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.     

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.     

Applied current density in the section of a type-II superconductor

A thermodynamic treatment suggests that the applied current density is located in the surface sheet in order to create a null magnetic local field inside the bulk superconductor according to the London penetration law, until there is no dissipation in the sample. A direct investigation of this evidence is performed by measuring the field created by the current near the surface of square- or rectangular-section samples. This field is known by the measurement of the flux variation in small pickup coils while the current is turned on and off. The main experimental result shows that the critical current intensity does not flow in a uniform distribution inside the sample section and so denies a physical meaning to the notion of critical current density.Laboratoire associé au C.N.R.S., 24 rue Lhomond, 75231 Paris Cedex 05.     

Effect of an Elliptical Inclusion on Critical Current Density of a Long Cylindrical High-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> Superconductor

An analytical investigation is presented to display the distribution of critical current flow and trapped magnetic field around an elliptical nonsuperconducting inclusion within a long cylindrical superconductor. The current streamlines, the critical current density, and the trapped field around the inclusion in the superconductor without deformation are obtained based on the Bean model and the method of conformal mapping. The results show that the critical current density of a superconductor will be decreased dramatically due to a macroscopic nonsuperconducting inclusion. Besides, the maximum trapped magnetic field is limited by the inclusion.     

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%.     

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.     

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.     

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.     

Study on cross section of high temperature superconducting coil

It is in particular of importance for HTS coils to secure a larger central magnetic field and/or a large stored energy with shorter length of HTS tapes. The critical current of an HTS tape depends on both the flux density and the flux angle against tapes. From this point, the performance improvement of HTS coils is taken into account with an analytical model. The minimum volume coil derived from the Fabry Factor constant curve is taken concerning the original coil shape, which is often employed in low temperature superconducting coils. The coil critical current was analyzed in consideration of the anisotropic properties of the tape.The electric field of HTS tapes in the coil was calculated at the coil critical current and the high electric field portion were cut out. The optimal coil cross section is obtained by iterating this calculation process. As a result, the critical current and the stored energy density of the coil were improved. The stored energy density increased about 17% and the central magnetic field was almost kept constant regardless of 19% reduction of HTS tapes, as compared with the original coil with the rectangular cross section.     

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.     

Influence of Critical Current Density Distribution on Transport AC Losses in Superconducting Wire in a DC Magnetic Field

In typical application-like conditions, the inhomogeneous distribution and anisotropy of critical current density must be considered simultaneously in transport AC loss calculation. In this paper, we derive the analytical formulas of transport AC losses for high-temperature superconductors (HTSs) with linear and quadratic distribution of critical current density under applied DC magnetic field. The influence of the inhomogeneous distribution and anisotropy of critical current density has been analyzed. The results show that the impact of the distribution form on transport AC loss is more obvious under applied DC magnetic field. And the influence of applied DC magnetic field will increase as the distribution form becomes steeper.     

Test Coils Made of Tl-1223 Tapes

Silver sheathed Tl-1223 tapes were prepared by a powder-in-tube process. The critical current density of short samples was 18 kA/cm² at 77 K. Longer tapes up to 1.2 m, prepared by sequential pressing, had a critical current density of 12 kA/cm². From these tapes we have wound two coils. A solenoid coil with 5 windings was made of 8 tapes with a total length of 4.5 m. At 77 K the critical current of the coil was 23 A in the self generated magnetic field (18 Gauss at the centre of the coil). Using an iron yoke the critical current remained at 22 A while the generated magnetic field increased to 120 Gauss. A pancake coil with 15 windings, made of 5 tapes with a total length of 5 m, generated a magnetic field of 149 Gauss at the critical current of 12 A. From measurements of the critical current density of our tapes in applied magnetic fields, we conclude that coils made of Tl-1223 tapes can be used to generate higher magnetic fields at 77 K.     

Effect of Critical Current Density and Critical Temperature on ac Susceptibility

Based on the flux creep equation, the effect of critical current density and critical temperature on ac susceptibility is investigated numerically in a superconducting slab immersed in an ac magnetic field. The current density dependence of the flux creep activation barrier is employed as the logarithmic law. The fundamental ac susceptibilities of the slab as a function of temperature for the same ac field have been derived in a unified picture. The results show that ac susceptibility in flux creep regime is affected by critical current density and critical temperature.     

Magnetization of a Current-Carrying Superconducting Disk with B-Dependent Critical Current Density

In the frame work of the critical state model (CSM), the magnetic response of a thin type-II superconducting disk that carries a radial transport current and is subjected to an applied magnetic field have been studied. To this end, we have studied the process of the magnetic flux-penetration. For a disk initially containing no magnetic flux but carrying a radial current, when a perpendicular magnetic field is applied, magnetic flux-penetration occurs in three stages: (1) the magnetic flux gradually penetrates from the edges of the disk until an instability occurs, (2) there is a rapid inflow of magnetic flux into the disk’s central region, which becomes resistive, and (3) magnetic flux continues to enter the disk, while persistent azimuthal currents flow in an outer annular region where the net current density is equal to J _c . Also the behavior of a current-carrying disk subjected to an AC magnetic field is calculated. The magnetic flux, the current profiles and the magnetization hysteresis loops are calculated for several commonly used J _c (B) dependences. Finally, the results of the applications of the local field-dependent of the critical current density J _c (B) are compared with those obtained from the Bean model.     

Optimization of superconducting solenoid

The maximum current of a superconducting solenoid is restricted by the maximum magnetic field. Therefore current density in low magnetic field regions becomes much smaller than the critical current density at those magnetic fields. This means that the superconductors are used inefficiently. A simple way to use superconductors more efficiently is to divide the solenoid into several sections according to their magnetic field strength. A method of minimizing the winding volume of the superconducting solenoid by such a division is described using certain approximations. This method is also very convenient for designing the solenoid with the highest current density or the most economical solenoid made with different superconducting materials.     

Dendritic flux avalanches in superconducting Nb3Sn films

The penetration of magnetic flux into a thin superconducting film of Nb₃Sn with critical temperature 17.8 K and critical current density 6 MA/cm² was visualized using magneto-optical imaging. Below 8 K an avalanche-like flux penetration in form of big and branching dendritic structures was observed in response to increasing perpendicular applied field. When a growing dendritic branch meets a linear defect in the film, several scenarios were observed: the branch can turn and propagate along the defect, continue propagation right through it, or “tunnel” along a flux-filled defect and continue growth from its other end. The avalanches manifest themselves in numerous small and random jumps found in the magnetization curve.     

Surface effect on the critical current density of superconducting niobium

Experiments are described which measure the critical current density of single and polycrystal niobium samples. The density measured is related to the ac losses of the sample caused by an applied ac field in the presence of a dc magnetic field. It was found that the critical current density depends upon the surface of the sample increasing with the surface smoothness.     

Flux-Pinning-Induced Stress and Deformation Analyses of a Long Rectangular Superconducting Bicrystal

The flux-pinning-induced stress and deformation of a long rectangular superconducting bicrystal with an arbitrary aspect ratio are analyzed based on the critical-state model and the finite element numerical method. The flux and current distributions in the superconductor with a low-angle grain boundary (GB) are obtained based on a constant GB critical current density assumption. The distributions of the stresses within the superconductor are obtained for different magnetization stages. The deformation and especially the shape distortion in the irreversible magnetostriction of the superconductor are analyzed. In addition, the relation between the maximum stress on the grain boundary and the ratio of the GB critical current density to the grain critical current density is discussed when the applied magnetic field is reduced to zero.     

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.     

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.