Halbach Magnet Research Articles

Signal-to-noise trade-offs between magnet diameter and shield-to-coil distance for cylindrical Halbach-based portable MRI systems for neuroimaging.

To investigate the trade-off between magnet bore diameter and the distance between the conductive Faraday shield and RF head coil for low-field point-of-care neuroimaging systems. Electromagnetic simulations were performed for three different Faraday shield geometries and two commonly used RF coil designs (spiral and solenoid) to assess the effects of a close-fitting shield on the RF coil's transmit and receive efficiencies. Experimental measurements were performed to confirm the accuracy of the simulations. Parallel simulations were performed to assess the static magnet ( ) field as a function of the magnet bore diameter. The obtainable SNR was then calculated as a function of these two related variables. Simulations of the RF coil characteristics and transmit efficiencies agreed well with corresponding experimentally determined parameters. Overall, the RF coil transmit efficiency was, as expected, higher when the gap between the shield and coil increased. The calculated intrinsic SNR showed that maximum SNR would be obtained for a cylindrical shield of diameter 310mm with an inner diameter of the magnet of 320mm (assuming 10mm for the gradient coils). This work presents an overview of the trade-offs in transmit efficiencies for RF coils used for POC MRI neuroimaging as a function of coil-to-shield distance and inner diameter of the Halbach magnet. Results show that there is a relatively shallow optimum between a magnet diameter of 290 and 330mm, with values falling more than 10% if either smaller or larger magnets are used.

Elliptical Halbach magnet and gradient modules for low-field portable magnetic resonance imaging.

This study aims to develop methods to design the complete magnetic system for a truly portable MRI scanner for neurological and musculoskeletal (MSK) applications, optimized for field homogeneity, field of view (FoV), and gradient performance compared to existing low-weight configurations. We explore optimal elliptic-bore Halbach configurations based on discrete arrays of permanent magnets. In this way, we seek to improve the field homogeneity and remove constraints to the extent of the gradient coils typical of Halbach magnets. Specifically, we have optimized a tightly packed distribution of magnetic Nd2Fe14B cubes with differential evolution algorithms and a second array of shimming magnets with interior point and differential evolution methods. We have also designed and constructed an elliptical set of gradient coils that extend over the whole magnet length, maximizing the distance between the lobe centers. These are optimized with a target field method minimizing a cost function that considers also heat dissipation. We have employed the new toolbox to build the main magnet and gradient modules for a portable MRI scanner designed for point-of-care and residential use. The elliptical Halbach bore has semi-axes of 10 and 14& cm, and the magnet generates a field of 87& mT homogeneous down to 5700& ppm (parts per million) in a 20-cm diameter FoV; it weighs 216& kg and has a width of 65& cm and a height of 72& cm. Gradient efficiencies go up to around 0.8& mT/m/A, for a maximum of 12& mT/m within 0.5& ms with 15& A and 15& V amplifier. The distance between lobes is 28& cm, significantly increased with respect to other Halbach-based scanners. Heat dissipation is around 25& W at maximum power, and gradient deviations from linearity are below 20% in a 20-cm sphere. Elliptic-bore Halbach magnets enhance the ergonomicity and field distribution of low-cost portable MRI scanners, while allowing for full-length gradient support to increase the FoV. This geometry can be potentially adapted for a prospective low-cost whole-body technology.

A Semi-Analytical Approach for the Optimization of High-Speed PMSM With Halbach Magnet Array

A Semi-Analytical Approach for the Optimization of High-Speed PMSM With Halbach Magnet Array

Design Considerations of High-Speed PMSM With Nonuniform Two-Segment Halbach Magnet Array

Design Considerations of High-Speed PMSM With Nonuniform Two-Segment Halbach Magnet Array

Forward modeling of single-sided magnetic resonance and evaluation of [formula omitted] fitting error based on geometric analytical method

Single-sided magnetic resonance (SSMR) offers advantages of portability and noninvasive measurement for water detection, with significant potential applications in groundwater exploration, petroleum well logging, and soil moisture monitoring. However, the inherent highly inhomogeneous static magnetic field and radiofrequency (RF) field in SSMR necessitate the utilization of the Carr–Purcell–Meiboom–Gill (CPMG) sequence measurement scheme. To accelerate forward modeling during pulse excitation, we introduce a Geometric Analysis Method (GAM) and assess T2 error using its primary parameters. The GAM involves applying spatial geometric rotations on the magnetization vector, leading to an analytical solution to the Bloch equation that disregards relaxation effects. Compared with the rotation matrix (RM) method, the GAM demonstrates high accuracy and reduces computational time by approximately 20.9%. By analyzing the primary parameters governing the magnetization vector in the analytical formula, we evaluated their impact on the transverse relaxation time (T2) obtained through fitting the SE signal. Ultimately, the forward modeling results of the CPMG sequence within the region of interest (ROI) of a single-sided Halbach magnet array are validated. The T2 fitting error increases as the primary parameters deviate from the ideal values, highlighting their significant role in the T2 fitting results. This study provides a theoretical foundation for optimizing the design of SSMR magnets and RF coils.

Advanced modeling of segmented Halbach cylinder for ironless brushless permanent-magnet two-phase motor

Compared with conventional permanent magnet (PM) cylinders, Halbach magnet cylinders have the advantage of strengthening the magnetic field on one side and canceling the field on the other side of the magnet structure. Outer-rotor radial-flux brushless ironless PM machines using a Halbach cylinder, therefore, can have a higher torque density compared with the ironless PM machines using a conventional magnet cylinder with the same magnet and coil volume and same air gap. For outer-rotor Halbach cylinder motors, existing designs usually take advantage of the fundamental harmonics of the magnetic field to obtain a linear toque model and to avoid the torque ripples from the higher-order field harmonics. To achieve this, the Lorentz coils must be placed where the fundamental harmonics of the field is dominant and the higher order harmonics can be negligible. With this, the coils should be sufficiently far from the magnet cylinder’s surface. However, how far the coils should be (from the magnet) is not clarified from the reported designs. To provide guidance on where to optimally place the Lorentz coils and to make the best use of the Halbach cylinders, there is a critical need for a simple but comprehensive analysis to find out all the field harmonics everywhere for both the ideal and segmented Halbach cylinders. This work is to provide that analysis.

Enhancing unilateral EMAT performance through topological optimization of Halbach permanent Magnet arrays

A novel unilaterally excited electromagnetic acoustic transducer (EMAT) is proposed as a solution to address the challenge of weak electromagnetic ultrasonic detection signals being susceptible to interference from clutter noise signals. EMAT employs Halbach permanent magnet array (HPMA) structure and a coil designed based on Huygens superposition principle. This design enables the generation and reception of highly directive Rayleigh surface waves in aluminum plates. To enhance the operational efficiency of EMAT while maintaining a high level of directivity for surface waves, a penalty function is implemented in COMSOL Multiphysics for the topological optimization of EMAT. The objective function in this optimization process is based on covariance (COV) of the magnetic induction intensity. The research results suggest that the homogeneity of the magnetic induction intensity within the coil region is enhanced by 50 % following topological optimization compared to the original design. The energy conversion efficiency of EMAT is enhanced by 5 times compared to traditional designs. The surface wave speed was determined to be 2631 m/s when measured at a frequency of 400 kHz. The value indicates a relative error of 6.37 % in comparison to the theoretical speed. The results indicate that EMAT has the capability to generate high-directional and pure Rayleigh waves.

Study on the Influences of an Outer-Coreless-Rotor Permanent Magnet Synchronous Machine Using Halbach Magnet Array

In order to evaluate the influences of the topology design of a Halbach Magnet Array (HA) on the performance of a motor, a PMSM with an outer coreless rotor using a Halbach Magnet Array (HAORPMSM) is proposed in this article. The design parameters of the HA could be separated into dividing methods per pole, magnet thickness, and initial magnetization direction angle. The phase Back-EMF under constant mechanical speed is chosen as the index to measure the performance of the motor. To start with, different dividing methods of the HA are evaluated. After that, the influence of thickness considering the utilization of the magnet is studied. Lastly, the relationship between initial magnetization direction and motor manufacturing is represented. The results show that the HA design meets the optimized performance considering the balance of the amount of magnet usage and manufacturing when using specific HA parameters.

Stochastic evaluation of quasi-zero stiffness magnetic spring using a reluctance-corrected analytical model

—In state of the art high-precision motion systems, which utilize magnetic levitation, a quasi-zero stiffness gravity compensation is one of the essentials to improve dynamic performance, eliminate position dependency and thus simplify controller design. Special configurations of permanent magnets, such as Halbach magnet arrays, can realize magnetic levitation as a form of magnetic spring. However, unlike conventional permanent magnet machines with large stiffness, the quasi-zero stiffness magnetic spring requires higher modeling accuracy for force estimation, which is affected by the nonlinear reluctance effect of permanent magnets. In this study, we propose an accurate magnetic modeling method for the quasi-zero stiffness magnetic spring. By correcting the reluctance effect of magnets, the proposed magnetic model achieves superior accuracy estimating levitation force and stiffness to the conventional surface current model. Using the reluctance-corrected magnetic model, tolerance analysis was performed to identify dominant geometric parameters affecting the uncertainty of the Halbach array magnetic spring performance. A Monte-Carlo simulation was used to estimate the overall tolerance of magnetic forces and stiffness. The experimental results fit in the tolerances.

Electromagnetic vibrational energy harvester with targeted frequency-tuning capability based on magnetic levitation

Electromagnetic vibrational energy harvester with targeted frequency-tuning capability based on magnetic levitation

Improving the homogeneity of Halbach arrays by optimizing magnet combinations using a genetic algorithm.

The purpose of this study was to test the effectiveness of using a genetic algorithm to find the optimal combination of permutations of permanent magnets in a Halbach magnet array in order to achieve the best magnetic field homogeneity in this work area. The test took place on a simple Halbach magnet array of 32 cubic permanent magnets. The magnetization of these magnets was preliminary assessed. Our calculations demonstrate that it is possible to achieve homogeneity of the magnetic field within the working area comparable to that of ideal identical magnetic blocks. Therefore, our study shows that combinatorics can be used to optimize homogeneity without selecting magnetic blocks, which can significantly reduce the cost of manufacturing the final structure.

Comparative Analysis and Design Optimization of Ferrite-Based Surface PM Vernier Machines

This paper presents the results of a comprehensive investigation into the comparative analysis and design optimization of ferrite-based surface permanent magnet vernier machines (SPMVMs). While SPMVMs boast a simple mechanical structure and enhanced torque density attributed to the flux modulation effect, they suffer from a persistent challenge of low power factor. Several factors hinder the adoption of low-cost ferrite magnets in SPMVMs. First, ferrite magnets are prone to irreversible demagnetization, constraining the allowable range of magnet thickness. Second, the reduced residual magnetic flux density of ferrite magnets exacerbates the decrease in power factor and machine efficiency. Thus, achieving optimal performance in ferrite-based SPMVMs necessitates the careful selection of various design parameters. To address these issues, this study employs a surrogate-based metaheuristic optimization algorithm with adaptive sampling to identify the optimal solution. Additionally, the integration of a Halbach array is explored to further enhance the performance of the three-slot/two-pole SPMVM topology. Subsequently, two ferrite-based SPMVM baseline models—one with a conventional SPM structure and another with a Halbach magnet array—are thoroughly designed, optimized, and subjected to detailed performance analysis using the 2D finite element method.

Modeling and Analysis of Short-Circuit Current for a Novel Dual Three-Phase Electric Machine With Mixed Iron-Pole Halbach Magnet Pattern

Modeling and Analysis of Short-Circuit Current for a Novel Dual Three-Phase Electric Machine With Mixed Iron-Pole Halbach Magnet Pattern

Low-field NMR with multilayer Halbach magnet and NMR selective excitation

This study introduces a low-field NMR spectrometer (LF-NMR) featuring a multilayer Halbach magnet supported by a combined mechanical and electrical shimming system. This setup offers improved field homogeneity and sensitivity compared to spectrometers relying on typical Halbach and dipole magnets. The multilayer Halbach magnet was designed and assembled using three nested cylindrical magnets, with an additional inner Halbach layer that can be rotated for mechanical shimming. The coils and shim-kernel of the electrical shimming system were constructed and coated with layers of zirconia, thermal epoxy, and silver-paste resin to facilitate passive heat dissipation and ensure mechanical and thermal stability. Furthermore, the 7-channel shim coils were divided into two parts connected in parallel, resulting in a reduction of joule heating temperatures from 96.2 to 32.6 °C. Without the shimming system, the Halbach magnet exhibits a field inhomogeneity of approximately 140 ppm over the sample volume. The probehead was designed to incorporate a solenoidal mini coil, integrated into a single planar board. This design choice aimed to enhance sensitivity, minimize B1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${B}_{1}$$\\end{document} inhomogeneity, and reduce impedance discrepancies, transmission loss, and signal reflections. Consequently, the resulting linewidth of water within a 3 mm length and 2.4 mm inner diameter sample volume was 4.5 Hz. To demonstrate the effectiveness of spectral editing in LF-NMR applications at 29.934 MHz, we selectively excited hydroxyl and/or methyl protons in neat acetic acid using optimal control pulses calculated through the Krotov algorithm.

A new radial quadrupole Nd2Fe14B Halbach ring for application in motor

A new Nd2Fe14B Halbach cylinder ring is fabricated by combining with magneto-mechanical molding and sintered process. It does not only exhibit larger surface magnetic flux density (ca.401mT), but also shows better magnetic field homogeneity comparing to spliced Halbach magnets (ca.324mT). Furthermore, performance of motor based on spliced and integrated Halbach magnet is also characterized and compared in detail. The power and torque of motor based on integrated Halbach magnet are effectively improved to be 20% and 9.4%, respectively. Moreover, the working efficiency of motor based on integrated Halbach magnet increases from 90% to 96% comparing to spliced Halbach magnet. These results do not only confirm formation of integrated Nd2Fe14B Halbach cylinder ring with high performance, but also provide a new method to improve performance of permanent magnet motor.

Development of a compact NMR system to measure pO2 in a tissue-engineered graft

Cellular macroencapsulation devices, known as tissue engineered grafts (TEGs), enable the transplantation of allogeneic cells without the need for life-long systemic immunosuppression. Islet containing TEGs offer promise as a potential functional cure for type 1 diabetes. Previous research has indicated sustained functionality of implanted islets at high density in a TEG requires external supplementary oxygen delivery and an effective tool to monitor TEG oxygen levels. A proven oxygen-measurement approach employs a 19F oxygen probe molecule (a perfluorocarbon) implanted alongside therapeutic cells to enable oxygen- and temperature- dependent NMR relaxometry. Although the approach has proved effective, the clinical translation of 19F oxygen relaxometry for TEG monitoring will be limited by the current inaccessibility and high cost of MRI. Here, we report the development of an affordable, compact, and tabletop 19F NMR relaxometry system for monitoring TEG oxygenation. The system uses a 0.5 T Halbach magnet with a bore diameter (19 cm) capable of accommodating the human arm, a potential site of future TEG implantation. 19F NMR relaxometry was performed while controlling the temperature and oxygenation levels of a TEG using a custom-built perfusion setup. Despite the magnet’s nonuniform field, a pulse sequence of broadband adiabatic full-passage pulses enabled accurate 19F longitudinal relaxation rate (R1) measurements in times as short as ∼2 min (R1 vs oxygen partial pressure and temperature (R2 > 0.98)). The estimated sensitivity of R1 to oxygen changes at 0.5 T was 1.62-fold larger than the sensitivity previously reported for 16.4 T. We conclude that TEG oxygenation monitoring with a compact, tabletop 19F NMR relaxometry system appears feasible.

An easy-built Halbach magnet for LF-NMR with high homogeneity using optimized target-field passive shimming method

The aim of this work is to develop a Halbach magnet that possesses characteristics such as easy-built, low cost and high homogeneity for use in a portable low-field NMR (LF-NMR) system. Considering portability, a 4-ring Halbach magnet was designed through simulation and mechanical modelling, which was successfully constructed in a general laboratory setting. The obtained field strength (B0) was 0.169 T, with an initial homogeneity of 8204 ppm within a sphere with a diameter of 20 mm. To enhance robustness, efficiency and effectiveness of shimming, an optimized target-field passive shimming method was proposed. Subsequently, the homemade spectrometer was used to run NMR experiments on the Halbach magnet. The 1H NMR linewidths of water samples became significantly narrower after passive shimming, e.g., the linewidth of a sample with a diameter of 3 mm and a length of 3 mm reduced from 452.3 Hz (62.5 ppm) to 12.9 Hz (1.8 ppm), which was much less than 102 Hz. The NMR results demonstrate that the proposed passive shimming method can achieve high homogeneity, and the developed Halbach magnet is capable of satisfying numerous LF-NMR applications.

An ultra-compact lightweight electromagnetic generator enhanced with Halbach magnet array and printed triphase windings

Electromagnetic generator (EMG) plays a pivotal role in in-situ power supply for low-power electronics. However, a major challenge associated with EMGs is the limited power density. To address this issue, various strategies have been proposed, including magnetic field augmentation of magnets, magnetic flux variation rate escalation at the coil, and structural miniaturization. In this study, we present an innovative ultra-compact electromagnetic generator (UL-EMG) in light weight that integrates the Halbach magnet arrays and printed circuit board (PCB) technologies. The UL-EMG incorporates a 12-layer printed triphase windings into its PCB stator, thereby upgrading both device compactness and output performance. To assess the performance of the UL-EMG, comprehensive bench tests were conducted. Interestingly, results indicate that at a low rotational speed of 200 rpm, the UL-EMG achieved a peak AC output power and power density of 54.9 mW and 1.25 kW/m3, respectively, representing a 22-fold expansion compared to conventional EMGs. Moreover, the UL-EMG exhibited exceptional output characteristics across a wide range of rotational speeds, significantly bolstering its capacity to drive various low-power electrical appliances. This study paves a novel path for heightening the power density of EMGs and highlights the promising application prospects of compact EMGs in in-situ power supply advancement.

A high-performance rotational electromagnetic energy harvester based on magnetic plucking: Design, simulation, and experiment

Harvesting rotational energy to supply low-powered electronic devices can optimize the whole power supply system layout. In this paper, we propose a high-performance rotational electromagnetic energy harvester and construct an electro-mechanical dynamic model. The harvester consists of the halbach magnet array (HMA), a radially magnetized cylindrical rotatable magnet, and a copper coil, respectively. The proposed energy harvester is tested in a rotating platform and the correctness of the mathematical model is verified by experimental results. As one of the important components of the harvester, the magnetic field characteristics of the HMA are simulated by the finite element method (FEM) and compared with other magnet arrangements. Additionally, the effect on output when the HMA is rotated individually has also been analyzed. Numerical and experimental results indicate that the rotational energy harvester also has an optimal speed, and the corresponding maximum output power decreases significantly with the increase of the distance between magnets. Numerical results indicate that the maximum power output can be obtained as 516.05 mW at 520 rpm, which is a pretty remarkable result. To verify practical application capability, a rectifier-stable circuit is constructed to light 54 LEDs in experiments.

Research of integrated shimming Halbach magnet for High strength, compact Benchtop NMR device

Due to production and assembly errors of magnets resulting in reduced magnetic field homogeneity, passive shimming (PS) is necessary when Halbach magnets are used in high-resolution Benchtop Nuclear Magnetic Resonance (BNMR) spectrometer. The conventional PS technique, which places independent PS devices inside the magnet aperture, is no longer applicable to small-aperture compact high-field-strength Halbach magnet studies. In this paper, based on spherical harmonic function expansion, we improve the magnetic field homogeneity by optimizing the moving step of the magnet moving arrays composed of Halbach magnets to generate the corresponding harmonic terms to compensate for the magnetic field. With this approach, the homogeneity of a 1 T Halbach magnet was improved from the original 3913 ppm to 8 ppm in a L10 mm × R2.5 mm of 0.64% copper sulfate doped water sample. This work explores the PS mechanism based on the movement of magnetic blocks, which can be applied in BNMR and other compact high-field strength high-homogeneity Halbach magnets application circumstances.