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 B0 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 B0 field is improved from 114.2 ppm to 26.9 ppm after using these shim coils.

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 coll＇s winding pattern, the selection of a penalty factor is discussed in detail.

Multi-objective optimization of gradient coil for benchtop magnetic resonance imaging system with high-resolution

Significant high magnetic gradient field strength is essential to obtaining high-resolution images in a benchtop mag- netic resonance imaging （BT-MRI） system with permanent magnet. Extending minimum wire spacing and maximum wire width of gradient coils is one of the key solutions to minimize the maximum current density so as to reduce the local heating and generate higher magnetic field gradient strength. However, maximum current density is hard to optimize together with field linearity, stored magnetic energy, and power dissipation by the traditional target field method. In this paper, a new multi-objective method is proposed to optimize the maximum current density, field linearity, stored magnetic energy, and power dissipation in MRI gradient coils. The simulation and experimental results show that the minimum wire spacings are improved by 159% and 62% for the transverse and longitudinal gradient coil respectively. The maximum wire width increases from 0.5 mm to 1.5 mm. Maximum gradient field strengths of 157 mT/m and 405 mT/m for transverse and lon- gitudinal coil are achieved, respectively. The experimental results in BT-MRI instrument demonstrate that the MRI images with in-plane resolution of 50 ~tm can be obtained by using the designed coils.

A novel approach to designing cylindrical-surface shim coils 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 cylin- drical 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.

Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils

The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows： 1） the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2） the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3） the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180°, there are two additional reverse concentrative areas on both sides of x axis.

General analytical method of designing shielded coils for arbitrary axial magnetic field

Magnetic coils for specific requirements are widely used in modern quantum physics. In this study, a general analytical method of designing the shielded coils for generating an arbitrary axial magnetic field is proposed. The theoretical formula for an axial magnetic field generated by a single shielded coil is obtained and used to construct specific coils. The structural parameters of these coils are determined by fitting the theoretical formula with their specific requirements. The feasibility of this method is proved by realizing four concrete kinds of coils: uniform magnetic field generating coils, gradient magnetic field generating coils, asymmetrical uniform magnetic field generating coils, and parabolic magnetic field generating coils. The correctness of these theoretical results is demonstrated by both the finite element simulations and the relevant experimental results. Furthermore, the application of this method is of great significance for developing the quantum physics and quantum devices in future.

Method of measuring rotation speed of high spinning projectile based on plane magnetic induction coil

For the test of rotation speed of high spinning projectile, the general formula of the motional electromotive force （MEMF） of planar magnetic induction coil （PMIC） is derived in case of 3D rotation in a stable magnetic field. Under a reasona-ble assumption, the MEMF of PMIC is simplified after the aforementioned general formula is used to calculate high spinning PMIC in the geomagnetic field environment. The determination approach of half-cycle is discussed and the method of rotation speed test is studied, and a test is conducted in the paper. The rotation speed curve obtained by the approach in this paper is consistent with the curve by telemetry.

Design of new resonant magnetic perturbation coils on the J-TEXT tokamak

The resonant magnetic perturbation(RMP)system is a powerful auxiliary system on tokamaks.On the J-TEXT tokamak,a set of new in-vessel coils is designed to enhance the amplitude of the RMP.The new coils are designed to be two-turn saddle coils.These two-turn saddle coils have been optimized in terms of their structure,support,and protection components to overcome the limitations of the narrow in-vessel space,resulting in a compact coil module that can be accommodated in the vessel.To verify the feasibility of this design,an electromagnetic simulation is performed to investigate the electrical parameters and the generated field of the coils.A multi-field coupled simulation is performed to investigate the capacity of heat dissipation.As a result of these efforts,the new RMP coils have been successfully installed on the J-TEXT tokamak.It has significantly enhanced the RMP amplitude and been widely applied in experiments.

Stress and Thermal Analysis of the In-Vessel Resonant Magnetic Perturbation Coils on the J-TEXT Tokamak

A set of four in-vessel saddle coils was designed to generate a helical field on the J- TEXT tokamak to study the influences of the external perturbation field on plasma. The coils are fed with alternating current up to 10 kA at frequency up to 10 kHz. Due to the special structure, complex thermal environment and limited space in the vacuum chamber, Jt is very important to make sure that the coils will not be damaged when undergoing the huge electromagnetic forces in the strong toroidal field, and that their temperatures don＇t rise too much and destroy the in- sulation. A 3D finite element model is developed in this paper using the ANSYS code, stresses are analyzed to find the worst condition, and a mounting method is then established. The results of the stress and modal analyses show that the mounting method meets the strength requirements. Finally, a thermal analysis is performed to study the cooling process and the temperature distribution of the coils.

Effect of power parameter and induction coil on magnetic field in cold crucible during continuous melting and directional solidification

Bottomless electromagnetic cold crucible is a new apparatus for continuous melting and directional solidification;however,improving its power efficiency and optimizing the configuration are important for experiment and production.In this study,a 3-D finite element (FE) method based on experimental verification was applied to calculate the magnetic flux density (Bz).The effects of the power parameters and the induction coil on the magnetic field distribution in the cold crucible were investigated.The results show that higher current intensity and lower frequency are beneficial to the increase of Bz at both the segment midpoint and the slit location.The induction coil with racetrack section can induce greater Bz,and a larger gap between the induction coil and the shield ring increases Bz.The mechanism for this effect is also discussed.

Design of a Rogowski Coil with a Magnetic Core Used for Measurements of Nanosecond Current Pulses

A Rogowski coil is developed to detect the nanosecond pulse signals of the discharge current with a wide bandwidth of 800 kHz to 106 MHz and high sensitivity of 2.22 V/A. Performance tests show that the Rogowski coil has both excellent dynamic and static characteristics. Calibrating results and the comparison between the standard current shunt and the developed Rogowski coil for the measurement of nanosecond discharge pulses demonstrate that the developed Rogowski coil can reproduce the actual waveform of the discharge current accurately.

AN EFFICIENT RF COIL FOR GENERATING A CIRCULAR POLARIZED MAGNETIC FIELD

The configuration, magnetic field calculation and field distribution of the birdcage RF coil is pre-sented. This type of coil can produce a circular Polarized magnetic field. It has been widely used in the MRIsystem for head and whole-body imaging which can achive nearly optimal RF field uniformity and signal-to-noise ratio(SNR). The rnagnetic field is evenly distributed over the coil. The features of the birdcage coil areanalyzed on the basis of numerical simulation and experimental studies.

Study on a New High Frequency Moving Coil Permanent Magnet Linear Motor

In order to improve the characteristics of a conventional moving coil permanent magnet linear motor （MCPMLM）, such as weak points on export force, response time, response speed, we studied a permanent magnet （PM） structure that is a key component of MCPMLM. Different magnetization techniques of single PM and differ- ent array structures of multiple PMs are compared, and a new MCPMLM magnetized along the external field force lines wing eight pieces of a tegular Halbach magnet array with air gaps is proposed as well. The analysis on magnetic field and experimental results of MCPMLM demonstrates that the force between the coil and the PM increases by more than 40%. The simulation frequeney is close to 350 Hz at -3 dB , and the response time is O. 005 s. In addition, the experiment frequency reaches 300 Hz at -3 dB and the response time is 0. 004 s, which agrees well with the simulation results. It means that the developed MCPMLM enjoys advantages in high frequency and rapid response, and can satisfy the requirements of a high speed electro-hydraulic proportional valve.

Distribution of Electromagnetic Force of Square Working Coil for High-Speed Magnetic Pulse Welding Using FEM

Magnetic pulse welding process, one of high speed welding processes, uses electromagnetic force from discharged current through a working coil which develops a repulsive force between the induced currents flowing parallel and in the opposite direction in the pipe to be welded. For achieving the successful weldment and using this process, the design of working coil is the most important factor, because working coil has to generate a high-intensity magnetic field on the surface of the workpiece during the process. Therefore, the objective of this study is to analyze the distribution of electromagnetic force of square working coil for magnetic pulse welding. For this, FE-model has been developed to analyze the distribution of electromagnetic force;after that, distribution of electromagnetic force, results of numerical analysis and experimental results for verifying the developed FE-model were compared. A 3-dimensional electromagnetic FE-model has been developed using a general commercial computer program, ANSYS/EMAG code. The shape and material of square working coil were decided through literature surveys. For the experiment, an MPW equipment W-MPW manufactured by WELDMATE Co., Ltd. was employed;also the materials were the Al 1070, SM45C for Al and Steel square pipe and rod respectively. After the experiment, leakage test was used to verify the weldability. Also weld joints were observed on longitudinal cross-section by microscope. The electromagnetic force generated was the greatest one at the center adjacent to square working coil, decreasing as moving into the edge. As the result of Al/Steel welding experiment, weldment of square Al pipe was not completed at the corner of weldment. These results are similar to the output data from developed electromagnetic FE-model where electromagnetic force decreases as moving into the corners of square working coil.

Modeling of Stochastic Magnetic Perturbation by RWMEF-Coils on NSTX

A 3-D field line integration code, TRIP3D has been modified to model stochastic magnetic perturbation produced by a resistive wall mode, error field （ RWMEF ） coil in the NSTX tokamak with very low aspect ratio. The RWMEF-coil has two turns, which may produce stochastic fields with the toroidal mode number of n = 1 or 3. In this study, it is found that the stochastic field of n = 3 is larger than that of n=-1 for the same coil current. Two divertor discharges with lower single null （ LSN ） and double null （ DN ） configurations in the NSTX have been modeled with different RWMEF-coil currents and toroidal modes.

Analytic calculation of magnetic force between two current-carrying coils

Current-carrying coils are basic elements in electromagnetic equipments, for example, in high field magnets from high temperature superconducting wires or tapes. In the assembly of these systems and their current-carrying operation, unavoidable mis- alignment and shift from the original position can be induced by disturbances such as the imbalance of magnetic force due to safety problems. For two current-carrying coils with non-coplanar axes, the analytic expression of the magnetic force between the two coils is presented according to the rule of Ampere circulation and the Biot-Savart law. Based on the expression, the dependence of the magnetic force on the size and the relative position of each other is further investigated, and the variation of the magnetic force is obtained with the above parameters.

A novel radio frequency coil for veterinary magnetic resonance imaging system

In this article, a novel designed radio frequency （RF） coil is designed and built for the imaging of puppies in a V-shape permanent magnetic resonance imaging （MRI） system. Two sets of Helmholtz coil pairs with a V-shape structure are used to improve the holding of an animal in the coil. The homogeneity and the sensitivity of the RF field in the coil are analysed by theoretical calculation. The size and the shape of the new coil are optimized and validated by simulation through using the finite element method （FEM）. Good magnetic resonance （MR） images are achieved on a shepherd dog.

Current-Bounded Commutation of a Long-Stroke Magnetically Levitated Stage with Moving Coils

Magnetically levitated stages（MLS） have potentials to obtain good motion performances in high vacuum environment. Yet the electromagnetic forces/torques corresponding to six degrees of freedom（DOF） motions have coupling relationship with each current of coil array, and this coupling is still associated with the relative positions between the mover and the stator of the stage. So it is quite difficult to control the 6-DOF motions of the stage. By reasonable commutation of coil array, this complicated coupling relationship can be decoupled. The analytical force/torque-decomposing model of the stage is established first. Then the initial currents of coil array are commutated based on the pseudo inverse of the analytical force/torque-decomposing model matrix. And then the coil array currents are commutated again with different current bounds given to the initial currents as well as in the sense of minimum 2-norm of currents vector. Using the long stroke magnetically levitated stage with moving coils under investigation as examples, the currents of coil array are commutated with different current bounds adopting the proposed commutation method, the determination of current bound and the current bounds＇ influences on the heat-losses in coil array are analyzed, and the effectiveness of implementation algorithm of proposed commutation method is discussed. Simulation, analysis and discussion results indicate that the currents of coil array within the given current bound can be solved analytically by proposed commutation method, and the implementation algorithm does not need any searching or iteration. By the current-bounded commutation method proposed, the amplitude of coil array currents can be limited within an appropriate current bound（This is very beneficial to the improvement of the reliability and motion performance of the stage）, as well as these currents can also generate the desired forces and torques.

Finite Element Based Analysis of Magnetic Forces between Planar Spiral Coils

This paper elaborates on the magnetic forces between current carrying planar spiral coils. Direct and concentric rings methods are employed in order to calculate the magnetic force between these coils. The results obtained by two calculation methods show the efficiency of the replaced rings method in both simplicity and calculation time. Simula-tions using the Finite Element Method (FEM) are carried out to analyze the distribution of the magnetic flux density around the coils. Also, coils with precise size have been constructed and tested. The experimental results as well as the results obtained by FEM are used to validate the accuracy of the calculations.

Recent Advances in ^(19)Fluorine Magnetic Resonance Imaging with Perfluorocarbon Emulsions

The research roots of 19fluorine （19F） magnetic resonance imaging （MRI） date back over 35 years. Over that time span, 1H imaging flourished and was adopted worldwide with an endless array of applications and imaging approaches, making magnetic resonance an indispensable pillar of biomedical diagnostic imaging. For many years during this timeframe, 19F imaging research continued at a slow pace as the various attributes of the technique were explored. However, over the last decade and particularly the last several years, the pace and clinical relevance of 19F imaging has exploded. In part, this is due to advances in MRI instrumentation, ~gF/1H coil designs, and ultrafast pulse sequence development for both preclinical and clinical scanners. These achievements, coupled with interest in the molecular imaging of anatomy and physiology, and combined with a cadre of innovative agents, have brought the concept of ~gF into early clinical evaluation. In this review, we attempt to provide a slice of this rich history of research and development, with a particular focus on liquid perfluorocarbon compound-based agents.