Current and current density distribution in parallel superconducting wires in a planar array in the meissner state

The current distribution in parallel superconducting wires is influenced by the Meissner effect. In order to treat this quantitatively, the behaviour of superconducting cylinders in an inhomogeneous magnetic field was examined and the results were applied to a planar arrangement of parallel superconducting wires. How the current distribution between the conductors and the current density distribution along the circumference of each wire behave, if the distance between the conductors is varied, is also discussed, together with the effect of varying the number of wires on the current distribution. Finally the current distribution in a planar array of superconducting wires is compared with the current density distribution in a thin superconducting layer. Experimental results supporting the above mentioned theoretical considerations will be presented.     

Electromagnetic field and ac loss enhancements in a layer of superconducting round wires

Recent designs for a superconducting power transmission cable consider a flexible system in which the current is carried in a layer of wires or strips, each having a superconducting surface, laid on the surface of a tube. Subdivision of the conductor in this way causes an enhancement of electric and magnetic fields, and of ac losses. The case considered here is when the individual conductors are round wires. Field enhancements are calculated and used to determine ac loss enhancements. These are averaged over the conductor surface to give an overall loss enhancement factor for the cable. Results are presented to cover a wide range of situations.     

Development of design for large scale conductors and coils using MgB2 for superconducting magnetic energy storage device

MgB₂ wires are commercially available, and their superconducting characteristics have been continuously developed in the last decade. The relatively high critical temperature of these wires has attracted the attention of researchers, especially in the field of superconducting magnetic energy storage (SMES) coil applications in terms of its relatively high critical temperature, as it enables the use of liquid hydrogen for cooling the coils. The sensitivity of multi-filament MgB₂ wires to bending strain makes the design of large-scale conductors and coils for an SMES system technologically difficult, and the careful investigation of the applied strains during manufacturing is required. Two-conventional methods have been introduced for the fabrication of the coils: wind-and-react (W&R) and react-and-wind (R&W). These methods have been demonstrated to be suitable for the production of large-scale MgB₂ magnets to maximize the coil performance. The W&R and R&W methods have been successfully applied to the designs of conductors and coils, and small W&R test coil fabrication, as well as stability demonstrations are performed in this study. Our study is the first to demonstrate the feeding of hundreds of amperes of transport current using multifilamentary MgB₂ wires at around liquid hydrogen temperature in the practical background magnetic field of 2 T. The minimum quench energy and normal zone propagation velocity are also experimentally investigated for the protection of the actual coils for SMES application.     

Magnetic vector potential based model for eddy-current loss calculation in round-wire planar windings

An analytical development of the magnetic vector potential is used to investigate the losses in round-wire planar windings. The current distribution in wires is affected by the skin effect and the field created by adjacent wires (proximity effect). This field depends on the current distribution in conductors, resulting in a closed-form problem. In this paper, we obtain the vector potential outside a conductor to estimate the effect of induced currents in the field shape over the neighboring conductors. We use the results to calculate the losses in planar windings such as those in domestic induction heaters. We obtain an equivalent resistance representing the losses in windings and compare it with measurements. This solution provides an accurate analytical approach to modeling the losses in close-packed windings.     

Investigation on Effect of Magnetic Field Dependency Coefficient of Critical Current Density on the AC Magnetizing Loss in HTS Tapes Exposed to External Field

High-temperature superconducting (HTS) technology is the most promising, advanced, and beneficial technological developments of the last two decades in terms of fabricating more efficient, compact, and reliable electrical power apparatus. The second-generation HTS wires are now quite competitive with traditional conductors from the cost point of view. In addition, they are of high interest in electrical machine manufacturing due to their unique merits such as high current density, high magnetic field, and low loss. The most significant issue for any superconducting devices which work with alternating current or magnetic field is the AC loss of the HTS tapes. Since HTS tapes are always exposed to an external magnetic field in electrical machine applications, it is vital to consider the effect of this external field on their AC magnetizing (ACMG) loss. It is well-known that external magnetic field decreases the current carrying capability of the wire. In real life, critical current density of HTS tapes is dependent to magnetic field but this dependency sometime was not considered in modeling stage in order to make it faster and simple. In this paper, the electromagnetic properties of HTS tapes for use in superconducting electric machines have been investigated with a particular focus on the ACMG loss of YBCO tapes. For this purpose, a two-dimensional finite element model has been implemented based on the H formulation in order to study the effect of dependency of critical current density to magnetic field on the variation of ACMG loss. The modeling results will be helpful for electrical machine designers to have a better understanding about this effect and have a more accurate estimate of ACMG loss in design stage.     

Field and temperature dependencies of critical current on industrial Nb3Sn strands

The increasing need for high field magnetic devices has focused attention on filamentary Nb₃Sn conductors, whose critical data are superior to NbTi conductors. To choose the suitable operating parameters and to determine the stability margin of magnet systems, it is very important to know the effect of temperature and magnetic field on the superconducting properties, especially on the critical current. Up to now, for design calculation, the so-called “Summers model” was assessed theoretically on experimental data obtained by Spencer et al., (The temperature and magnetic field dependence of superconducting critical current densities of multiinflammatory Nb₃Sn and NbTi composite wires. IEEE Trans Mag, Mag-15 (1979) 76) and Suenaga et al., Superconducting critical-current densities of commercial multifilamentary Nb₃Sn(Ti) wires made by the bronze process. Cryogenics (1985) 25, 123). Apart these very useful preliminary experimental data, very little has been done on the very different industrial strands which are now produced in the industry. Industrial Nb₃Sn strands are generally tested and checked only at 4.2 K and their operating design temperature is often very different, sometimes around 6 K. It is now urgent to validate the model and to confirm that the data taken up to now in the design calculations are conservative.     

Computation of screening currents in superconducting persistent current devices

The penetration of screening currents induced in a hollow superconducting cylinder exposed to a transverse magnetic field is calculated two-dimensionally using a numerical model which simulates the superconductor by a system of parallel wires. Assuming the critical state model and taking account of the dependence of critical current density on magnetic field, the penetration depth and local current density is computed.     

Computations of voltage-current characteristics for a stabilized inhomogeneous superconductor with thermal resistance across the boundary between the superconducting wire and the substrate

A quench in modern multifilament conductors with voltage-current characteristics, broadened due to a longitudinal inhomogeneity of a critical current, occurs at electric fields high enough to be easily registered. It provides an opportunity to control superconducting solenoids made of such conductors, even in the case when steady-state stabilization is absent.Use of a semiempirical relationship for voltage-current characteristics of multifilament wires permits the computation of the main characteristics of a combined conductor consisting of such wires and of a stabilizing substrate. Presence of a thermal resistance across the boundary between the wire and the substrate decreases the quench current insignificantly, but causes a considerable drop in the electric field at which the quench occurs.     

Study of AC Loss Characteristics of HTS-coated Conductor with?Magnetic Substrate Using FEM Analysis

A high-T _c superconducting (HTS)-coated conductor with a magnetic substrate is promising as a low-cost conductor because Ni alloy can be well texturized by a simple process. However, it has been reported that the magnetism of the substrate makes an AC transport current loss and an AC magnetization loss increase from those losses of the HTS-coated conductor of a nonmagnetic substrate sharply. However, the assembled conductor which bundled many HTS-coated conductors with a magnetic substrate is hardly reported. In this paper, the AC loss and the current distribution in the superconducting layer of the HTS-coated conductor with a magnetic substrate are analyzed using the edge-based hexahedral finite element method (FEM) taking account of both the nonlinear E?CJ characteristics and the nonlinear magnetic property of the substrate at 77 K. Moreover, AC loss characteristics of HTS-coated conductors with a magnetic substrate arranged with an infinite number of the coated conductors are examined and the effect of the gap length between adjacent conductors on the AC loss is also investigated.     

On the distribution of a transport current inside a multifilamentary superconducting wire in a rapidly changing transverse magnetic field

For the current distribution inside a multifilamentary superconducting wire carring a dc transport current in a rapidly changing transverse magnetic field, inconsistencies with the existing models are shown by the following experimental evidence: when a transverse magnetic field is applied, the distribution of transport current is not unaltered but is forced to concentrate into the inner circular cross section region during a characteristic time constant τ_c, called the coupling time constant. Secondly, the characteristic time constant for the transport current distribution inside the inner region to approach a uniform distribution is not τ_c but a new time constant τ₁ called the ‘uniforming time constant’, though the variation in the distribution does not occur unless the external magnetic field changes with time.It is shown that the model of the current distribution based on the above experimental evidence exhibits a remarkable difference from the existing models, especially for the wires containing very fine superconducting filaments.     

Losses in Coated Conductors Under Nonsinusoidal Currents and?Magnetic Fields

The study of AC losses in superconducting wires and tapes is usually restricted by consideration of applied sinusoidal currents and/or magnetic fields. However, currents in electric power systems contain a wide variety of harmonics. The currents become strongly nonsinusoidal in the operation of converters and nonlinear reactors, and during transient and overload conditions. Recently it has been shown that the contribution of higher harmonics to AC losses in superconducting bulk and thin film samples can be tens times larger than in normal-metal samples of the same form, and the 5% harmonic can increase the losses by up to 20%. Here we report the results of an analysis of the influence of higher harmonics of the current and magnetic field on AC losses in coated conductors. Analytical expressions are obtained in the framework of the critical state model, neglecting the response of the normal-metal substrate and stabilization layers. Losses in the superconducting and normal-metal parts of a coated conductor are compared for various designs of the conductor. It is also shown that the 5% third current harmonic can increase the losses in the normal-metal parts by up to 60%. This increase is caused by a nonlinear response of the superconducting layers and should be taken into account in the determination of the optimal operation regimes of superconducting devices.     

Stability limit field in superconductors. Part 2 multifilamentary composites

Magnetic instabilities or flux jumps in multifilamentary superconducting composite conductors, exposed to a time-varying magnetic field perpendicular to the superconducting filaments, are studied. In particular, expressions for the stability limit field are determined for cases when the magnetic diffusivity is greater than the thermal diffusivity and vice versa. Examples are presented for NbTi composite conductors with CuNi matrix and Cu matrix.     

Worldwide cryogenics — Switzerland Cryogenics at BBC Brown,Boveri and Co

Brown Boveri and CIE started activities in the field of superconductors and superconducting magnets in 1963. Since then NbTi filamentary wires and cables were developed and used in some most spectacular magnet coils as for instance the Omega magnet at CERN and the two muonchannels at SIN.Development continues and activities are now concentrated on A 15 filamentary conductors and high current cables for pulsed operating conditions. Also investigations in the field of current leads and mechanical and thermal properties of structural materials are important for cryogenic engineering. This article shall give an over view of these activities and present some recent results.     

A loss-less superconducting kilo-oersted ac magnetic field system

A simple superconducting system which allows almost loss-less ac magnetic field to be generated in the kilo-oested region and in the frequency range from dc up to more than 1 kHz is described. The behaviour of commercially available superconducting wires and the influence of winding of the coils are also considered.     

Development of niobiumtin conductors at SLE

Superconductors Lips ECN is a recently formed company which produces NbTi and Nb₃Sn multifilament wires as well as superconducting cables. Multifilamentary Nb₃Sn wire, produced by the powder route, is developed commercially. About 30 km of strand material has been produced for the SULTAN 12 T project. These wires showed good performance. Developments are underway to reduce gradually the filament diameter at the same current performance to meet the full requirements for the NET and LHC conductors.     

Calculation of AC Magnetizing Loss of ReBCO Superconducting Tapes Subjected to Applied Distorted Magnetic Fields

In recent years, there are fast-increasing concerns on the utilizations of superconducting rotating electrical machines in different application areas, such as ship propulsion systems, aircraft drivers, and wind turbine generators, since these machines exhibit the merits of high current density, compact design, high power density, light weight, high torque density as well as high efficiency. One of the main limitations in front of the vast use of superconducting tapes in the fabrication of electrical machineries is AC magnetizing loss when tapes are exposed to an external magnetic field, which can decrease the critical current density of wires, as well. In the literature, most of the research works have been done on calculation of the AC magnetizing loss under a pure external magnetic field, while in reality, magnetic flux lines in AC electrical machines are usually distorted with harmonics because of different reasons such as distorted leakage flux, distributed coils of a winding in several slots, cogging fields, mechanical faults, etc. Since these distorted fields contain harmonics, then in this paper, the AC magnetizing loss of superconducting tapes has been electromagnetically modeled and calculated when they are subjected to nonsinusoidally distorted external magnetic fields. The magnetic field dependency of critical current density has been considered in a proposed finite element model. The results have shown that the AC magnetizing loss increases significantly under a distorted applied field compared with a sinusoidal one. In addition, the loss increase depends on the harmonic content which would increases drastically with total harmonic distortion of the applied magnetic field.     

Measurement of critical temperature as a function of field

The critical temperature has been measured for various magnet conductors as a function of the perpendicular applied magnetic field. The isothermal environment was provided by a variable temperature cryostat which fits into the bore of a 10 telsa solenoid. The temperature gradient across the sample volume was measured to be less than 25 millikelvins. The superconducting to normal state transition was measured resistively, using sample current densities from 0.01 to 2 A cm^?2. The maximum applied magnetic field was 10 T and varied less than 0.5% in the sample volume. The critical transport current range of the samples measured from tens to thousands of amperes in the presence of a 10 T perpendicular magnetic field at 4.2 K.     

Comparison study of cable geometries and superconducting tape layouts for high-temperature superconductor cables

High-temperature superconductor (HTS) rare-earth-barium-copper-oxide (REBCO) tapes are very promising for use in high-current cables. The cable geometry and the layout of the superconducting tapes are directly related to the performance of the HTS cable. In this paper, we use numerical methods to perform a comparison study of multiple-stage twisted stacked-tape cable (TSTC) conductors to find better cable structures that can both improve the critical current and minimize the alternating current (AC) losses of the cable. The sub-cable geometry is designed to have a stair-step shape. Three superconducting tape layouts are chosen and their transport performance and AC losses are evaluated. The magnetic field and current density profiles of the cables are obtained. The results show that arrangement of the superconducting tapes from the interior towards the exterior of the cable based on their critical current values in descending order can enhance the cable’s transport capacity while significantly reducing the AC losses. These results imply that cable transport capacity improvements can be achieved by arranging the superconducting tapes in a manner consistent with the electromagnetic field distribution. Through comparison of the critical currents and AC losses of four types of HTS cables, we determine the best structural choice among these cables.     

Influence of a transverse conductance on current sharing in a two-layer superconducting cable

A simplified model is used to study the current sharing in a two-layer superconducting cable. Since the matrix in the case of the composites, and the copper oxide in the case of the cables are conductors, they can couple wires together electrically so that the resulting current redistribution no longer depends only on the mutual and self-inductance coefficients. The boundary conditions assigned by the series resistance at the input terminals then lead to a particular sharing which propagates along the conductor according to a diffusion equation. Several typical examples are calculated which point out the absolute necessity of using fully transposed cables, to achieve equal sharing for pulsed currents. The transverse conductance associated with series resistance can help distribution for very slowly rising currents in small coils. Also it can help to carry the current when a wire happens to return to the normal state or to be broken in a pulsed magnet.     

Iron chalcogenide superconductors at high magnetic fields

Iron chalcogenide superconductors have become one of the most investigated superconducting materials in recent years due to high upper critical fields, competing interactions and complex electronic and magnetic phase diagrams. The structural complexity, defects and atomic site occupancies significantly affect the normal and superconducting states in these compounds. In this work we review the vortex behavior, critical current density and high magnetic field pair-breaking mechanism in iron chalcogenide superconductors. We also point to relevant structural features and normal-state properties.