Shim coil design for Halbach magnet by equivalent magnetic dipole method

Low-field nuclear magnetic resonance magnet(2 MHz) is required for rock core analysis. However, due to its low field strength, it is hard to achieve a high uniform B_0 field only by using the passive shimming. Therefore, active shimming is necessarily used to further improve uniformity for Halbach magnet. In this work, an equivalent magnetic dipole method is presented for designing shim coils. The minimization of the coil power dissipation is considered as an optimal object to minimize coil heating effect, and the deviation from the target field is selected as a penalty function term. The lsqnonlin optimization toolbox of MATLAB is used to solve the optimization problem. Eight shim coils are obtained in accordance with the contour of the stream function. We simulate each shim coil by ANSYS Maxwell software to verify the validity of the designed coils. Measurement results of the field distribution of these coils are consistent with those of the target fields.The uniformity of the B_0 field is improved from 114.2 ppm to 26.9 ppm after using these shim coils.     

A novel approach to designing cylindrical-surface shimcoils for a superconducting magnet of magnetic resonance imaging

For a superconducting magnet of magnetic resonance imaging (MRI), the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylindrical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.     

Development of a temperature-variable magnetic resonance imaging system using a 1.0T yokeless permanent magnet

A temperature variable magnetic resonance imaging (MRI) system has been developed using a 1.0 T permanent magnet. A permanent magnet, gradient coils, radiofrequency coil, and shim coil were installed in a temperature variable thermostatic bath. First, the variation in the magnetic field inhomogeneity with temperature was measured. The inhomogeneity has a specific spatial symmetry, which scales linearly with temperature, and a single-channel shim coil was designed to compensate for the inhomogeneity. The inhomogeneity was drastically reduced by shimming over a wide range of temperature from −5 °C to 45 °C. MR images of an okra pod acquired at different temperatures demonstrated the high potential of the system for visualizing thermally sensitive properties.     

高性能核磁共振弛豫分析仪匀场系统的设计与实现

磁场的高均匀性是高性能核磁共振弛豫分析仪实现短弛豫时间样品和微弱信号核磁共振（NMR）检测的基本保障.该文以0.45 T双极型永磁体作为设计核心部件,在大范围磁体空间-25.4 mm球空间（DSV）内,基于目标场法设计了X、Y、Z、XY、XZ、YZ、Z²共7组有源匀场线圈,根据线圈供电要求,设计了可编程恒流电源,搭建了可用于高性能核磁共振弛豫分析仪磁体的有源匀场系统,介绍了系统的基本结构、设计过程及匀场方法.实验测试结果验证了大范围磁体空间内该匀场系统的实用性.     

Modeling the static fringe field of superconducting magnets

The resonance frequency-space and the frequency gradient-space relations are evaluated analytically for the static fringe magnetic field of superconducting magnets used in the NMR diffusion measurements. The model takes into account the actual design of the high-homogeneity magnet coil system that consists of the main coil and the cryoshim coils and enables a precise calibration of the on-axis magnetic field gradient and the resonance frequency inside and outside of the superconducting coil.     

基于边界元方法的超导核磁共振成像设备高阶轴向匀场线圈优化算法

在磁共振成像设备中,为了消除目标区域内的高阶谐波磁场分量,传统方法采用无源匀场,但该方法匀场精度较低,针对性较差,适用于全局匀场,而有源匀场则可以通过优化线圈分布来产生所需要的特定的磁场分布.但是,由于匀场线圈线型的复杂度会随着线圈阶数的增加而增加,难以满足设计需要,因此本文提出了一种用于磁共振成像超导匀场线圈系统的多变量非线性优化设计方法.该方法基于边界元方法,将匀场线圈所产生的磁场与目标磁场之间的偏差作为目标函数,线匝间距、线圈半径等作为约束条件,通过非线性优化算法,得到满足设计要求的线圈分布.通过一个中心磁场为0.5 T的开放式双平面磁共振成像超导轴向匀场线圈的设计案例,说明本方法具有计算效率高、灵活性好的特点.     

舰船电力系统用1MJ高温超导环型储能磁体的设计研究

介绍了舰船电力系统用 1MJ环型高温超导储能磁体的设计优化步骤 ,进行了环型磁体线圈最大磁场的优化、环型磁体单元尺寸的优化和环型磁体单元数目的优化 ,并得出了合适的磁体线圈尺寸。磁体线圈上的最大磁感应强度为 3-4 T,单元数目较大的环型磁体适用于 1MJHTS- SMES     

Globally optimal superconducting magnets part II: symmetric MSE coil arrangement

A globally optimal superconducting magnet coil design procedure based on the Minimum Stored Energy (MSE) current density map is outlined. The method has the ability to arrange coils in a manner that generates a strong and homogeneous axial magnetic field over a predefined region, and ensures the stray field external to the assembly and peak magnetic field at the wires are in acceptable ranges. The outlined strategy of allocating coils within a given domain suggests that coils should be placed around the perimeter of the domain with adjacent coils possessing alternating winding directions for optimum performance. The underlying current density maps from which the coils themselves are derived are unique, and optimized to possess minimal stored energy. Therefore, the method produces magnet designs with the lowest possible overall stored energy. Optimal coil layouts are provided for unshielded and shielded short bore symmetric superconducting magnets.     

矩阵梯度线圈研究现状与发展趋势

梯度和匀场线圈性能的好坏直接影响磁共振成像质量．常规线圈在成像过程中存在一些固有的不足,如产生的磁场形态单一、不灵活,需要的线圈种类较多,结构较复杂等．而新型矩阵梯度线圈可以较好地弥补这些缺点．本文首先介绍了矩阵梯度线圈的概念及其特性,然后根据结构和功能对其研究现状进行分类汇总,在此基础上对矩阵线圈未来的发展趋势进行分析．此外,本文还对矩阵梯度线圈的前期研究基础进行了介绍．     

A design of novel type superconducting magnet for super—high field functional magnetic resonance imaging by using the harmonic analysis method of magnetic vector potentials

The approach of expanding the magnetic scalar potential in a series of Legendre polynomials is suitable for designing a conventional superconducting magnetic resonance imaging magnet of distributed solenoidal configuration. Whereas the approach of expanding the magnetic vector potential in associated Legendre harmonics is suitable for designing a single-solenoid magnet that has multiple tiers, in which each tier may have multiple layers with different winding lengths. A set of three equations to suppress some of the lowest higher-order harmonics is found. As an example, a 4T single-solenoid magnetic resonance imaging magnet with 4×6 layers of superconducting wires is designed. The degree of homogeneity in the 0.5m diameter sphere volume is better than 5.8 ppm. The same degree of homogeneity is retained after optimal integralization of turns in each correction layer. The ratio B_m/B₀ in the single-solenoid magnet is 30% lower than that in the conventional six-solenoid magnet. This tolerates higher rated superconducting current in the coil. The Lorentz force of the coil in the single-solenoid system is also much lower than in the six-solenoid system. This novel type of magnet possesses significant advantage over conventional magnets, especially when used as a super-high field functional magnetic resonance imaging magnet.     

Analysis of the magnetic field, force, and torque for two-dimensional Halbach cylinders

The Halbach cylinder is a construction of permanent magnets used in applications such as nuclear magnetic resonance apparatus, accelerator magnets and magnetic cooling devices. In this paper the analytical expression for the magnetic vector potential, magnetic flux density and magnetic field for a two dimensional Halbach cylinder are derived. The remanent flux density of a Halbach magnet is characterized by the integer p. For a number of applications the force and torque between two concentric Halbach cylinders are important. These quantities are calculated and the force is shown to be zero except for the case where p for the inner magnet is one minus p for the outer magnet. Also the force is shown never to be balancing. The torque is shown to be zero unless the inner magnet p is equal to minus the outer magnet p. Thus there can never be a force and a torque in the same system.     

高分辨超导NMR谱仪的匀场

本文详细叙述了超导磁体的磁场分布和匀场线圈的设计。并对匀场电源、匀场线圈的精度和稳定性等要求作了估算。     

Combined passive and active shimming for in vivo MR spectroscopy at high magnetic fields

The use of high magnetic fields increases the sensitivity and spectral dispersion in magnetic resonance spectroscopy (MRS) of brain metabolites. Practical limitations arise, however, from susceptibility-induced field distortions, which are increased at higher magnetic field strengths. Solutions to this problem include optimized shimming, provided that active, i.e., electronic, shimming can operate over a sufficient range. To meet our shim requirements, which were an order of magnitude greater than the active shim capacity of our 7T MR system, we developed a combined passive and active shim approach. Simple geometries of ferromagnetic shim elements were derived and numerically optimized to generate a complete set of second-order spherical harmonic shim functions in a modular manner. The major goals of the shim design were maximization of shim field accuracy and ease of practical implementation. The theoretically optimized ferro-shim geometries were mounted on a cylindrical surface and placed inside the magnet bore, surrounding the subject's head and the RF coil. Passive shimming generated very strong shim fields and eliminated the worst of the field distortions, after which the field was further optimized by flexible and highly accurate active shimming. Here, the passive-shimming procedure was first evaluated theoretically, then applied in phantom studies and subsequently validated for in vivo 1H MRS in the macaque visual cortex. No artifacts due to the passive shim setup were observed; adjustments were reproducible between sessions. The modularity and the reduction to two pieces per shim term in this study is an important simplification that makes the method applicable also for passive shimming within single sessions. The feasibility of very strong, flexible and high-quality shimming via a combined approach of passive and active shimming is of great practical relevance for MR imaging and spectroscopy at high field strengths where shim power is limited or where shimming of specific anatomical regions inherently requires strong shim fields.     

Designing shielded radio-frequency phased-array coils for magnetic resonance imaging

In this paper, an approach to the design of shielded radio-frequency (RF) phased-array coils for magnetic resonance imaging (MRI) is proposed. The target field method is used to find current densities distributed on primary and shield coils. The stream function technique is used to discretize current densities and to obtain the winding patterns of the coils. The corresponding highly ill-conditioned integral equation is solved by the Tikhonov regularization with a penalty function related to the minimum curvature. To balance the simplicity and smoothness with the homogeneity of the magnetic field of the coil’s winding pattern, the selection of a penalty factor is discussed in detail.     

Magnetic field homogeneity: a new approach to orthogonalizing and optimizing shim gradients

A new approach to optimizing shim coil currents for magnetic resonance magnets is presented. The new approach orthogonalizes the shim coil gradients to allow a simple one-dimensional optimization for each orthogonalized "composite shim." The technique demands no specialized equipment, requiring only the acquisition of simple one-dimensional NMR spectra. Examples from two high-resolution NMR spectrometers are presented, where the shim currents found by the new algorithm provide higher resolution than was obtained by the spectrometer vendor's installation engineers using field-mapping techniques. The examples shown demonstrate the advantages of the technique for high-resolution NMR, but we expect the approach will also find application in a broad variety of areas including imaging and in vivo spectroscopy.     

25T超导磁体优化中线圈数量影响分析

20 T以上强磁场在高场科学工程中有着不可替代的作用. 电工研究所正在研制一个25 T全超导磁体系统, 包括15 T背景磁场和10 T高温超导内插磁体. 在磁体的设计和优化中, 线圈的数量和种类对于最终优化结果十分关键. 为了研究磁体数量和磁体相关参数的关系, 计算了20 组不同的线圈组合下磁体的优化结果. 优化中除了考虑必要的限制条件以外, 还采用了一种结合局部优化算法和全局优化算法的方法. 通过对比分析发现, 线圈数量和磁体造价之间, 存在一个“V”形的关系. 更进一步地, 本文分析了不同超导体在磁体中应该贡献的最佳磁场, 以及背景磁体统一供电给优化结果带来的影响.     

On some consequences of an external magnetic field applied to HTS coils

A computational model which enables to evaluate the distribution of the critical currents, electric fields and the voltage in the winding of a solenoidal high temperature superconducting (HTS) magnets subjected to an external magnetic field parallel with the magnet axis, was developed. The model comes out from the well-known power law between the electric field and the transport current of the HTS tape short sample. It allows to predict the voltage–current V(I) characteristics of both the pancake coils and the complete magnet. The model was applied to the magnet system consisting of 22 pancake coils made of multifilamentary Bi(2223)/Ag tape at 20 K, which is subjected to an external uniform magnetic field parallel with the coil axis. A rather unexpected behavior of the magnet at different operating conditions (operating current and external magnetic field strength) is predicted, analyzed and reported together with a theoretical explanation. On one hand, the external uniform magnetic field parallel with the coil axis increases the resulting magnetic field strength, however, on the other hand it simultaneously decreases the angle between the resulting magnetic field and the tape surface. Thus, the effect of higher magnetic loading caused by the presence of an external magnetic field strength which is acting on individual turns located close to the coil’s flanges is compensated by more favorable orientation of the tape with respect to the resulting magnetic field. As a result, increase in the critical currents of these turns is expected. Further, the results indicate, that in case of the high field HTS insert coils the anisotropy in the I_c(B) characteristic does not play a substantial role. As a consequence, the technology of the production of the tapes for high field insert HTS coils should concentrate rather on the tapes having the current carrying capacity as high as possible, than on the attempt how to decrease the anisotropy in the I_c(B) by changing the architecture of the filaments in the tape.     

Surface and Gradiometer Coils near a Conducting Body: The Lift-off Effect

The use of surface coils in magnetic resonance is widespread. Examples include MRI, detection of subsurface aquifers by NMR, and, more recently, landmine detection by nuclear quadrupole resonance. In many of these cases a finite-sized sample to be examined is contained within a larger medium that is a poor electrical conductor, and eddy currents induced by the RF fields provide a loss mechanism that reduces the effective quality factorQof the transmitter and receiver coils. Here the losses induced in a circular surface coil (a horizontal loop antenna) separated a distance from a dissipative medium are calculated and compared to measurements. It is shown that often the overall efficiency of the coil for magnetic resonance can be improved by displacing the coil away from the conducting medium a prescribed “lift-off” distance. The use of a gradiometer as a surface coil is also examined, and it is shown by theory and experiment that in certain circumstances such a gradiometer can be more efficient than a conventional surface coil for inspection of conducting media.     

A portable Halbach magnet that can be opened and closed without force: the NMR-CUFF

Portable equipment for nuclear magnetic resonance (NMR) is becoming increasingly attractive for use in a variety of applications. One of the main scientific challenges in making NMR portable is the design of light-weight magnets that possess a strong and homogeneous field. Existing NMR magnets can provide such magnetic fields, but only for small samples or in small regions, or are rather heavy. Here we show a simple yet elegant concept for a Halbach-type permanent magnet ring, which can be opened and closed with minimal mechanical force. An analytical solution for an ideal Halbach magnet shows that the magnetic forces cancel if the structure is opened at an angle of 35.3° relative to its poles. A first prototype weighed only 3.1 kg, and provided a flux density of 0.57 T with a homogeneity better than 200 ppm over a spherical volume of 5mm in diameter without shimming. The force needed to close it was found to be about 20 N. As a demonstration, intact plants were imaged and water (xylem) flow measured. Magnets of this type (NMR-CUFF = Cut-open, Uniform, Force Free) are ideal for portable use and are eminently suited to investigate small or slender objects that are part of a larger or immobile whole, such as branches on a tree, growing fruit on a plant, or non-metallic tubing in industrial installations. This new concept in permanent-magnet design enables the construction of openable, yet strong and homogeneous magnets, which aside from use in NMR or MRI could also be of interest for applications in accelerators, motors, or magnetic bearings.     

A uniplanar three-axis gradient set for in vivo magnetic resonance microscopy

We present an optimized uniplanar magnetic resonance gradient design specifically tailored for MR imaging applications in developmental biology and histology. Uniplanar gradient designs sacrifice gradient uniformity for high gradient efficiency and slew rate, and are attractive for surface imaging applications where open access from one side of the sample is required. However, decreasing the size of the uniplanar gradient set presents several unique engineering challenges, particularly for heat dissipation and thermal insulation of the sample from gradient heating. We demonstrate a new three-axis, target-field optimized uniplanar gradient coil design that combines efficient cooling and insulation to significantly reduce sample heating at sample-gradient distances of less than 5 mm. The instrument is designed for microscopy in horizontal bore magnets. Empirical gradient current efficiencies in the prototype coils lie between 3.75 G/cm/A and 4.5 G/cm/A with current and heating-limited maximum gradient strengths between 235 G/cm and 450 G/cm at a 2% duty cycle. The uniplanar gradient prototype is demonstrated with non-linearity corrections for both high-resolution structural imaging of tissue slices and for long time-course imaging of live, developing amphibian embryos in a horizontal bore 7 T magnet.