AC losses in multifilamentary HTS-composite tapes based on BiPbSrCaCuO

Some results of AC loss measurements are presented for 19, 61, 127-filamentary Bi-2223/Ag tapes prepared by the ‘powder-in-tube' method. All measurements have been made at T=77 K under sinusoidal transport current with frequency in the range of 30–600 Hz and the current amplitude up to 30 A. The measurements have been carried out both in self field conditions and at the external magnetic field applied to the tape at the different angles. The dependencies of the AC losses on current amplitude and frequency have been obtained. It is found that for all tapes the current amplitude dependencies of the AC losses show good agreement with the Norris prediction for an elliptical or strip geometry. The AC loss dependencies on frequency were linear. The measurements of AC losses in external magnetic field show that the change of AC losses is only through the change of the critical current. So the transport AC losses in the tapes are the ‘saturation losses' that is they are different from classic hysteresis losses.     

Finite element analysis of AC loss in non-twisted Bi-2223 tape carrying AC transport current and/or exposed to DC or AC external magnetic field

AC losses in Bi-2223 superconducting tapes carrying AC transport current and/or exposed to DC or AC magnetic field are calculated with a numerical model based on the finite element method. Superconducting property is given by the E–J characteristic represented by a power law using equivalent conductivity. First, transport loss and magnetization loss are calculated numerically and compared with measured values. The calculated losses almost agree with the measured losses. Frequency dependencies of calculated and measured transport losses are compared with each other. Next, the influence of DC external magnetic field on the transport loss is studied. DC external magnetic field reduces n that is an exponent in the power law connecting resistivity and current density. The numerically calculated transport loss increases with increasing DC magnetic field. Finally, the total loss of superconducting tape carrying AC transport current in AC magnetic field is calculated. In the perpendicular magnetic field, the calculated total loss is lager than the sum of the transport loss and the magnetization loss, while they almost agree with each other in the parallel magnetic field.     

AC transport current loss of assembled conductor of HTS tapes

We study experimentally and theoretically the AC transport current loss characteristics of a tape in multiple tapes assembled in single layer and subject to external field produced by transport currents of adjacent tapes. We measured the AC transport current losses of a Bi2223 silver-sheathed tape in a single layer arrangement of three tapes using our newly developed potential leads arrangement to avoid spurious loss components caused by the magnetization in the adjacent tapes. In the paper, the influence of the external AC field produced by adjacent tapes on the loss characteristics is studied based on the experimental results and theoretical analysis.     

传输交流的Bi2223/Ag高温超导带在不同取向交流外场下的交流损耗

在高温超导的电力应用中，如超导电机、变压器等，多数情况下，高温超导带材在通以交流传输电流的同时还处于交变磁场中。此时，超导体的交流损耗不仅依赖于磁场的大小，还与磁场相对于超导带面的取向有关。本文在77K及工频50Hz情况下，实验研究了单根多芯Bi2223/Ag高温超导带及两带并联时的交流损耗随着外磁场与带面夹角的变化情况；以及交流磁场对临界电流的影响情况；并对单根带及两带并联的实验结果进行了比较与分析。     

Numerical and theoretical evaluations of AC losses for single and infinite numbers of superconductor strips with direct and alternating transport currents in external AC magnetic field

AC losses in a superconductor strip are numerically evaluated by means of a finite element method formulated with a current vector potential. The expressions of AC losses in an infinite slab that corresponds to a simple model of infinitely stacked strips are also derived theoretically. It is assumed that the voltage-current characteristics of the superconductors are represented by Bean’s critical state model. The typical operation pattern of a Superconducting Magnetic Energy Storage (SMES) coil with direct and alternating transport currents in an external AC magnetic field is taken into account as the electromagnetic environment for both the single strip and the infinite slab. By using the obtained results of AC losses, the influences of the transport currents on the total losses are discussed quantitatively.     

AC coupling losses in superconducting multistage cables with and without additional co-twisted copper strands

A simple technique is proposed to evaluate interstrand AC coupling losses deposed in superconducting multistage cables under low excitation of the transverse homogeneous time-varying magnetic field. The technique uses the superposition of the solutions for the induced coupling currents and interstrand or intersubcable AC losses in pairs of strands or subcables, constituting a multistage cable. The technique is valid under assumption of no resistance offered by strands and subcables for the longitudinal currents. The method allows one also to take into account the effect of additional co-twisted pure copper strands or subcables.     

AC losses and transverse resistivity in filamentary MgB2 tape with Ti barriers

We measured and analyzed AC losses of MgB₂ tape with 19 filaments surrounded by Ti barriers and embedded in copper stabilization, exposed to external magnetic field with frequencies from 30 mHz up to 1.4 Hz and amplitudes up to 0.8 T at 4.2 K. Using the measured frequency dependence of the total AC losses we determined the contribution of hysteresis and coupling losses. The transverse resistivity determined from the coupling losses is considerably higher than that corresponding to the resistivity of copper stabilization before the tape processing due to diffusion of Ti. From the measured penetration field critical current densities were determined using results of theories for circular as well as rectangular filaments.     

外场下机械振动对高温超导带材交流损耗的影响

高温超导带材在磁场中传输交变电流时,将受到电磁力的作用而产生机械振动,振动对带材的交流损耗将产生影响.本文讨论了振动情况下交流损耗的测量方法,在平行于带面的直流磁场下,测量了Bi-2223/Ag高温超导带材在不同振动情况下的交流损耗.结果显示:当传输电流频率偏离样品的共振频率时,振动对带材的交流损耗影响不大;只有当电流频率在共振频率附近时,样品产生剧烈振动,交流损耗才有明显的增加;另外,带材振动时的交流损耗随频率变化曲线的斜率比不振动时略有增加.     

A simple electromagnetic method of cyclic loss measurement for superconducting wires in a combined alternating transverse magnetic field and transport current

We measured cyclic losses in a superconducting wire, carrying alternating transport current, simultaneously exposed to an alternating transverse magnetic field. Samples of Bi-2223 Ag-sheathed tapes have configuration of a double-layer non-inductive coil, which itself is a pickup coil to measure the AC losses. Potential taps were attached to both terminals of the sample coil. The external field was applied along the axis of the sample coil. In this procedure, we can estimate an averaged Poynting's vector on a cylindrical surface between the two layers by means of signals from a pair of the potential taps and from pickup coils for the external magnetic field and the transport current. We can also measure a magnetization and an extended transport-current components of AC losses in addition to a total cyclic loss for a combined alternating external field and transport current. Obtained results are compared with numerical predictions of the critical state model taking into account the magnetic field dependence of critical current density.     

Calculation of AC losses in HTSC wires with arbitrary current voltage characteristics

A method for the calculation of magnetic field dynamics and AC losses in superconductors with smooth current–voltage characteristics is described. It is based on an integral equation for the current density, recently used by Brandt for magnetic relaxation. Brandt's equation is generalized to include arbitrary external magnetic fields and transport currents. One of the benefits of the integral equation formulation is that no boundary conditions ‘at infinity' are required, thus restricting the calculation region to the conductor cross section. The method is applied to superconducting tapes in oblique external fields. A further extension of the theory is shown to be applicable to the calculation of coupling losses in twisted multifilamentary superconductors.     

Effect of carbon substitution on low magnetic field AC losses in MgB2 single crystals

The DC magnetization and AC magnetic susceptibilities were measured for MgB₂ single crystals, unsubstituted and carbon substituted with the composition of Mg(B_0.94C_0.06)₂. AC magnetic losses were derived from the AC susceptibility data as a function of the AC amplitude and the DC bias magnetic field. From the DC magnetization loops critical current densities were derived as a function of temperature and DC field. Results show that the substitution with carbon decreases critical current densities at low external magnetic fields, in contrast to the well known effect of an increase of the critical current densities at higher magnetic fields.     

高温超导带材的交流损耗

介绍了交流损耗的物理机制及其与外场强度、频率等物理量间的关系 ;给出了单芯及多芯超导体中的交流损耗的实验结果及理论描述 ;指出了交流损耗研究中尚存在的某些问题。     

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency ω. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.     

高温超导YBCO带材的交流损耗的FEM仿真分析

对高温超导带材YBCO的交流损耗进行了仿真分析。运用有限元FEM方法,基于Maxwell方程组的数值建模,引入了基于实验数据的power-law对交流损耗进行计算。首先对自场下的交流损耗值进行了仿真计算并分析了带材的电流密度与磁场分布情况,并通过与实验测量数据做比较验证仿真方法的有效性。其次分别对不同幅值下的平行场与垂直场下的交流损耗进行了计算,将自场、平行场以及垂直场下的电流密度与磁场强度的分布以及交流损耗值进行了对比分析。     

High-Tc superconductors and AC loss in electrotechnical devices

To replace conventional normal conducting solutions in electrotechnical devices, high-T_c superconductors must offer distinct economical and technical benefits in terms of lower overall loss, volume and weight. Based on AC loss theory we design appropriate 50 Hz reference conductors for cables, transformers and other applications, calculate admissible limits for the conductor variables filament diameter, twist and matrix resistance and compare this to the present state of Bi-2223-tape conductors and AC loss measurements. Further the influence of perpendicular AC field components on losses is addressed. High current devices will require multistrand conductors, where nonuniform current distribution due to unbalanced magnetic coupling may result in partial saturation and enhanced losses. As an example we discuss the multilayer HTSC-cable and present a solution based on a ‘zero flux condition' for azimuthal and axial magnetic fields.     

45 kVA单相高温超导变压器交流损耗特性研究

本文研究以多芯不锈钢加强Bi2223/Ag带材绕制的45 kVA单相高温超导变压器的交流损耗特性.变压器绕组置于具有室温孔径的环形玻璃钢杜瓦内,铁芯穿过杜瓦室温孔径以保证铁芯与绕组分离并工作于室温环境.在77 K和工频下,基于Bean模型和绕组中的磁场分布计算了绕组的交流损耗,计算结果与传统电测法和热测法测量的变压器交流损耗结果一致;表明在77K绕组中交流损耗以磁滞损耗为主,涡流损耗和耦合损耗可以忽略不计.     

Measuring transport current loss of BSCCO/Ag tapes exposed to external AC magnetic field

BSCCO/Ag tape superconductors are developed for electrical power applications at liquid nitrogen temperatures. In these applications, e.g., superconducting transformers and power cables, an AC transport current and an AC magnetic field are present at the same time. A set-up to measure the influence of external AC magnetic field on the transport current loss, i.e., the voltage drop across a sample supplied with an AC transport current, has been developed. The magnetic field can be applied both parallel and perpendicular to the broad side of the tape conductor. An increase of the transport current loss due to the external AC magnetic field is observed. When a DC external magnetic field is applied the increase of the self-field loss can be described well by the decrease of the critical current due to the magnetic field. In the case of an AC external magnetic field this is only a minor effect. For magnetic field amplitudes higher than a certain threshold value the transport current loss is described reasonably well by the self-field loss and a dynamic resistance contribution calculated from the DC voltage–current relation in AC magnetic field.     

AC losses of YBa2Cu3O7−x high temperature superconductors

AC losses of randomly oriented and oriented grained YBa₂Cu₃O_7−x superconductors having different microstructures and silver content were studied at 77 K and frequency range between 0.5 Hz and 60 Hz. The measurements were made by an electrical technique applying an external sinusoidal magnetic field parallel to the longer axis of the specimen. In the randomly oriented samples, the results indicate that the addition of silver has no effect on the losses of the Y-123 superconductor. Unlike the behavior of the randomly oriented samples, the oriented material does not show grain decoupling and intergranular losses and its behavior is similar to that of conventional type II superconductors. The results also show that the oriented sample has a modest surface barrier against flux entry. In general, it is found that the critical state model can be used to describe the hysteretic dissipation of Y-123 superconductors, although some refinements need to be considered.     

Self-sustained firing activities of the cortical network with plastic rules in weak AC electrical fields

Both external and endogenous electrical fields widely exist in the environment of cortical neurons. The effects of a weak alternating current (AC) field on a neural network model with synaptic plasticity are studied. It is found that self-sustained rhythmic firing patterns, which are closely correlated with the cognitive functions, are significantly modified due to the self-organizing of the network in the weak AC field. The activities of the neural networks are affected by the synaptic connection strength, the external stimuli, and so on. In the presence of learning rules, the synaptic connections can be modulated by the external stimuli, which will further enhance the sensitivity of the network to the external signal. The properties of the external AC stimuli can serve as control parameters in modulating the evolution of the neural network.     

Effective AC Response of Nonlinear Spherical Coated Composites

Under alternating current electric field, effective response of granular nonlinear composites with spherical coated inclusions is investigated in the dilute limit by using the perturbation approach. For an external sinusoidal applied field with finite frequency ω, the local fields and potentials of composites in general consist of components at all harmonics for cubic nonlinear constitutive relationships. We derive the local potentials of spherical coated composites at harmonics. Moreover, we give the formulae of the nonlinear effective AC susceptibility at the third harmonic frequency.