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.     

On some consequences of an external magnetic field applied to HTS coils

A computational model which enables to evaluate the distribution of the critical currents, electric fields and the voltage in the winding of a solenoidal high temperature superconducting (HTS) magnets subjected to an external magnetic field parallel with the magnet axis, was developed. The model comes out from the well-known power law between the electric field and the transport current of the HTS tape short sample. It allows to predict the voltage–current V(I) characteristics of both the pancake coils and the complete magnet. The model was applied to the magnet system consisting of 22 pancake coils made of multifilamentary Bi(2223)/Ag tape at 20 K, which is subjected to an external uniform magnetic field parallel with the coil axis. A rather unexpected behavior of the magnet at different operating conditions (operating current and external magnetic field strength) is predicted, analyzed and reported together with a theoretical explanation. On one hand, the external uniform magnetic field parallel with the coil axis increases the resulting magnetic field strength, however, on the other hand it simultaneously decreases the angle between the resulting magnetic field and the tape surface. Thus, the effect of higher magnetic loading caused by the presence of an external magnetic field strength which is acting on individual turns located close to the coil’s flanges is compensated by more favorable orientation of the tape with respect to the resulting magnetic field. As a result, increase in the critical currents of these turns is expected. Further, the results indicate, that in case of the high field HTS insert coils the anisotropy in the I_c(B) characteristic does not play a substantial role. As a consequence, the technology of the production of the tapes for high field insert HTS coils should concentrate rather on the tapes having the current carrying capacity as high as possible, than on the attempt how to decrease the anisotropy in the I_c(B) by changing the architecture of the filaments in the tape.     

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.     

Magnetic ac loss in multi-filamentary Bi-2223 / Ag tapes

The ac loss in high-T_c superconducting tapes with twisted and non-twisted filaments has been studied by a magnetic method. A brief overview of the theoretical background and the experimental set-up is presented. Measurements were made at 77 K in a magnetic field of 50 Hz frequency and 0.001–0.7 T amplitude. Application of dc transport current made it possible to distinguish between the loss components, arising from intra-grain and from filament currents. The magnitude of the filament loss component indicates that the filaments are fully coupled, which agrees with theory. In other measurements, the orientation of the external field with respect to the tape was varied. Knowledge of the ac loss in parallel and in perpendicular field is sufficient to predict the ac loss for any intermediate orientations of the field.     

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.     

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.     

Comparison of transport and magnetic AC losses in Bi-2223/Ag tapes — the role of superconducting core geometry

AC losses were measured by 4-probe transport method and by external magnetization method in three samples of Bi-2223/Ag tape: a multifilamentary tape with separated filaments, another multifilamentary tape with ‘bridges' between filaments, and a two-shell tape. The transport losses agreed with those calculated using I_c from DC experiment. Magnetization experiments gave indications about the various paths of induced currents. For the tape with well separated filaments the main part of screening current closes inside individual filaments. Additional screening of the whole filamentary zone involves the normal metal matrix, leading to frequency dependent losses. In the case of tape with ‘bridged' filaments, supercurrents interconnect the filaments into bundles whose screening (and loss) is frequency-independent. Matching the experimental data indicates that a typical bundle was composed of 8 filaments. Magnetic losses of the two-shell tape were explained by a model for magnetization of superconducting wire with elliptical cross-section.     

Magnetic properties of (NdxY1-x)Co2(1⩾ x ⩾ 0)

The concentration dependence of T_c and T_R (T_c magnetic ordering temperature, T_R spin reorientation temperature) of the pseudobinary system (Nd, Y)Co₂ is reported. Furthermore the influence of an external magnetic field on the spin reorientation and the magnetization is studied. The observed variation of the magnetization in the vicinity of the spin reorientation is compared with theoretical results. For the calculation a Hamiltonian with terms describing a molecular field, a cubic crystal field, and an external field is used.     

Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy

While magnetoresistance (MR) has generally been found to be symmetric in applied field in nonmagnetic or magnetic metals, we have observed antisymmetric MR in Co/Pt multilayers. Simultaneous domain imaging and transport measurements show that the antisymmetric MR is due to the appearance of domain walls that run perpendicular to both the magnetization and the current, a geometry existing only in materials with perpendicular magnetic anisotropy. As a result, the extraordinary Hall effect gives rise to circulating currents in the vicinity of the domain walls that contributes to the MR. The antisymmetric MR and extraordinary Hall effect have been quantitatively accounted for by a theoretical model.     

On diamagnetism and non-dissipative transport

The states of free electrons in a magnetic field confined to a box of finite volume are determined and used to calculate the average magnetic moment and the non-dissipative electric and heat current in an unambiguous way. It is shown that for infinite volume the average magnetic moment coincides with the magnetization calculated by Landau. Similarly, for infinite volume, the non-dissipative transport coefficients coincide with those calculated by Zyryanov and Silin who use Landau's method and subtract the purely diamagnetic parts from the total currents. We think that our considerations give an answer to the often discussed question, why the Landau calculation of the magnetization and similar calculations of the non-dissipative transport coefficients are correct for a large system.     

Numerical modelings of superconducting wires for AC loss calculations

Superconducting properties of superconducting wires as well as the influence of their composite structure and twisting should be taken into account for their numerical modeling for AC loss calculations. Furthermore, complicated electromagnetic conditions in electrical apparatuses under which superconducting wires are used influence their AC loss properties; superconducting wires carry their transport current and are exposed to the external magnetic field whose direction and magnitude vary spatially. A series of numerical models of superconducting tapes based on the finite element method has been developed. In each model, some of the above-mentioned factors that could influence the AC loss properties are taken into account. The models are formulated with the current vector potential and the scalar magnetic potential (T–Ω method). Superconducting property is given by the E–J characteristic represented by a power law. The current distributions in non-twisted and twisted superconducting tapes carrying their transport current and/or exposed to the external magnetic field are calculated with these models to estimate their AC loss. The current distribution in a short piece of superconducting tape exposed to AC magnetic field is also calculated.     

Acoustic wave in a suspension of magnetic nanoparticle with sodium oleate coating

The ultrasonic propagation in the water-based magnetic fluid with doubled layered surfactant shell was studied. The measurements were carried out both in the presence as well as in the absence of the external magnetic field. The thickness of the surfactant shell was evaluated by comparing the mean size of magnetic grain extracted from magnetization curve with the mean hydrodynamic diameter obtained from differential centrifugal sedimentation method. The thickness of surfactant shell was used to estimate volume fraction of the particle aggregates consisted of magnetite grain and surfactant layer. From the ultrasonic velocity measurements in the absence of the applied magnetic field, the adiabatic compressibility of the particle aggregates was determined. In the external magnetic field, the magnetic fluid studied in this article becomes acoustically anisotropic, i.e., velocity and attenuation of the ultrasonic wave depend on the angle between the wave vector and the direction of the magnetic field. The results of the ultrasonic measurements in the external magnetic field were compared with the hydrodynamic theory of Ovchinnikov and Sokolov (velocity) and with the internal chain dynamics model of Shliomis, Mond and Morozov (attenuation).     

Calculations of the axial and azimuthal fluxes contained in a type II superconducting cylinder in a force-free configuration

The force free equation, J∧ B = 0, is expressed in an undimensionalized form for a reversible, Type II, superconducting cylinder carrying a transport current in a longitudinal magnetic field. Using a simple model, the form of the current distribution inside the specimen is varied, and this equation is solved to yield the total axial and azimuthal fluxes. For fixed values of the transport current and applied field it is shown that the total axial flux insensitive to the current distribution, whilst the total azimthal flux varies considerably. It is concluded, therefore, that measurements of the axial magnetization alone cannot discriminate between various force-free models.     

用外磁场控制电流感应磁化翻转效应中的临界电流方法

应用基于磁动力学方程的宏观唯象模型,研究了弱外磁场下纳米尺度赝自旋阀结构的电流感应磁化翻转效应.在统一考虑铁磁/非磁界面的自旋相关散射以及铁磁层中的自旋积累和弛豫过程后,给出了赝自旋阀结构在弱外磁场下的磁化翻转条件和临界电流.对该效应的数值计算解释了弱外磁场下赝自旋阀结构的电阻-电流回线的偏移,并给出了用外磁场控制电流感应磁化翻转效应中的临界电流方法. 关键词： 电流感应磁化翻转 外磁场 临界电流 赝自旋阀     

Influence of DC external magnetic field on AC transport current loss of HTS tape

We measured the AC transport current loss of Bi 2223 multifilament Ag-sheathed tape under DC external magnetic field of 0–0.2 T. There were discrepancies between the measured data and Norris' formula for elliptical model in the range of low value of I_p/I_c (I_p and I_c are peak of the AC transport current and critical current of the tape respectively), while without DC background field, the loss of the tape was close to Norris' formula. Theoretically speaking, even with the DC background field and decreased critical current the AC transport current loss of the tape follows Norris' formula which is derived from the Bean model. When DC background field is applied to the HTS tape, n value of the power law E–J characteristics decreases together with the decrease of J_c. Dependence of the AC transport current loss on the n value was analyzed by numerical calculation. The results show that the loss depends on the n value and that decrease of the n value is one of the causes of the discrepancies between the measured data and Norris' formula.     

Investigation of the static and dynamic magnetic properties of CoFe2O4 nanoparticles

We have investigated the magnetic behavior of cobalt ferrite nanoparticles with a mean diameter of 7.2 nm. AC susceptibility of colloidal cobalt ferrite nanoparticles was measured as a function of temperature T from 2 to 300 K under zero external DC field for frequencies ranging from f=10 to 10,000 Hz. A prominent peak appears in both χ′ and χ″ as a function of T. The peak temperature T₂ of χ″ depends on f following the Vogel–Fulcher law. The particles show superparamagnetic behavior at room temperature, with transition to a blocked state at T_B^m94 K in ZFC and 119 K in AC susceptibility measurements, respectively, which depends on the applied field. The saturation magnetization and the coercivity measured at 4.2 K are 27.3 emu/g and 14.7 kOe, respectively. The particle size distribution was determined by fitting a magnetization curve obtained at 295 K assuming a log-normal size distribution. The interparticle interactions are found to influence the energy barriers yielding an enhancement of the estimated magnetic anisotropy, K=6×10⁶ erg/cm³. Mössbauer spectra obtained at higher temperatures show a gradual collapse of the magnetic hyperfine splitting typical for superparamagnetic relaxation. At 4.2 K, the Mössbauer spectrum was fitted with two magnetic subspectra with internal fields H_int of 490, 470 and 515 kOe, corresponding to Fe³⁺ ions in A and B sites.     

高温超导磁体临界电流影响因素的研究

临界电流值是描述Bi2223高温超导带材性能的一个基本参数,在一定的温度条件下,Bi2223高温超导带材的临界电流是带材所在位置磁场大小和磁场方向的函数,其短样的临界电流值可以通过四引线法测量,单根超导带材的自场很小,磁场对临界电流的影响可以忽略.高温超导磁体的临界电流被定义成引发该磁体失超的最小电流,高温超导磁体的自场比单根超导带材的自场要大得多,磁体各个位置的磁场大小和方向各不相同,很难用理论的方法准确计算磁体的临界电流.对于高温超导磁体而言,除了磁场的影响因素以外,绕制磁体所用的超导带材自身的均匀性也是影响其临界电流的一个重要因素.本文对这两个因素进行探讨,并着重讨论高温超导带材自身的均匀性对临界电流大小的影响,本文的结论可以为高温超导磁体的设计、磁体绕制时带材的选择、磁体运行时安全工作电流的确定提供帮助.     

Influence of magnetic field on the interlayer interaction in (Co/Si/Gd/Si)n films

A singularity sensitive to the external magnetic field was observed in the temperature dependences of the magnetization of multilayer (Co/Si/Gd/Si)₂₀ films in the vicinity of compensation temperature. Possible mechanisms responsible for the unusual behavior of the magnetization are discussed.     

Magnetocaloric and magnetoresistance properties of La2/3Sr1/3Mn1−xCoxO3 compounds

Structural, magnetic, magnetoresistance and magnetocaloric studies on La_2/3Sr_1/3Mn_1−xCo_xO₃ compounds were reported. The samples were prepared by the conventional ceramic method. X-ray analysis showed the presence of one phase only, in all studied samples. From electrical resistance measurements it was found that the samples show large negative magnetoresistance behavior. The magnetic measurements were performed in a large temperature range, 4.2–750 K and external magnetic fields up to 5 T. The adiabatic magnetic entropy changes, |ΔS|, were determined from magnetization data. Large magnetocaloric effect (MCE) has been obtained in all studied samples.     

The distribution of equilibrium magnetization currents in systems with dimensional quantization in a finite magnetic field

The distribution of equilibrium magnetization currents in two-dimensional bounded systems placed in an external magnetic field is studied. A half-plane, a quantum disk, and a wide quantum ring are considered. The passage from classical to quantizing magnetic fields is investigated. The edge currents near the boundary of the half-plane are shown to experience damped (far from the boundaries) spatial oscillations related to the Fermi electron wavelength. The region occupied by currents was found to narrow with increasing field. Apart from these oscillations, the current contains a component that smoothly changes with distance but oscillationally depends on the position of the Fermi level relative to the Landau levels. The suppression of the oscillations by temperature is studied. The spatial distribution of the current in a circular disk and a ring is shown to significantly depend on the position of the Fermi level.