在线发表日期:2024-02-13
通讯作者: *Tel: 18266639901, E-mail: guoliang@upc.edu.cn; #Tel: 13356635188, E-mail: rxh@upc.edu.cn.
基金资助:
山东省自然科学基金资助项目(ZR2021ME093)

A Passive Shimming Method for Halbach Magnet Based on Numerical Optimization Algorithm

LI Zhengzhe¹, GUO Liang¹^,^*(), REN Xuhu²^,^#()

1. College of Control Science and Engineering, China University of Petroleum (East China), Qingdao 266580, China
2. School of Ocean and Spatial Information, China University of Petroleum (East China), Qingdao 266580, China

Received:2023-12-11 Published:2024-06-05 Online:2024-02-13
Contact: *Tel: 18266639901, E-mail: guoliang@upc.edu.cn; #Tel: 13356635188, E-mail: rxh@upc.edu.cn.

摘要/Abstract

摘要：

小型化的核磁共振谱仪由于其便携性的优势，成了当下核磁共振领域的研究热点．近年来，Halbach磁体在小型化核磁共振波谱仪领域得到了广泛应用．永磁体磁场的不均匀性对无源匀场方法提出了较高的要求．因此，本文基于机械可调的Halbach永磁体阵列结构进行了无源匀场研究．首先研制了由12个机械可调的磁块构成的Halbach磁体，并建立了磁块位置和磁场均匀性的最小二乘问题，随后利用了一种结合Levenberg-Marquardt法和拟牛顿法的优化算法，通过改变磁块的径向位置来优化磁场的均匀性．通过这种方法，成功将1.03 T的Halbach磁体中心区域（半径为2.5 mm）的均匀度从7 391×10^-6提升到154.23×10^-6．本文提出的匀场方法相对于传统的无源匀场方法更加灵活和简便，有望应用于核磁共振波谱仪和其他需要高磁场均匀度的仪器．

关键词: 核磁共振波谱仪, Halbach磁体, 无源匀场, Levenberg-Marquardt方法, 拟牛顿方法

Abstract:

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.

Key words: nuclear magnetic resonance spectrometer, Halbach magnet, passive shimming, Levenberg-Marquardt method, quasi-Newton method

中图分类号:

O482.53

李正喆, 郭亮, 任旭虎. 基于数值优化方法的Halbach磁体无源匀场方法研究[J]. 波谱学杂志, 2024, 41(2): 128-138.

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.

图/表 8

图1

图2

图3

图4

图5

图6

表1

图7

参考文献 21

[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. doi: 10.11938/cjmr20223002
[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. doi: 10.1016/j.jmr.2016.01.014 pmid: 26874333
[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. doi: 10.1002/anie.201000221 pmid: 20446281
[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.

参数	匀场前	匀场后
磁块1径向移动距离	0 mm	-1.13 mm
磁块2径向移动距离	0 mm	+0.76 mm
磁块3径向移动距离	0 mm	-0.35 mm
磁块4径向移动距离	0 mm	+0.53 mm
磁块5径向移动距离	0 mm	-0.48 mm
磁块6径向移动距离	0 mm	-1.25 mm
磁块7径向移动距离	0 mm	-0.45 mm
磁块8径向移动距离	0 mm	+1.20 mm
磁块9径向移动距离	0 mm	+1.34 mm
磁块10径向移动距离	0 mm	+0.85 mm
磁块11径向移动距离	0 mm	-1.96 mm
磁块12径向移动距离	0 mm	-1.40 mm
磁体口径	30 mm	27.6 mm
x方向均匀度	4 571 ppm	19.2 ppm
y方向均匀度	4 601 ppm	144.3 ppm
z方向均匀度	2 226 ppm	106.03 ppm
区域均匀度	7 391 ppm	154.23 ppm

基于数值优化方法的Halbach磁体无源匀场方法研究

A Passive Shimming Method for Halbach Magnet Based on Numerical Optimization Algorithm

RichHTML

PDF

评审附件

可视化

摘要/Abstract

引用本文

使用本文

图/表 8

参考文献 21

相关文章 6

编辑推荐

Metrics

本文评价

[1]	毛文平，李云燕，刘造，鲍庆嘉，刘朝阳*. 具有快速调制功能NMR发射机的设计与实现[J]. 波谱学杂志, 2013, 30(1): 12-20.
[2]	肖颖, 郑振耀, 蔡淑惠, 陈忠. 基于FPGA小型化谱仪控制台的设计[J]. 波谱学杂志, 2012, 29(3): 346-353.
[3]	杨亮, 鲍庆嘉, 毛文平, 刘朝阳. 自主研制核磁共振波谱仪的性能评估[J]. 波谱学杂志, 2012, 29(1): 78-85.
[4]	包长虹, 孙惠军, 包立君, 裘晓俊, 陈忠. 高场核磁共振波谱仪宽带前置放大器的研制[J]. 波谱学杂志, 2011, 28(2): 216-227.
[5]	胡鹏, 杨亮, 胡少斌, 刘朝阳. 核磁共振波谱仪接收机的设计与实现[J]. 波谱学杂志, 2011, 28(1): 42-49.
[6]	姜婷婷, 陈义群, 方惠如, 刘朝阳. 一种NMR谱仪控制台软件系统的多层架构设计[J]. 波谱学杂志, 2009, 26(4): 497-503.