Effect of conductor crossings on propagation margins

The effects of conductor delineation technique on magnetic bubble propagation across the conductor edge are described. Propagation margins are obtained for bubble circulation around 18-μm diameter Permalloy discs which cross four edges of an Al-Cu feature. Specifically investigated are isotropic wet etching, anisottopic wet etching to achieve a uniform taper, ion beam milling, and metal lift-off to provide a planar structure. Margins are obtained at ± 40°C, with the most significant degradation observed at the lower temperature. Permalloy magnetic continuity in the crossings can be inferred from hysteresis loop measurements of a Permalloy sheet deposited over a grating pattern formed by the above processing techniques. Although the least anisotropic loops are invariably obtained with smoothly tapered Al-Cu edges under the Permalloy, propagation margins are not maximized with such structures, but rather favor a planar crossing. The results suggest that although patterned stress is still an important concern in functional operation, other geometric effects can be more significant. In particular, poor magnetic step coverage as inferred from loop measurements leads to spurious pole formation from the drive field, while even with adequate step coverage, static bias-field distortions can result because of the component of the field along the step.     

Magnetic field analysis by edge elements of magnetic components considering inhomogeneous current distribution within conductor windings

For magnetic field analysis by edge elements of the magnetic components, the method considering inhomogeneous current distribution within the conductor windings is investigated. To consider the inhomogeneous current distribution within the windings, we utilized the magnetic vector potential represented by edge elements and the current conservation equation represented by nodal elements in the region of the windings. In the first application, the eddy-current model, which has the conventional wire winding, was analyzed. For correct analysis using our method, it is required that all turns of the wire winding be divided into meshes. However, if the region of the wire winding does not exceed the winding window of the magnetic core, even the combination of our method and the solidly modeled wire winding enables us to correctly analyze the transformer and the inductor with conventional wire winding. In the second application, a flat transformer with conductor winding, such as a copper foil or sheet, was analyzed. The magnetic flux densities within the flat core and the inductance calculated by our method were in good agreement with the experiments. Thus, we confirmed the effectiveness of our method considering inhomogeneous current distribution within the conductor windings.     

Induced circumferential currents and losses in flexible superconducting cables

In most designs for flexible ac superconducting cables each phase is carried by a co-axial pair of conductor tubes formed from a single layer of helically laid conductor strands. It is shown that the cable current would generate a net axial magnetic flux and hence an alternating circumferential electric field outside each co-axial pair. If, as in some cable designs, each conductor pair is to be contained in its own helium pipe, circumferential currents will be induced in the pipe wall. The losses depend on the pipe material but are typically three orders of magnitude too large. One solution is to line the pipe with superconductor, such as lead, but this could require more niobium in the conductor itself. Alternatively the co-axial pair could be redesigned so that there is no net axial flux. One possibility is to form conductor tubes from two layers of conductor strands laid in helices of opposite sense.The induced current problem is avoided if all three phase conductors are contained in a common helium pipe, provided that there are no zero sequence components to the phase currents. Losses from any zero sequence component could be readily reduced to an acceptable level, for example by laying a ferromagnetic strip alongside the conductors inside the helium pipe.Since circulating currents will also be induced in the electrostatic screens adjacent to the conductor strands the screens must be of semiconducting rather than metallic, tape.     

Eddy current analysis of a conductor with a groove by surface integral equation with one unknown

In this paper, we study how to solve eddy currents induced in a conductor with a narrow groove in the case of thick skin depth by using surface integral equations, of which unknowns are the surface electric and magnetic currents. When the skin depth is small, the surface integral equations give accurate solutions except around the sharp edge and corner. Some edges and corners of the groove are so close that it is difficult to get accurate solutions; moreover, as the width of the groove becomes narrower, the surface integral equations become ill conditioned. In order to solve these problems, we propose a method to analyze the eddy currents induced in a conductor with a groove by introducing a lumped loop magnetic current, which is formulated by a surface integral equation derived from the normal component of the electric field.     

Electromagnetic field and ac power loss enhancements at the edges of adjacent strips in a superconducting cable

In most flexible superconducting cables the current is carried by a series of strips laid along the length of the cable with small gaps between their edges to accommodate bending. One consequence of dividing the conductor into strips is an enhancement of the electromagnetic fields in the vicinity of the gaps. The ac losses in the superconductor are thereby also enhanced. Data are presented which enable the effects of these field and loss enhancements on cable performance to be assessed. In particular it is found that there is an optimum corner radius for the strips to achieve a minimum increase in loss compared to a smooth tube and that this increase need not be large for a suitably rounded corner. A non-uniform distribution of the strips around the cross-section of the cable can be deleterious while any radial displacements are likely to increase the losses considerably.     

Ramp-rate limitation experiment using induced current method. Part 1: experimental results

This paper describes a methodology of performing ramp-rate limitation experiments using only a background magnet without a power supply for the tested cable. Three-strand U-shape cable-in-conduit conductor (CICC) samples were prepared with various parameters; three different surface contact resistance conditions and two hybrid cables with a pure copper wire or a stainless steel wire. Samples showed distinctive ramp-rate limitation phenomena with very sharp and sensitive transition between no-quench and quench results. Multiple quench-recovery processes during the continuous magnetic field ramp were also observed due to fast recovery of the sample after quench. The induced strand-to-strand loop current is believed to play the most important role in a quench of CICC during the ramped field.     

Microwave impedance control over a ferrite boundary layer

We simulated microwave far-field radiation by using a coaxial cable, inside which a ferrite layer with a ground plane was loaded. The ferrite layer is magnetically biased near ferrimagnetic resonance by a permanent magnet generating a global bias magnetic field inside the ferrite layer. In addition, a magnetic bias coil near the ferrite layer generates a second dc bias magnetic field so as to locally tune the permeability of the ferrite layer. By observing the frequency change in the resonant modes of the cavity formed by the coaxial cable, we can determine the permeability of the ferrite layer. Calculations compare nicely with experiments.     

Superconductive dc transmission lines: design study study and cost estimates

A conservative design study of a dc superconductive power line based on present day technology is presented. Power is transmitted by opposing currents in coaxial conductors, formed from helically wound tapes of composite, with a potential difference between them. Conductor temperature stability and fault current conditions are shown to be the factors which dominate the conductor cost; both are analysed. The capital cost of a cable is expressed as a function of a cable dimension, the basic cable parameters, and the material properties. This cost may be minimized with respect to cable radius. The resultant optimum magnetic fields vary little with power rating and are quite low at about 1–2 × 10⁵ A m^?1. The capital cost of such cables, exclusive of terminal costs, is less than the cost of conventional dc cables at power levels above about 1 GVA. Although extensive development would be necessary, the basic principles needed to build a dc superconductive cable are known.     

导电薄板内裂纹尖端区域的电磁应力

为了研究电磁应力对导电薄板内裂纹尖端的作用,从基本电磁理论出发,通过对导体表面所受电场力的分析,推得了导电薄板内裂纹边缘处电场力的表达式.在此基础上,通过导电薄板内裂纹尖端区域磁场的确定,得到裂纹尖端区域的电磁应力表达式.裂纹尖端电磁应力的计算表明,金属薄板中裂纹尖端的电磁应力是由裂纹尖端指向金属内部的压应力,并且当电流密度为103～104A/mm2的数量级时,裂纹尖端的压应力数值可达数兆帕到数百兆帕.因此,在研究裂纹止裂问题上,其影响不容忽视.     

Circuit analysis model for AC losses of superconducting YBCO cable

Information about AC losses and electromagnetic behaviour is essential when designing superconducting cables. In this work, AC losses of coaxial YBCO cables are determined using circuit analysis based computational model tailored for the needs of the YBCO cable design work. In the equivalent circuit superconducting layers are connected in parallel, the layers have an inductive coupling between each other and AC loss within a layer generates an effective resistance. The layer currents can be solved from a set of circuit equations. The computational model takes into account that the current in the cable creates magnetic field, which generates magnetisation loss and affects strongly the critical current of the YBCO tapes. The model was applied on several coaxial superconducting YBCO cable designs, which had nominal currents of 1-10 kA (rms). Low AC loss values were predicted for these compact YBCO cable designs. For example, AC losses less than 4 W/m were predicted for 10 kA cables.     

Effect of self-field and current non-uniformity on the voltage-temperature characteristic of the ITER central solenoid insert coil by numerical calculations

For the optimisation of a magnet design with cable-in-conduit conductor (CICC) technology it is essential to comprehend the scaling of the critical current from the separate strand characteristics to the finally assembled cable performance in a coil. Several model coils have been tested in the framework of research for the International Thermonuclear Experimental Reactor (ITER). At present, the scaling of the critical current from the strand to the full cable performance and the apparent decrease of the n-index from strand to cable in the voltage-current curves is not understood. It is important to recognize the mechanisms behind this phenomenon in relation to the cost of the superconducting strand, which is significant in the manufacture of the magnets. Therefore, basic phenomena like the cable conductor self-field, the current unbalance introduced by the non-uniformity of the joints and a possible reversible or irreversible degradation of the voltage current characteristic of a strand during cable manufacture or electromagnetic loading of the magnet have to be considered. The voltage-current characteristic of the strand is extensively explored for the relevant range of magnetic field, temperature and axial strain space. Accordingly a numerical six-element network model is developed to simulate the conditions and behaviour of the last stage cable elements of a full-size ITER conductor. The experimental data, mainly in terms of voltage-current (VI) or -temperature (VT) characteristics, are obtained on the central solenoid insert coil (CSIC) experiment performed in Naka (Japan) in the framework of the research for ITER.The numerical model, which is briefly introduced, is used to study the cable performance by using experimentally obtained cable parameters like inter-strand (and bundle) contact resistance, strand critical current data as a function of magnetic field, temperature and applied axial strain, and external cable self-field measurements by Hall sensors for reconstruction of the current non-uniformity.The effect of a current redistribution due to the cable self-field on the voltage-temperature curve is calculated in correlation with the transverse resistance between the strands and last cabling stage bundles (petals). A realistic unbalanced current distribution is established by introducing non-uniform joints at the extremities of the CS-insert cable.It appears that the cable self-field effect hardly gives any change in the shape of the VT curve but merely a shift towards lower temperature giving a reduction of the current sharing temperature T_cs (10 μV/m) of <0.1 K. For typical CICCs with Cr-coated Nb₃Sn strands, there is practically no current redistribution due to the cable self-field, because of the high inter-strand contact resistance.An unbalanced current distribution also gives an earlier voltage rise in the VT curve, mainly at low levels of the electric field. At a 10 μV/m criterion practically no reduction of the T_cs (<0.1 K) is found by the numerical simulation. However, in the CSIC the experimentally obtained overall reduction in T_cs from strand to cable is 0.7 K for an operating current of 40 kA at 12.5 T background field.According to the results of the numerical simulation, the cable self-field effect and the non-uniform current distribution, which is unavoidably caused by the joints, cannot explain the early voltage rise and low n-index in the VT curve of the CS-insert coil. It is very likely that electromagnetic forces play a role in causing reversible degradation in critical current or even irreversible due to strand (filament) damage. Neither can it be excluded that strand deformation during cabling has an impact on the final conductor performance as well. Therefore additional effort is required in detailed 3D modeling of the possible strand deformations inside a cable and the impact it has on the strand performance by experimental verification on strand level.     

A strong electromagnetic field generated by a dipole

A strong electromagnetic field generated by a steep current pulse passing in a conductor dipole was measured. The current was created by an ultrashort voltage pulse formed in a coaxial transmitting line of a high-current picosecond electron accelerator.     

Braking forces and damping coefficients of eddy current brakes consisting of cylindrical magnets and plate conductors of arbitrary shape

A method for analyzing a magnetic damper (eddy current brake) consisting of a cylindrical magnet and a plate conductor of arbitrary shape is considered. Since the magnetic flux is a function of the position, the analytical solution to obtain the eddy current, braking force, and damping coefficient is obtained by dividing the magnetic flux into the narrow circular bands, and the unit step function is applied to solve the differential equation of the electromagnetic fields. The boundary condition of the plate conductor of arbitrary shape is satisfied directly by making use of the Fourier expansion collocation method. Numerical calculations have been carried out for the conductor of rectangular plates, circular plates with eccentric fluxes. The theoretical results are in very good agreement with the experimental ones.     

50 Hz loss measurements on superconducting niobium coaxial conductors

A method is described for the measurement of ac losses in a cylindrical conductor forming part of a coaxial superconducting pair. Results given for 25 μm niobium are substantially lower than previous values obtained for this material when tested in the form of narrow strips, and show that, if used as the conductor in a superconducting power cable, the material could carry a peripheral current density of 360 A cm^?1 with tolerable losses (< 10 μW cm^?2) at temperatures of up to 7 K.     

Effect of displacement current in magneto–electro-elastic plates subjected to dynamic loading

Dynamic response of moderately thick magneto?Celectro-elastic plate using magnetic vector potential in finite element formulation is presented in this paper. Dynamic loading generate time varying electric and magnetic fields in magneto?Celectro-elastic continuum. Displacement current is associated with the generation of magnetic field due to time varying electric field. The non-conservative electric field is represented using electric scalar potential and magnetic vector potentials. Studies are carried out for CCCC, CCFC, CFFC and FCFC boundary conditions of the plate excited with time-harmonic mechanical excitation, the frequency range being chosen based on the critical frequency of the plate analyzed. The magnetic flux density in longitudinal x-direction is not affected by the electric displacement current for all the boundary conditions. The longitudinal y-direction and transverse direction components of magnetic flux density are showing variations for FCFC boundary condition when displacement current is accounted. The effect of displacement current is significant when two opposite edges of the plate are clamped.     

Effective thermal conductivity of the conductor insulation of the ITER toroidal field model coil at operation temperature

During current transients in the toroidal field model coil (TFMC), the radial plates carry eddy currents that generate Joule heat. The heat sink is the forced flow helium cooling of the conductor. Vice versa, during accidents, the radial plates act as a heat sink during the heat up of the conductor. In both cases, the time constant of heat transfer is given by the thermal conductivity of the insulation of the conductor. The code system MAGS (magnet system) is used to recalculate fast discharge experiments of the TFMC at the TOSKA facility. The model takes into account the transient magnetic field, the current in the conductor circuit, in the radial plates and coil case, the ac-losses in the conductor and the helium flow. The results clearly indicate that the power distribution in the radial plate should be taken into account and the thermal conductivity of the insulation is considerably lower than assumed up to now.     

有角点支座矩形板自振分析

撤去角点支座代之以角点力得板自由振动分析的基本结构。原结构振形函数表达式由基本结构所固有的基本振形和角点力所激发的附加振形组成,它应满足振动微分方程和板挠度与角点力间的微分关系。为表示板双向振动规律,基本振形在二个坐标轴方向上有各自独立的振形曲线,分别符合相应方向边界所限定的、与微分方程直接关联的变形和受力特征：在支承边界上振幅为零而剪力分布不为零值;在自由边界上振幅不为零而剪力分布为零值;在自由角点处对应的振幅不为零而角点力为零值。附加振形在角点处要满足振幅与角点力的微分关系,在每条边界上要符合边界所限定的振幅与剪力分布的振动特征。文中导出二邻边和对角点支承矩形板,一边支承和一角点或二角点支承矩形板的振形曲线,并计算了不同边长比时板的自振频率。     

Electromagnetic field spikes in thin metal slabs

The effect of specimen surface conditions on the propagation of electromagnetic waves in metals under anomalous skin effect conditions is analyzed. If the specimen is placed in a magnetic field parallel to the surface, the electromagnetic field penetrates into the metal in the form of narrow spikes whose basic parameters are highly sensitive to the quality of the conductor surface. In a thin slab the amplitude of the transmitted electromagnetic wave depends on the state of both of its faces. The intensity and width of the field spikes are essentially different from those in a half-space. The reason is that the formation of a high-frequency field near the plate surface opposite the skin layer is determined by electrons moving along that surface at shallow angles, just as the high-frequency screening current in the skin layer is determined by electrons slipping along the surface at which the field is incident. The shape of the spikes is analyzed in detail as a function of their location within the specimen. The transparency and impedance of the plate are calculated for the size-effect conditions when the spike emerges on the conductor surface. Experimental investigation of the size effect can be an effective method of studying the interaction of conduction electrons with the metal surface.     

脉冲磁场激励下圆柱导体内瞬态涡流场的快速计算

建立了脉冲磁场激励下圆柱导体内瞬态涡流场的理论模型。实现了瞬态涡流场的快速计算。通过实例表明上述圆柱导体内瞬态涡流场的快速计算方法有效。     

A Numerical Study on AC Losses of a Double Layer Polygonal BSCCO Conductor by Finite Element Method

High-temperature superconductor (HTS) cables are candidates for power transmission cables in the near future. A cylindrical arrangement of HTS tapes for the cable has proved able to reduce the AC loss. Many studies on AC loss characteristics of HTS cables have been done, but few numerical models of the cable were verified by experiments. In this paper, a numerical model of the double-layer polygonal bismuth strontium calcium copper oxide (BSCCO) conductor is developed. Current density and magnetic field intensity distribution in the inner and outer layers are also investigated. The numerical results of the AC loss for different layer current distributions are identical with the experimental ones. Accordingly, the reliability of the numerical model is verified. By using this model, the influence of distance between the inner and outer layers, gap between two neighboring wires, and layer current distribution on AC losses of different layers is evaluated. The results show that increasing distance between layers and narrowing gap between wires are effective to reduce AC loss, while the unbalance of layer current distribution increases the AC loss of the double-layer conductor.