Angular Dependence of Transport AC Losses in Superconducting Wire with Position-Dependent Critical Current Density in a DC Magnetic Field

Transport AC losses play a very important role in high temperature superconductors (HTSs), which usually carry AC transport current under applied magnetic field in typical application-like conditions. In this paper, we propose the analytical formula for transport AC losses in HTS wire by considering critical current density of both inhomogeneous and anisotropic field dependent. The angular dependence of critical current density is described by effective mass theory, and the HTS wire has inhomogeneous distribution cross-section of critical current density. We calculate the angular dependence of normalized AC losses under different DC applied magnetic fields. The numerical results of this formula agree well with the experiment data and are better than the results of Norris formula. This analytical formula can explain the deviation of experimental transport current losses from the Norris formula and apply to calculate transport AC losses in realistic practical condition.     

3D simulation of AC loss in a twisted multi-filamentary superconducting wire

In the AC loss simulation, it is a huge challenge to model the twisted wire at the filament level, due to the complex structure as well as long-time computation consumption. In this paper, we use 3D finite-element method based on H-formulation to study the AC loss in a twisted superconducting wire. The wire is treated as a homogenous material with the anisotropic conductivity in the filament region. We quantitatively simulate the AC loss induced by the AC transport current and magnetic field profile, and the effect of the twist pitch on the AC loss. In the case of AC transport current, larger pitch length leads to higher loss, and the pitch length effect is contrary to the case of applied magnetic field. The influences of the magnetic field direction and non-uniform current distribution subjected to the strand bending are also investigated. It is observed that, the transverse magnetic field has a more significant influence on the AC loss than the longitudinal magnetic field. The non-uniform current distribution can result in a higher AC loss, compared to a corresponding uniform current distribution.     

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.     

Influence of Critical Current Density on Guidance Force Decay of HTS Bulk Exposed to AC Magnetic Field Perturbation in a Maglev Vehicle System

Superconducting maglev vehicle is one of the most promising applications of HTS bulks. In such a system, the HTS bulks are always exposed to AC external magnetic field, which is generated by the inhomogeneous surface magnetic field of the NdFeB guideway. In our previous work, we studied the guidance force decay of the YBCO bulk over the NdFdB guideway used in the High-temperature superconducting maglev vehicle system with the application of the AC external magnetic field, and calculated the guidance force decay as a function of time based on an analytic model. In this paper, we investigated the influence of the critical current density on the guidance force decay of HTS bulk exposed to AC field perturbation in the maglev vehicle system and try to adopt a method to suppress the decay. From the results, it was found that the guidance force decay rate was higher for the bulk with lower critical current density. Therefore, we could suppress the guidance force decay of HTS bulk exposed to AC external magnetic field perturbation in the maglev vehicle system by improving critical current density of the bulk.     

Investigations on the Magnetization Switching Dynamics in Spin Valve Multilayers Under Periodic Applied Magnetic Field

Magnetization switching dynamics in a spin valve nanopillar, induced by spin transfer torque in the presence of a periodic applied field is investigated by solving the Landau–Lifshitz–Gilbert–Slonczewski equation. Under steady state conditions, the switching of magnetization occurs in the system, above a threshold current density value J _c. A general expression for the critical current density is derived and it is shown that this further reduces when there is magnetic interface anisotropy present in the free layer of the spin valve. We also investigated the chaotic behavior of the free layer magnetization vector in a periodically varying applied magnetic field, in the presence of a constant DC magnetic field and spin current. Further, it is found that in the presence of a nonzero interfacial anisotropy, chaotic behavior is observed even at much smaller values of the spin current and DC applied field.     

Losses in a multifilamentary superconducting wire caused by a simultaneous sweep of current and magnetic field

A theoretical discussion is presented on the energy loss in a multi-filamentary superconducting wire when an applied transport current and an external transverse magnetic field are varied simultaneously with a repeating pulsive wave form. In the present calculation, the effects of the ‘uniforming time constant’ which has been introduced by the authors as a characteristic time constant for the change in the transport-current distribution inside the wire is taken into account, together with the field dependence of the critical current density of superconducting filaments.Thus the present analytic expression for the energy loss of multi-filamentary wire is available to the whole range of the external magnetic field. It is shown that the contribution of the dynamic resistance loss to the total loss is strongly dependent on the position of the wire inside a coil.     

The Effect of Dy Doping on the Magnetic Behavior of YBCO Superconductors

The effect of dysprosium (Dy) doping on yttrium barium copper oxide (YBCO) prepared by conventional solid-state reaction method has been investigated by means of XRD, AC susceptibility, and DC magnetization measurements. AC susceptibility measurements for sintered YBCO pellets have been performed as a function of temperatures at constant frequency and AC field amplitude in the absence of a DC bias field. DC magnetization measurements were done at 5, 20, and 77 K upon zero field cooling (ZFC) process. The magnetization measurements showed a paramagnetic behavior existing at high magnetic fields. The magnetic field dependence of critical current density of the samples has been estimated from DC magnetization data. The partial Dy substitution for Y on YBCO superconductors improves the bulk critical current density at high magnetic fields and at high-temperature regions (higher than 20 K).     

Electromagnetic behavior of lap-joints for fusion magnet system

The joint between superconducting Cable-In-Conduit-Conductors (CICC) is a key technology in a magnetic confinement fusion apparatus. Several hundreds of joints are involved in one apparatus generally. DC resistance of the lap-joint is typically designed less than several n-ohms and the allowable joule loss is several watts. AC loss due to external magnetic field is also limited to less than several watts. Reduction of the AC loss and low joint resistance are required simultaneously and those are conflicting trade-off.The lap-joint had been examined under both self-field and external-transverse-field experimentally. In this study, we established a numerical model for the joint and analyzed for electromagnetic behavior of it numerically. In the simulation, modeling of contact resistances between twisted strands is important. Circuit constants, e.g., conductance between strands, were determined to reproduce the experimental results; those are the circuit constants and the DC joint resistance. The relation between the joint resistance and the AC loss was discussed. Constitution of the joint does not only influence on the joint resistance and the AC loss but also current distribution in the cable. Non-uniform current distribution among the strands is reported to result in the degradation of the stability. We successfully simulated mentioned phenomena and found our numerical model was useful in joint design to find a good compromise.     

Analysis of Current and Magnetic Distributions in REBCO Superconducting Coated Conductors in Self- and External Fields

The influence of a self-field on the critical current density J _c for a REBCO superconducting tape is presented in this paper. The distributions of the current density and magnetic field are analyzed in the tape under three kinds of conditions, i.e., applying an external magnetic field only, applying a transport current only, and applying a transport current together with an external magnetic field. In the analysis, the two-dimensional Poisson equation for the vector potential is employed. For the convenience of calculation, that the dependence of critical current versus the perpendicular and parallel fields tested from experiment is substituted for the traditional Kim-type or Bean model. The results show that the distributions of the current density and magnetic field in the REBCO tape change for the different frequencies and amplitudes of the transport current I _a and applied magnetic field B _a.     

New Type of Non-magnetically Sheathed MgB2 Wires��First Sight to AC Losses with Numerical Simulations

AC losses of MgB₂ wires can be substantially decreased with nonmagnetic sheath materials and multifilament structure. In this paper, AC losses of two low loss samples are computed in AC?CAC domain, which means that the samples were exposed to alternating transport current and field simultaneously. The losses were computed with modified Brandt??s method, which takes J _c(B)-dependence into account, and for these computations, the superconductors?? cross-section is determined directly from photographs. The losses were computed in wide magnetic field range with various transport currents. The results suggest that the AC losses of these samples are relatively low because large magnetization current loops are not formed. Additional simulations show that below the penetration field, the losses can be approximated using constant critical current density based on the self-field critical current of the sample. However, after the penetration field, this leads to too high loss values. Finally, the results are compared to analytical loss formulas in case of sole transport current and sole magnetizing field.     

Transport and Magnetic AC Losses in Ag/Tl-1223 Tape and the Effect of Mechanical Damage

In this paper we present the results of AC loss measurements on silver clad monocore tapes of Tl-1223 prepared by the powder-in-tube method. Losses arising from an external AC magnetic field are compared with those generated by AC transport currents (self-field losses). Critical current densities are derived from magnetic loss data and compared with those measured by the four point transport method. It was found that mechanically induced stresses (introduced by bending) only have a significant effect on the transport losses, via the critical current degradation. Such changes are not seen in measured magnetic losses, which are independent of mechanical stress, and remain unchanged, at least in the stress range used in our experiment.     

Thickness-Dependent Current Density and Flux Distribution in Thin Current-Carrying Superconducting Films Exposed to a Magnetic Field

With the rapid development of high-temperature superconductors, it is of great significance to get the precise current density and flux distribution within thin high-temperature superconducting films subjected to a transport current and an applied magnetic field. The transport current distribution and flux density in thin high-temperature superconducting films are calculated by a numerical method based on the Kim model and exponential model in this paper. The influences of transport current, applied magnetic field, width, and thickness of a superconducting film on the current distribution are discussed. The results reveal that the thickness has a significant effect on the critical current density of superconducting films.     

Effect of twist on the longitudinal field loss for an in situ superconductor

The effect of twist on the full penetration loss of an in situ superconductor is calculated for the case of a longitudinal applied magnetic field. An increase in hysteresis with increasing twist is predicted due to a large anisotropy in the critical current density. The anisotropy results from the fact that the critical current density along the length of a filament in the in situ material is determined by the filament, while along the thickness it is determined by the proximity effect in the matrix surrounding the filament. From the measurements of Braginski and Wagner the ratio of these critical current densities is calculated to be about 70, which is in order of magnitude agreement with the value previously found from transverse field measurement.     

The Influence of BaZrO3 on the Magnetic Response of (Bi,Pb) : 2223 High-Temperature Superconductors

DC magnetization and AC complex susceptibility measurements on (Bi,Pb) : 2223 high-temperature superconductors impurified with various amounts of BaZrO₃ are presented. The results are discussed in the frame of the critical state model, and the values of the inter- and intragranular critical current density as well as of the field for full penetration are estimated. The values of the intergranular critical current density are consistent with those obtained from transport measurements. The intragranular critical current density and the field for full penetration have similar values from both DC magnetization and AC susceptibility measurements. It was shown that, in the (Bi,Pb) : 2223 system, BaZrO₃ impurification changes only the properties of the intergrain matrix, while the superconducting properties of the grains are not modified.     

Evidence of high dissipation in magnetization reversal processes of five Co/Cu bilayers

Heat and charge transport perpendicular to the plane in five Co/Cu stacks are studied using AC temperature gradients in the presence of a DC current. Large peaks in AC voltage response versus applied field are observed. This effect, measured only in reversible magnetization reversal modes and at sharp values of magnetic fields, suggests that an extra dissipation process is produced at well-defined magnetic configurations.     

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.     

Experimental Presentation of Microwave Absorption due to Shaking of JV by AC Magnetic Field in Bi2212 and Bi2223

The Josephson Vortex dynamics in high anisotropy superconductors Bi2212 and Bi2223 induced by AC magnetic field collinear to DC magnetic field and parallel to the layers is studied via their interaction with microwave field. Experimental results as function of DC magnetic field, AC magnetic field and temperature are presented. The AC induced microwave dissipation is larger than dissipation without AC field. The results are explained by the theoretical interpretation reported recently due to shaking by the AC field that depins the JV (Shaltiel et al., Phys. Rev. B 77, 014508, 2008). Similar behavior in these two compounds as a function of the variables involved discloses that the shaking effect should be observed in any high anisotropy superconductors. It shows that the AC field interacting with JV has an active and not the usual passive modulating role of the DC field in EPR dissipation experiments. The technique can be used to investigate JV dynamics and JV phase diagram.     

AC loss properties of elliptic superconducting wires exposed to a transverse magnetic field with an arbitrary angle

Analytical expressions of alternating current (AC) losses are derived in a superconducting wire with an infinite length and elliptic cross-section for limiting cases in which the amplitude of an external transverse magnetic field is much smaller or larger than the full penetration field. Since it is assumed that the superconducting wire is subject to Bean’s critical state model, in which the critical current density is independent of the magnitude of the local magnetic field, the AC losses under consideration are completely hysteretic. The expressions obtained explicitly include the effects of the aspect ratio of the wire cross-section and the external-field angle with respect to the broadest face. An approximated curve of the AC loss, which becomes equal to the analytical results under the limiting conditions mentioned above, is also proposed for a wide range of external-field amplitudes. In order to validate the proposed curve, the AC losses in the elliptic wires are numerically calculated by means of the minimization of magnetic energy. It is concluded that the discrepancy between the approximated curves and the numerical results of the AC losses is less than 40%.     

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.     

Numerical Simulation of Magnetic Flux Penetration and AC Loss in?HTSC Coated Conductor Tapes

The critical state model developed nearly 50 years ago by Bean (Phys. Rev. Lett. 8:250, 1962) allows finding analytical solutions for the magnetization of a superconducting slab in a parallel field and for a thin strip in perpendicular field, as well as the transport of AC current by a tape with elliptic or strip-like cross-section. Direct application of these models to the currently available HTSC coated conductor tapes is problematic because of several factors:

• Dependence of critical current on the magnitude of magnetic field and its orientation
• Non-uniformity of superconductor properties across the tape width or thickness
• Magnetism of the substrate

Plausible solution is a numerical model for the process of magnetic flux penetration and associated time evolution of current density distribution. State-of-the-art commercial codes for finite element could cope with this problem. The numerical method based on the relation between the current density and the change of vector potential of magnetic field in two-dimensional geometry is presented and the results obtained for coated conductor tapes are reported. Influence of mesh parameters (density and shape of elements) as well as the thickness of boundary between opposite current densities on the calculated AC loss is analyzed. The recommendations for practical use of simulation method are formulated.