Magnetic Coil Optimization for Quadrupole-Stabilized Mirror Systems

A numerical technique is presented to optimize the design of quadrupole magnetic coil systems, such as presently used in tandem mirror fusion experiments. The optimization is carried out with respect to various plasma physics properties (e.g., MHD stability and reduced radial transport of particles) which depend on the magnetic field geometry. The coils are treated as filaments of infinitesimal thickness and the magnetic field is computed in the paraxial limit. Constraints on the coil shape and on the magnetic geometry can be incorporated into the method. It is demonstrated that coil solutions can be found which match given paraxial field profiles or which directly minimize a scalar functional of these profiles. As an interesting application of the latter technique, a filamentary coil design for a nearly omnigenous anchor is obtained.     

平板型感应耦合等离子体源的线圈配置对功率耦合效率的影响

基于感应耦合等离子体的变压器模型，分析了感应耦合等离子体的功率耦合效率与线圈配置(几何尺寸、电学参量)及等离子体基本参量(等离子体电子密度、电子-中性粒子有效碰撞频率)之间的关系；然后，改变平板型线圈的匝数从而改变了线圈的几何尺寸、电学参量，并且测量出了不同的线圈所对应的功率耦合效率.实验结果表明，线圈的电感量是能否实现放电的决定性因素；而功率耦合效率则与感应线圈的Q值、放电参量(气压、功率)等密切相关，射频输入功率的增加、放电气压的上升都会导致感应耦合等离子体耦合效率的提高，这与感应耦合等离子体的变压器模型预测结果是符合的. 然而，变压器模型给出的提高线圈Q值可导致耦合效率增强的预测结果仅适用于同等电感量的线圈条件. 本文对于单线圈的感应耦合等离子体源的研究为线圈的优化设计甚至大面积的多线圈感应耦合等离子体源研制提供了理论依据. 关键词： 感应耦合等离子体 功率耦合效率 变压器模型     

Eliminating islands in high-pressure free-boundary stellarator magnetohydrodynamic equilibrium solutions

Magnetic islands in free-boundary stellarator equilibria are suppressed using a procedure that iterates the plasma equilibrium equations and, at each iteration, adjusts the coil geometry to cancel resonant fields produced by the plasma. The coils are constrained to satisfy certain measures of engineering acceptability and the plasma is constrained to ensure kink stability. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible. The method is applied with success to a candidate plasma and coil design for the National Compact Stellarator Experiment [Phys. Plasmas 8, 2083 (2001)]].     

Short planar gradient coils for MR microscopy using concentric return paths

The aim of this work is to design a set of gradient coils with an optimal geometry for magnetic resonance microscopy studies. Designs for a three-axis gradient coil system particularly suited for studies with small radiofrequency coils are presented. The novel geometry involves a planar section with concentric return paths to keep the coil short. Reduction of the external field has been attempted by varying the positions of the return paths using a simulated annealing algorithm. A biplanar version of x- and z-directed prototype gradients was built and tested. A 2D-MR image of a grid phantom has been obtained on a 7-T MR instrument to demonstrate the theory. A three-axis set used as a surface gradient set has also been built and used to obtain high-resolution MR images.     

Sample-Induced Resistance Estimation in Magnetic Resonance Experiments: Simulation and Comparison of Two Methods

Signal-to-noise ratio estimation in magnetic resonance experiments requires the knowledge of sample-induced resistance value, where the sample can be protein solutes, cell suspensions, plants, animals, portions of human body or saline solution phantoms. Many authors studied sample–coil interaction using homogeneous infinitely long cylinders, spheres or half-space as approximations of the sample geometry. However, in real magnetic resonance experiments, both sample shape and dimensions can be very different with respect to these models. This paper describes and compares two different methods developed by the authors for sample-induced resistance estimation, both useful for predicting the performance of radio-frequency coils strictly coupled to the sample, where the knowledge of a sample–coil interaction model permits to estimate the different noise contributors. The main goal of our research is testing the proposed algorithms and finding their limitations by comparing their performances for a simple case which uses a sample simplified geometry. The first method, based on the magnetostatic approach, employs vector potential calculation and can be easily implemented for simple coils and sample geometries. The second method uses finite-difference time-domain algorithm and permits to simulate systems with various geometries, without approximations in sample and coil geometries. Comparison with experimental data, performed on three homebuilt surface coils each of them successively tuned at three different frequencies, demonstrated the differences in accuracy of the developed methods.     

Determination of current distribution in EM gun armature by leastsquares fitting of BSi (small-induction) coilvoltage

The electromagnetic (EM) plasma rail-gun current distribution was determined by fitting (using the method of least squares) the voltage induced on small induction (B_Si) coils to a derived function model. The voltage function model was derived using the Biot-Savart equation. The model was derived assuming that the current flowed in sheets perpendicular to the rails. The sheets of currents varied in time and in the rail direction but were assumed to be constant (at a given time) perpendicular to the bore direction. The plasma current distribution in the bore direction, the initial length, and expansion characteristics of the plasma were determined from B _Si coil voltage measurements taken at short time increments. Fitted parameters correlate well with measurements taken by other sensors     

A Novel Magnetic Resonance Phased-Array Coil Designed with FDTD Algorithm

Radio-frequency receiver phased-array coils in magnetic resonance imaging systems are used to pick up the signals emitted by the nuclei with high signal-to-noise ratio and a large region of sensitivity. Since the quality of obtained images strongly depends upon the correct choice of the coil geometry and position, array coils have to be designed by minimizing the mutual interaction among nearby coil elements and this is generally achieved by overlapping such adjacent elements. In this paper, we describe the use of a numerical solver based on finite-difference time-domain method to determine the optimal overlap distance, which guarantees the maximum decoupling level between the coil loops, for array coils constituted by various geometry elements. A novel array coil was designed, constituted by a couple of elliptical geometry elements in “folding” version around the animals’ spine curvature, for small animals’ imaging applications.     

短腔、自屏蔽磁共振成像超导磁体系统的混合优化设计方法

本文提出一种用于短腔、自屏蔽磁共振成像超导磁体系统的混合优化设计方法,通过结合线性规划和非线性优化算法,设计出的磁体系统具有建造成本低、结构简单、以及线圈中最高磁场、电流安全裕度和电磁应力可控等优点.首先,通过线性规划算法在欲布置线圈空间范围内建立二维连续网格划分,搜索满足磁场约束条件的网格电流分布图;其次,将电流分布图中的非零电流簇离散成螺线管线圈,通过非线性优化算法计算出满足成像区域磁场均匀度要求、5 Gs杂散场限制、线圈中最高磁场限制、电流安全裕度以及线圈间尺寸间隔等约束条件的线圈结构参数.文中给出一个中心磁场为1.5T自屏蔽磁共振成像超导磁体系统的设计案例,在50 cm球形成像区域所产生的磁场峰峰值不均匀度为10 ppm,线圈最大长度为1.32 m.该设计方法可用于对称、非对称螺线管线圈系统以及开放式双平面线圈系统的磁共振成像磁体系统设计.     

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.     

Investigation of high-resolution functional magnetic resonance imaging by means of surface and array radiofrequency coils at 7 T

In this investigation, high-resolution, 1×1×1-mm³ functional magnetic resonance imaging (fMRI) at 7 T is performed using a multichannel array head coil and a surface coil approach. Scan geometry was optimized for each coil separately to exploit the strengths of both coils. Acquisitions with the surface coil focused on partial brain coverage, while whole-brain coverage fMRI experiments were performed with the array head coil. BOLD sensitivity in the occipital lobe was found to be higher with the surface coil than with the head array, suggesting that restriction of signal detection to the area of interest may be beneficial for localized activation studies.     

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.     

Design of small-scale gradient coils in magnetic resonance imaging by using the topology optimization method

A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy. Unlike the popular stream function method, the proposed method has design variables that are the distribution of conductive material. A voltage-driven transverse gradient coil is proposed to be used as micro-scale magnetic resonance imaging(MRI) gradient coils, thus avoiding introducing a coil-winding pattern and simplifying the coil configuration. The proposed method avoids post-processing errors that occur when the continuous current density is approximated by discrete wires in the stream function approach. The feasibility and accuracy of the method are verified through designing the z-gradient and y-gradient coils on a cylindrical surface.Numerical design results show that the proposed method can provide a new coil layout in a compact design space.     

核磁共振高信噪比弱信号检测的理论与实验研究

基于小型射频线圈的核磁共振检测探头在波谱分析和成像研究中具有广泛的应用,如化学位移波谱分析、磁共振成像和勘探测井等技术领域。但是,由于外加静磁场作用下,自旋体系发生塞曼能级分裂后,高低能态之间的核自旋数量之差很小,普遍存在检测信噪比很低的问题,而且初级磁共振接收信号的质量受所用探头线圈电气参数的影响较大。研究结果表明,在特定的被测样品和接收线圈占空比以及静磁场等条件不变的情况下,检测信噪比与单位电流产生的射频磁场成正比,而与线圈高频电阻的平方根成反比。在永磁0.39Tesla主磁场条件下,研究了趋肤效应影响下小型螺线管线圈几何参数的优化设计方法。理论仿真和实际的测量结果表明,几何参数为线径0.5 mm、直径5.5 mm的10匝微螺线管线圈,在16.9 MHz谐振频率上,相对信噪比取得一个极大值点,对应的Q值约为199.8,与阻抗分析仪测得结果有较好的吻合,验证了该核磁共振检测线圈设计新方法是合理的。本文提出的基于线圈电磁特性的高信噪比检测探头设计方法,可推广到目前的质子密度成像、岩心弛豫谱分析等应用中。     

New approaches on application of multipole moments for determination of toroidal plasma shift

An application of multipole moments for the determination of toroidal plasma column shift is presented. First, we present analytical details for using this technique. Then, the principle of different models based on this technique for design and fabrication of a six coils will be presented: four modified Rogowski coils (two cosine coils and two sine coils) and two saddle coils (saddle sine coil and saddle cosine coil). As continuous measurements of magnetic field distribution around the toroidal plasma can be made using these coils, this technique is a good method for the determination of toroidal plasma column shift.     

Design of a capacitively decoupled transmit/receive NMR phased array for high field microscopy at 14.1T

A design is presented for a "phased array" of four transmit/receive saddle-geometry volume coils for microimaging at 600 MHz within a 45 mm clear-bore vertical magnet. The small size of the coils, approximately 10 mm in length, and high frequency of operation both present considerable challenges for the design of a phased array. The particular design consists of four saddle coils, stacked vertically, in order to produce an array suitable for imaging samples, typical of many microimaging studies, with a large length:diameter ratio. Optimal coil overlap is used to reduce the mutual inductance between adjacent coils, and capacitive networks are used to maximize the isolation between all of the coils. Standard 50 Omega input impedance preamplifiers are used so that the preamplifiers do not have to be integrated directly into the probe. Isolation between coils was better than 20 dB for all coil pairs. An increase in signal-to-noise of 70 +/- 3% was achieved, averaged over the whole array, compared to a single coil of the same dimensions. High resolution phased array images are shown for ex vivo tissue samples.     

基于Pareto优化理论的多目标超椭梯度线圈设计

磁共振系统梯度线圈设计是一个多目标优化问题,在设计时需要综合考虑能耗、磁场能、线性度等设计要求.这些设计要求通常难以同时获得极小解,因此在设计梯度线圈时需要权衡线圈的各方面的设计需求.本文基于柱面可展性和流函数设计方法,结合Pareto优化方法实现了在超椭圆柱设计表面上梯度线圈的多目标设计.分别分析了磁场能、能耗目标对梯度线圈线性度、线圈构型的影响;并在Pareto解空间中分析各目标的相互变化关系,通过数值算例验证了该方法在超椭梯度线圈设计时的有效性与灵活性.优化结果显示,在满足线性度误差小于5%,能耗与磁场能分别小于用户设定值的设计约束下,梯度线圈的多目标设计存在多个局部优化解.该方法可以直观地比较相同目标函数值的情况下各单目标的具体表现,有利于实现不同的设计要求下梯度线圈的最终定型设计.     

Low-Field MR Coils: Comparison between Strip and Wire Conductors

This work describes how the cross-sectional shape of radio-frequency coil conductors affects coils performance. This is of particular importance at low Larmor frequencies such as those of low-field magnetic resonance imaging systems where conductor and capacitor losses are the dominant power dissipation mechanisms. We demonstrate that conductors having a circular cross section allow the coil to achieve significantly better performance than the one built using flat strips. The change in coil quality factor due to conductor geometry was verified to be due only to changes in the conductors’ resistance and not their inductance. The results are not limited to low-field proton imaging but they are equally applicable to other situations where the Larmor frequency is in the megahertz range, including nuclear magnetic resonance of other nuclear species at intermediate fields.     

A design methodology for short,whole-body,shielded gradient coils for MRI

A series of designs is presented for restricted length, whole-body, shielded gradient coils. By using the real space optimization technique, simulated annealing (SA), it is possible to produce viable gradient sets with a length-to-diameter ratio (LDR) of just 1.0. Radially remote return paths for the transverse coils aid in producing such short coils. While the linear regions of such coils cannot be as large as longer coils, they produce homogeneous linear regions suitable for use in whole-body imaging. The coil sets are well shielded even at such small LDRs.     

Modified birdcage coils for targeted imaging

The design of a radiofrequency coil of U-shaped geometry, specifically intended to image individual knuckle joints of the hand, has been investigated. The coil geometry is that of a “split and opened” birdcage coll. The optimum leg positions for such a U-shaped coil have been theoretically predicted using a novel technique that considers both the signal-to-noise ratio and the homogeneity of the field-of-view. Two particular coils of this type have been constructed, each optimum for a different size of image space and assuming a different source of image noise (sampledominated or coil-dominated). The experimentally determined radiofrequency fields produced by the coils correspond well to theory. Either coil can be used to obtain good-quality, high-resolution (130 μm × 130 μm in-plane) images in vivo of the first, second, or fifth metacarpophalangeal joints of the hand, sites of particular interest in the study of arthritis.