Calculating transport AC losses in stacks of high temperature superconductor coated conductors with magnetic substrates using FEM

In this paper, the authors investigate the electromagnetic properties of stacks of high temperature superconductor (HTS) coated conductors with a particular focus on calculating the total transport AC loss. The cross-section of superconducting cables and coils is often modeled as a two-dimensional stack of coated conductors, and these stacks can be used to estimate the AC loss of a practical device. This paper uses a symmetric two dimensional (2D) finite element model based on the H formulation, and a detailed investigation into the effects of a magnetic substrate on the transport AC loss of a stack is presented. The number of coated conductors in each stack is varied from 1 to 150, and three types of substrate are compared: non-magnetic weakly magnetic and strongly magnetic. The non-magnetic substrate model is comparable with results from existing models for the limiting cases of a single tape (Norris) and an infinite stack (Clem). The presence of a magnetic substrate increases the total AC loss of the stack, due to an increased localized magnetic flux density, and the stronger the magnetic material, the further the flux penetrates into the stack overall. The AC loss is calculated for certain tapes within the stack, and the differences and similarities between the losses throughout the stack are explained using the magnetic flux penetration and current density distributions in those tapes. The ferromagnetic loss of the substrate itself is found to be negligible in most cases, except for small magnitudes of current. Applying these findings to practical applications, where AC transport current is involved, superconducting coils should be wound where possible using coated conductors with a non-magnetic substrate to reduce the total AC loss in the coil.     

Discrete temperatures in high-temperature superconductors

The low-amplitude AC susceptibility on intact and deformed Bi2223/Ag tapes has been measured as a function of temperature, frequency, AC amplitude and DC magnetic field. The deformation resulted in the splitting of the χ″(T) peak into three peaks situated near 30, 58 and 90 K. In zero magnetic field, these temperatures were identified as the Kosterlitz–Thouless transition temperatures of low number stacks of superconducting layers. An external magnetic field redistributed the dissipation among the peaks, and moved them to lower temperatures (and suppressed the highest temperature peak). In a finite field, each peak corresponds to the stack melting temperature T_m. The melting temperature in each stack was found to be a field-dependent parameter, with a minimum value=T_KT of a stack of thickness that is less by one layer. The T_m decreases exponentially with the field, and the rate of decrease depends on the interstack Josephson and magnetic interactions. With a universal set of T_KT, the vortex melting line of a tape is a linear combination of the T_m(H) for the low-number stacks.     

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.     

Decrease of magnetic AC loss in twisted-filament Bi-2223 tapes

In AC power-engineering applications, a large part of the AC loss in the superconductor is due to magnetization by the external field. This magnetic AC loss has been well described for the low-T_c conductors. In Bi-2223 tapes the picture is different due to strong anisotropy, granularity and flux creep. Magnetic AC loss in various twisted and non-twisted Bi-2223 tapes has been measured at power frequencies by a pickup method. The results are compared to theoretical models of magnetization loss. When the field is parallel to the tape plane, the filaments in twisted tapes can be decoupled and the AC loss is decreased even when the matrix is pure silver. The extra effect of higher-resistance matrix materials is studied. In perpendicular field it is more difficult to decouple the filaments, due to the particular tape geometry. Contrary to a wire, there are essential differences between the AC loss mechanisms in a long twisted tape and those in a short piece of non-twisted tape. Finally, the dynamic resistance caused by the AC magnetic field is examined.     

Influence of the carbon substitution on the critical current density and AC losses in MgB<Subscript>2</Subscript> single crystals

The DC magnetization and AC complex magnetic susceptibilities were measured for MgB₂ single crystals, unsubstituted and carbon substituted with the composition of Mg(B_0.94C_0.05)₂. The measurements were performed in AC and DC magnetic fields oriented parallel to the c-axis of the crystals. From the DC magnetization loops and the AC susceptibility measurements, critical current densities (J _c were derived as a function of temperature and the DC and AC magnetic fields. Results show that the substitution with carbon decreases J _c ) at low magnetic fields, opposite to the well known effect of an increase of J _c at higher fields. AC magnetic losses were derived from the AC susceptibility data as a function of amplitude and the DC bias magnetic field. The AC losses were determined for temperatures of 0.6 and 0.7 of the transition temperature T _c , so close to the boiling points of LH₂ and LNe, potential cooling media for magnesium diboride based composites. The results are analyzed and discussed in the context of the critical state model.     

90° pulsed magnetization of ferrite-garnet films with easy-plane anisotropy

The process of pulsed 90° magnetization of ferrite-garnet films was studied. These films, in addition to easy-plane anisotropy, have biaxial anisotropy in the film plane with an effective field H _K2 ? 40–55 Oe. the pulsed magnetization curve contains two portions separated by a kink observed at a field pulse amplitude H _p=H _p ^* ? 16–18 Oe. An analysis of the magnetization signals showed that the restoring torque, which is mainly caused by biaxial-anisotropy forces, is overcome in fields H _p ≥ H _p ^* and that magnetization rotation occurs. In fields H _p < H _p ^* , the magnetization vector rotates at the initial stage only and the angle of rotation ?_in is less than 25°–26°. The field H _p ^* and angle ?_in are calculated. The results of the calculations are confirmed by experimental data. In fields H _p > H _p ^* , the process of magnetization is accompanied by oscillations of the magnetization vector. In contrast to free magnetization oscillations, these oscillations are nonlinear and the frequency of the first harmonic (≈5 × 10⁸ Hz) is much lower than that for free oscillations, (7–12) × 10⁸ Hz. Oscillations are excited at a pulse rise time of ≈6 ns.     

Electrical and magnetic properties of hot extruded Bi-2223/Ag concentric tapes

Summary In this work we report on the anisotropic physical properties of silver-sheathed Bi-2223 tapes fabricated by means of hot extrusion and repeated pressing and sintering processes. The obtained Bi-2223/Ag short tapes, having critical current densitiesJ _c of 20–30 kA/cm² at 77 K, 0 T, were measured in external magnetic fields up to 0.5T applied in two different orientations (i.e. μ₀H‖(a,b)-planes and μ₀H ⊥(a,b)-planes). The magnetic characterizations were performed in a wide range of temperatures and magnetic fields to study the first magnetization curve of tapes evaluating the lower critical fields μ₀H_c1⊥ab and ⊥₀H_c1#x2016;ab and their dependences on temperature. TheJ _c values at different fields in the temperature range 4.6–90 K, calculated from the magnetization data by the critical state model, are also presented. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Precursor diamagnetism in superconducting Al films

The precursor diamagnetism is studied in a stack of Al films whose thickness is much smaller than the coherence length. The magnetization shows the (T ? T_c)^?1 behavior in a finite range of temperature above T_c. At T_c, in low magnetic fields constant magnetization independent of the field strength is observed. The results are in agreement with the theories of the two-dimensional superconductor.     

AC losses in multifilamentary Bi(2223) tapes with an interfilamentary resistive carbonate barrier

For the most common AC application frequencies, the main component of the AC losses in multifilamentary Bi(2223) tapes are caused by hysteresis- and coupling losses. These losses can be reduced enhancing the matrix resistivity and applying a twist to the filaments. We report on the AC loss properties of 37-filament tapes with AgAu (8 wt.%) matrix, and novel 19-filament tapes with SrCO₃ barriers between the filaments. We performed transport AC loss and magnetic AC loss measurements in parallel and perpendicular magnetic fields. Both kinds of tapes were also prepared with filament twists below a twist pitch of 20 mm. The influence of the different tape modifications on the AC loss behaviour is presented and compared with theoretical models to understand the effect of the resistive matrix. In the case of magnetic AC loss measurements, reduced AC losses due to decoupled filaments were observed for the twisted tapes with a resistive matrix in low parallel fields.     

Imaging magnetic responses of nanomagnets by XPEEM

The Spin-resolved Photoelectron Emission Microscope (SPEEM) is a permanently installed set-up at Helmholtz-Zentrum Berlin (HZB). Due to its specific contrast it is mainly used for magnetic imaging and micro-spectroscopy with quantitative analysis. A crucial point in magnetic imaging is the application of magnetic fields. Many experiments require observation of magnetic responses or the preparation of a certain magnetic state during the measurement. We present a dedicated magnetic sample holder combining magnetic field during imaging with additional temperature control. This set-up enables SPEEM to measure magnetization curves of individual Fe nanocubes (18 nm)³ in size. If additionally alternating magnetic fields are applied we can image the local magnetic AC susceptibility (χ_AC) as a function of temperature. The latter is ideally suited to visualize local variations of the Curie temperature (T_C) in nano- and microstructures.     

Study on electro-magnetic properties of La substituted Ni–Cu–Zn ferrite synthesized by auto-combustion method

(Ni_0.25Cu_0.20Zn_0.55)La_xFe_2−xO₄ ferrite with x=0.00, 0.025, 0.050 and 0.075 compositions were synthesized through nitrate–citrate auto-combustion method. Crystalline spinel ferrite phase with about 16–19 nm crystallite size was present in the as-burnt ferrite powder. These powders were calcined, compacted and sintered at 950 °C for 4 h. Initial permeability, magnetic loss and AC resistivity of different compositions were measured in the frequency range from 10 Hz to 10 MHz. Saturation magnetization and hysteresis parameters were measured at room temperature with a maximum magnetic field of 10 kOe. Permeability and AC resistivity were found to increase and magnetic loss decreased with La substitution for Fe, up to x=0.025. Saturation magnetization and coercive field also increases up to that limit. The electromagnetic properties were found best in the ferrite composition of x=0.025, which would be better for more miniaturized multi layer chip inductor.     

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。     

Very high field magnetization and AC susceptibility of native horse spleen ferritin

The magnetization of native horse spleen ferritin protein is measured in pulsed magnetic fields to 55 T at T=1.52 K. The magnetization rises smoothly with negative curvature due to uncompensated Fe³⁺ spins and with a large high field slope due to the underlying antiferromagnetic ferritin core. Even at highest fields the magnetic moment is only ∼4% of the saturation moment of the full complement of Fe³⁺ in the ferritin molecule. The AC magnetic susceptibility, χ_AC(T,f), responding to the uncompensated spins, reaches a maximum near the superparamagnetic blocking temperature with the temperature of the maximum, T_M, varying with excitation frequency, T_M⁻¹ α log f for 10?f?10⁴ Hz.     

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.     

A characteristic class of quantities in nonequilibrium thermodynamics and a statistical justification of the local equilibrium approximation

A theory of bandwidth anisotropy in metallic ferromagnets developed previously is specialised to the case of 5d electrons in a hexagonal close-packed lattice. This theory is combined with a model for 5d electrons in the heavy rare earth metals to give a new theory for the low temperature values of the magnetic anisotropy coefficientsκ ₂ ⁰ andκ ₄ ⁰ in Tb, Dy, Ho, Er and Tm. In this theory the magnetic anisotropy is due to a combination of (i) crystal fields acting on 5d and 4f electrons and (ii) bandwidth anisotropy associated with a dependence of 5d bandwidths on magnetization direction. After use is made of empirical upper limits on the eighth order magnetic anisotropy in Gd, there remain four partially adjustable parameters of importance in the theory. These can be chosen to give a good fit to the six observed values forκ ₂ ⁰ andκ ₄ ⁰ in Tb, Dy and Ho. Crystal fields corresponding to negative point charges are seen by 5d electrons, but because of 4f – 5d interactions effective fields of larger magnitude and opposite sign act on 4f shells. Bandwidth anisotropy gives a significant contribution toκ ₄ ⁰ of opposite sign to that due to crystal fields, and dominates the latter in Tb and Er.     

Interfilamentary coupling properties of Bi2223/Ag tapes with oxide barriers subjected to AC perpendicular magnetic field

In this paper, we fabricated Bi2223 tapes with interfilamentary oxide barriers and evaluated interfilamentary coupling properties under an AC perpendicular magnetic field at 77 K. To avoid the side effect on Bi2223 phase formation during sintering process, SrZrO₃ was selected for barrier materials. Moreover, 20 wt.% Bi2212 was mixed with SrZrO₃ to improve its ductility for cold working. Monocore Ag-sheathed rods were coated by the oxide barriers with slurry before stacking with a honeycomb structure. By twisting the filament with twist pitch length below 10 mm and introducing interfilamentary barriers, the coupling frequency (f_c) under an AC perpendicular field, which is inversely proportional to the decay time constant (τ_c) of coupling current, exceeded 100 Hz. At perpendicular field amplitude above full-penetration field, the magnetization losses of the twisted barrier tape were reduced by 30–40% around power-grid frequency, compared with analytical values for fully-coupled filaments. However, the loss values were still considerably higher than the prediction of the hysteresis loss (Q_h) for the completely decoupled filaments. From the frequency dependence of losses, it was suggested that the loss reduction of twisted barrier tape around power-grid frequency were limited by not only the contribution of coupling current loss (Q_c) but also the insufficient Q_h reduction due to the presence of physical connection among the filaments positioned near the center of a tape section.     

Anomalous magnetization of CsFeCl3 appearing at the applied magnetic fields exceeding 33 T

The magnetization of a singlet-ground-state magnet CsFeCl₃ at 4.2 and 1.3 K is measured by the pulsed magnetic field up to 40 T applied parallel to the crystal c-axis. In both temperatures, a large linear increase in the magnetization appears between 4 and 12 T, which is consistent with the magnetization observed using the static magnetic fields. Above 12 T, the magnetization increases gradually up to 33 T. A metamagnetic transition appears around 34 T suggesting a new magnetic structure. The possible models are discussed.     

Magnetization anomalies in melt-spun Ni–Mn–Ga ribbons

Temperature and field dependencies of the magnetization of melt-spun ribbons of Ni_45.7Mn_37.2Ga_17.1 (T_C<T_A) and Ni_54.3Mn_20.5Ga_25.2 (T_C>T_A), where T_A and T_C are the reverse martensitic transformation and Curie temperatures, respectively, have been studied in broad ranges of magnetic fields (±30 kOe) and temperatures (10–350 K). It was found that the magnetic and thermomagnetic properties have a number of peculiarities and anomalies. Particularly, the magnetization values measured at both low and high magnetic fields increase significantly after annealing. Low-temperature anomalies of magnetization suggest the presence of the superparamagnetic behavior and/or phenomena related to the concurrent exchange interactions in the as-spun state. The obtained results can be explained by the influence of concentration inhomogeneities and atomic disordering in the rapidly quenched ribbons, which can be reduced by annealing.     

Magnetization processes of CuMn below the freezing temperature Tf

A simple classical model [5] that is based on a blocking of magnetic clusters in a uniaxial anisotropy field explains characteristic properties of magnetization processes of Cu(5–15 at.%) Mn as transition states between the “zero point magnetization” M₀ = M(T → OK) and the thermal equilibrium magnetization M_∞ = M(t → ∞, T). Further it shows two facts the experimental confirmations of which we report in this paper: (a) a magnetization decrease with increasing temperature in high fields and (b) a superposition rule for the magnetization processes in small fields and at low temperatures.