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.     

Levitation performance of the magnetized bulk high-Tc superconducting magnet with different trapped fields

To a high-T_c superconducting (HTS) maglev system which needs large levitation force density, the magnetized bulk high-T_c superconductor (HTSC) magnet is a good candidate because it can supply additional repulsive or attractive force above a permanent magnet guideway (PMG). Because the induced supercurrent within a magnetized bulk HTSC is the key parameter for the levitation performance, and it is sensitive to the magnetizing process and field, so the magnetized bulk HTSC magnets with different magnetizing processes had various levitation performances, not only the force magnitude, but also its force relaxation characteristics. Furthermore, the distribution and configuration of the induced supercurrent are also important factor to decide the levitation performance, especially the force relaxation characteristics. This article experimentally investigates the influences of different magnetizing processes and trapped fields on the levitation performance of a magnetized bulk HTSC magnet with smaller size than the magnetic inter-pole distance of PMG, and the obtained results are qualitatively analyzed by the Critical State Model. The test results and analyses of this article are useful for the suitable choice and optimal design of magnetized bulk HTSC magnets.     

The permanent magnet systems generating strong stray fields with large localization region

Three systems of permanent magnets, which produce strong magnetic stray fields (SFs) with H>B_r=4πM_r were studied in this work. Remarkable feature of the developed systems is localization of the strong fields in large region with linear dimension Δr comparable to characteristic magnet dimension a. The first system composed of uniformly magnetized magnets generates sufficiently homogeneous strong SFs, which amounts up to 1.5 of magnets induction B_r. The second system with nonuniform magnetization is represented by cylindrical and hemispheric magnets their magnetization vector directed at every point along the radius. Such distribution of magnetization is assumed to be the consequence of magnet radial crystal texture resulting in a high uniaxial anisotropy field H_K. It is shown that maximal SFs can exist on the flat surface of cylindrical magnet at the distance r from its axis and their limiting value equals to 4πM_r ln(2a/r). Here, the localization region of the fields is comparable to diameter of cylindrical magnet Δr≈2R. As for the hemisphere its SFs are less than corresponding SFs for the cylinder. The third so-called quasi-nonuniform system consists of uniformly magnetized cylindrical sectors their magnetization vector is directed along the sector bisectrix. The strong SFs and their localization region are calculated in details for this case. The passage to radial magnetized cylinder is considered.     

Magnetic guns with cylindrical permanent magnets

The motion of a cylindrical permanent magnet (projectile) inside a tubular permanent magnet, with both magnets magnetized axially, illustrates nicely the physical principles behind the operation of magnetic guns. The force acting upon the projectile is expressed semi-analytically as derivative of the magnetostatic interaction energy. For comparison, the forces involved are also calculated numerically using finite elements methods. Based on the conservation of the magnetostatic and kinetic energies, the exit and asymptotic velocities are determined. The derived formulas can be used to optimize the generated forces and motion of the inner cylindrical magnet.     

Angular dependence of vertical force and torque when magnetic dipole moves vertically above flat high-temperature superconductor

The interaction between a permanent magnet (PM) assumed as a magnetic dipole and a flat high-temperature superconductor (HTS) is calculated by the advanced frozen-image model. When the dipole vertically moves above the semi-infinite HTS, the general analytical expression of vertical force and that of torque are obtained for an arbitrary angle between the magnetization direction of the PM and the c axis of the HTS. The variations of the force and torque are analyzed for angle and vertical movements in both zero-field cooling (ZFC) condition and field cooling (FC) condition. It is found that the maximum vertical repulsive or attractive force has the positive or negative cosine relation with the angle. However, the maximum torque has the positive or negative sine relation. From the viewpoint of the rotational equilibrium, the orientation of the magnetic dipole with zero angle is deemed to be an unstable equilibrium point in ZFC, but the same orientation is considered as a stable equilibrium point in FC. In addition, both of the variation cycles of the maximum force and torque with the angle are π.     

Structure and magnetic field of periodic permanent magnetic focusing system with open magnetic rings

The magnetic field along the central axis for an axially magnetized permanent magnetic ring was investigated by analytical and finite element methods. For open magnetic rings, both calculated and measured results show that the existence of the radial magnetic field creates a remarkable cosine distribution field along the central axis. A new structure of periodic permanent magnet focusing system with open magnetic rings is proposed. The structure provides a satisfactory magnetic field with a stable peak value of 120 mT for a traveling wave tube system.     

STUDIES OF THE FIELD DISTRIBUTION OF THE MODULATING WIDTH MULTIPOLE PERMANENT MAGNETS

In this paper,the magnetic field distribution of the modulating width multipole permanent magnets is analyzed. Only radially magnetized permanent magnet segments are used and the required magnetic field is formed by modulating the widths of the segments in this project. In 2-dimensional ideal case pure 2N-pole magnetic field can be formed. The spatial expressions of the scalar potential for the ideal and real 2-dimensional cases are given. And the methods for reducing the undesirable higher harmonics of the magnetic field in the real case are also discussed.     

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.     

Synthesis of magnetic systems producing field with maximal scalar characteristics

A method of synthesis of the magnetic systems (MSs) consisting of uniformly magnetized blocks is proposed. This method allows to synthesize MSs providing maximum value of any magnetic field scalar characteristic. In particular, it is possible to synthesize the MSs providing the maximum of a field projection on a given vector, a gradient of a field modulus and a gradient of a field energy on a given directing vector, a field magnitude, a magnetic flux through a given surface, a scalar product of a field or a force by a directing function given in some area of space, etc. The synthesized MSs provide maximal efficiency of permanent magnets utilization. The usage of the proposed method of MSs synthesis allows to change a procedure of projecting in principal, namely, to execute it according to the following scheme: (a) to choose the sizes, a form and a number of blocks of a system proceeding from technological (economical) reasons; (b) using the proposed synthesis method, to find an orientation of site magnetization providing maximum possible effect of magnet utilization in a system obtained in (a). Such approach considerably reduces a time of MSs projecting and guarantees maximal possible efficiency of magnets utilization. Besides it provides absolute assurance in “ideality” of a MS design and allows to obtain an exact estimate of the limit parameters of a field in a working area of a projected MS.The method is applicable to a system containing the components from soft magnetic material with linear magnetic properties.     

Improvement of a magnetization method on a small-size superconducting bulk magnet system

A pulsed-filed magnetization (PFM) is an important technique for industrial applications of superconducting bulk magnets, and several advanced PFM methods are proposed to enhance the trapped field. In the well-known IMRA method, the channel through the magnetic flux is formed by the flux flow caused by heat generation when applying the strong pulsed-field, and the magnetic flux is made to penetrate into the bulk through the channel in the following pulse application. On the other hand, large applied field leads to large heat generation, and, therefore, the trapped field is decreased greatly.This paper proposes an effective magnetizing method in which the channel composed of magnetic field is artificially formed by field-cooling (FC) using a permanent magnet and the magnetic flux by PFM is induced to the channel. To confirm the validity of this method, the bulk was magnetized by FC using Nd–Fe–B magnets of the rectangular and the ring shapes, and thereafter, a pulsed-field of 6.2 T was applied. As a result, the trapped field of the bulk magnetized by FC using the ring magnet was increased by about 20–25% as compared with that of the conventional PFM, and, moreover, it was observed that the channel was formed partially by measurement of the magnetic field distribution.     

Performances and design of ironless loudspeaker motor structures

This paper presents several kinds of structures of ironless loudspeaker motors. The proposed devices go from simple structures, in terms of manufacturing process, to structures in which the magnet rings can be stacked, with different magnetization directions or values. The structures are studied and compared according to their created induction level and uniformity across the coil displacement range, which are directly linked to the loudspeaker performances (force factor). The model used is the coulombian model of magnets to calculate the magnetic field created, therefore all the calculations are analytical. The paper shows that no structure is universal when it comes to the loudspeaker design: some are well adapted to micro displacements of the coil while other structures are adapted to large displacements.     

An Efficacious Target-Field Approach to Design Shim Coils for Halbach Magnet of Mobile NMR Sensors

The main magnetic fields of mobile nuclear magnetic resonance (NMR) magnets differ from those of conventional NMR and magnetic resonance imaging (MRI) magnets. In the Halbach magnet, the main field B ₀ is perpendicular to the longitudinal axis, the symmetry of the current distribution with respect to the symmetry of the magnetic field differs from that in conventional target-field applications, and the current distribution on the coil surface cannot be expressed in terms of periodic basis functions. To obtain the winding pattern of the coil, an efficacious target-field approach. The surface of a coil is divided into small discrete elements, where each element is represented by a magnetic dipole. From the stream function of the elements, the resultant magnetic field is calculated. The optimization strategy follows an objective function defined by the power dissipation or efficiency of the coil. This leads to the optimum stream function on the coil surface, whose contour lines define the winding patterns of the coil. This paper shows winding patterns designed of shim coils for Halbach magnet and illustrates the craft of a shim coil using flexible printed circuit board. The performance of the coils is verified by simulating the fields they produce over the sensitive volume.     

辅助永磁体厚度对单畴GdBCO超导体捕获磁场分布及其磁悬浮力的影响

研究了两种磁悬浮系统组态中圆台形辅助永磁体厚度对高温超导体捕获磁场和超导磁悬浮力的影响。结果表明,圆台形辅助永磁体的下表面和GdBCO超导体上表面同处在一个水平面上,磁化用圆台形辅助永磁体的厚度H从5 mm增加到45 mm时,超导体捕获磁场和磁悬浮力与圆台形辅助永磁体的厚度直接相关。（1）当圆台形辅助永磁体的北极垂直向上且用液氮冷却后移除辅助永磁体时,最大磁悬浮力从21.8 N增大到26.5 N,再减小到22.9 N;（2）当圆台形辅助永磁体的北极垂直向下且用液氮冷却后移除辅助永磁体时,最大磁悬浮力从20.5 N减小到11.9 N ,再增加到20.4 N;（3）两种磁悬浮系统组态中最大磁悬浮力不一致,与零场冷情况下的最大磁悬浮力14.6 N也不同。在超导磁悬浮应用系统设计中,只有科学选择辅助永磁体形状和尺寸,合理设计组合方式,才能获得较强的磁场强度,提高超导磁悬浮力特性,该结果对促进高温超导体的实际应用具有重要的指导作用。     

CCT型超导组合磁体样机结构设计

基于斜螺线管型(Canted-Cosine-Theta,简称CCT)线圈结构,研制了一台四极与六极组合的超导磁体样机,它的四极和六极梯度场分别为22 T/m和120 T/m2.该组合型磁体的好场区范围为Φ0.16 m × 1.3 m,有效长度为1.3m.其中四极与六极磁体均采用两层骨架结构,每层骨架的线槽内并排放置多层...     

Mechanics of a magnet and a Meissner superconducting ring at arbitrary position and orientation

The force and torque exerted by a magnetic dipole on a superconducting ring (or hollow cylinder) in the Meissner state at arbitrary position and orientation are calculated using a Maxwell-London model previously proposed by the authors. The center of the ring is an unstable equilibrium point for the magnet. At this point the ring tends to align the magnet but tends to expel it for any small axial deviation from the center. There is also a non-monotonic and oscillatory dependence of the forces and torques on the position caused by the finiteness of the ring and a torque arises when the magnet is displaced both radially and axially from the center of the cylinder which corresponds to the experimental data. Therefore, the use of a magnet in a Meissner superconducting ring as a self aligning bearing requires a centered position and that the axial unstability to be compensated by additional mechanical means.     

Pure multipoles from strong permanent magnets: analytic and experimental results

We present the construction of arbitrary multipole field configurations from strong permanent magnets for trapping charged or neutral particles. A general analytic method for the design of three-dimensional magnetic multipoles is discussed for an idealized continuously varying magnetisation taking advantage of the superposition principle. Simple recipes for constructing magnetic dipole and quadrupole fields are given with two types of elements, axially and radially magnetised rings. Cylindrical magnet components not only give free access to the experimental region of interest, but also allow for some tunability to reduce undesirable higher multipole orders. Measurements confirm theoretical predictions achieving useful magnetic fields of 1 T and steep gradients of 3 T/cm with high purity over several ccm.     

Bi2223／Ag带HTS双饼磁体实验

用国产Bi2223／Ag带（西北有色金属研究院提供）设计的中心场3．0T．贮能35kJ的传导冷却高温超导磁体正在建造中．磁体由绕组内径150mm．外径272mm的32个双饼磁体组成．磁体在温度T=20K下．设计临界电流Ic=132A．额定运行电流I=100A.在T=20K附近进行四双饼组合磁体实验，得到磁体Ic=140A，中心场Bcc=1．14T，相应Bi2223／Ag带上最大轴向场Brmax=1．91T．Bi2223／Ag带上最大垂直场Brmax=1．14T．四双饼组合磁体的实验结果预示：35kJ HTS贮能磁体的设计目标能够达到．     

Stabilization of a movable magnet in the field of a stationary one by rotation

It is shown that a rotating body containing a permanent magnet may be in stable noncontact equilibrium when placed in the field of a stationary magnet. It is assumed that the magnets are of a cylindrical shape and their magnetizations are aligned with the cylinder axis. The field of the magnets is simulated by two turns with direct current, which makes it possible to analytically find the forces and force moments acting on the movable magnet subjected to the field of the stationary one. Instability of the equilibrium state of a suspended body when its weight is counterbalanced by the repulsive force exerted by a stationary magnet follows from the Earnshaw theorem. It is demonstrated here that such instability may be removed with gyroscopic forces due to rotation of the suspended body. It turns out that the rotation of the movable magnet may stabilize not only its unstable angular but also translational degrees of freedom, which is a newly discovered effect.     

辅助永磁体的引入方式对单畴GdBCO超导块材磁场分布及其磁悬浮力的影响

通过对永磁体辅助下单畴GdBCO超导体和方形永磁体在液氮温度、 零场冷、 轴对称情况下磁悬浮力的测量, 研究了三种不同组态中辅助永磁体的引入方式对单畴GdBCO超导块材磁场分布及其磁悬浮力的影响. 实验结果表明, 如果处在超导体上方的测量用方形永磁体N极向下, 则在轴对称情况下, 当方形辅助永磁体N极向上与超导体下表面贴在一起时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N增加到31.8 N, 提高到222%; 当方形辅助永磁体放置在超导体上表面、 N极垂直向上且场冷后去掉辅助永磁体时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N增加到21.6 N, 增加到151%; 当方形辅助永磁体放置在超导体上表面、 N极垂直向下且场冷后去掉方形辅助永磁体时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N减小到8.6 N, 减小为无辅助永磁体时的60%.这些结果说明, 只有通过科学合理地设计超导体和永磁体的组合方式, 才能获得较高的磁场强度, 有效地提高超导体的磁悬浮力特性, 该结果对促进超导体的应用具有重要的指导意义.     

利用轴向磁化的永磁环制造轴向梯度磁场

首先叙述了由单个轴向磁化环所产生的磁场,并就两个永磁环所产生的纵向磁场进行了分析.对于两个沿同一方向磁化的永磁体环,沿磁环中心线将会产生一个强度较为均匀的轴向磁场.如果两者的磁化方向相反,则在两磁铁间的区域将产生一个纵向的梯度磁场,其磁场强度介于-B₀到+B₀之间.设计制造了一个高梯度的轴向磁场,其磁场梯度为47.2Tm,测量结果与计算结果非常一致.文中还讨论了产生变梯度磁场的方法.由于永磁环所产生的磁场和螺线管的磁场较为相似,磁铁外部空间将有较大的漏场,最后还讨论了屏蔽漏场的问题.