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 loss of low temperature superconducting AC wire caused by longitudinal and azimuthal AC magnetic field components

We investigated the AC loss characteristics of a low temperature NbTi AC wire by measuring the AC transport current losses in the external AC magnetic field whose components are the longitudinal and transverse ones. The measurement results showed that the AC losses were significantly dependent on the directions and magnitudes of the external longitudinal field component. The AC losses caused by the longitudinal and azimuthal field components were estimated by our previously derived model. The theoretical results well explained the dependence of the AC losses on the longitudinal field components. It was also shown that the AC losses can be substantially reduced by the proper choice of the twisting way.     

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.     

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.     

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.     

Energy losses in a thin-wall tube multifilament composite superconductor carrying a transport current in a time-varying transverse magnetic field

An approach and formulae are given to calculate the hysteresis, coupling, eddy-current and Ohmic losses in a thin-wall tube multifilament composite superconductor carrying a transport current under low excitation by a homogeneous transverse time-varying magnetic field, taking into account possible filament saturation and current sharing effects. The technique can be applied to a single layer superconducting cable twisted around a thin-wall normal conducting tube.     

交变磁场下超导薄圆筒的交流损耗研究

通过数值模拟方法研究了超导薄圆筒在交变磁场下的交流损耗特性.这种超导体的几何模型为一个通有与外加磁场同相位的交流电且厚度可忽略的圆筒.基于Bean临界态模型,通过数值方法得到了交流损耗Q,与实验结果符合得很好.此值模拟方法仅适用于超导薄圆筒,对涂层超导体具有一定的应用价值.     

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.     

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.     

AC power loss for superconducting strips of arbitrary thickness carrying a transport current

The magnetic field and current distributions are computed numerically for a superconducting strip in the critical state with infinite length, but finite thickness and width. The width to thickness ratio is varied from 1 to 100, covering the range from square bars to thick films. For large aspect ratios (>10) the current and field distributions differ significantly from the 2D solution, because the Norris solution does not take into account (and thus does not shield) the transverse field parallel to the strip. Power loss exponents are calculated and found to vary from roughly 3 in a square bar to 4 in a highly aspected thin strip. In particular in the thin strip case the power loss exponents are current dependent due to the contribution of the loss caused by the transverse magnetic field. The loss in a multifilamentary conductor (or cable) is also estimated, taking into account the loss in the filaments. It is found that the overall loss (without coupling) is enhanced by a factor 1+1/n, where n is the number of filaments.     

Numerical calculation of current density distributions in high temperature superconducting tapes with finite thickness in self field and external field

The current density distribution of high temperature superconducting (HTS) tapes is modeled for the combined case of an alternating self and applied magnetic field. This numerical analysis is based on the two-dimensional Poisson equation for the vector potential. A one-dimensional current (z-direction) and a one-dimensional applied field (y-direction) are assumed. The vector potential is rewritten into an equation of motion for the current density J(x,y,t). The model covers the finite thickness of the conductor and an n-power E–J relation. The magnetic field dependence of J_c is also included in this E–J relation. A time-dependent two-dimensional current distribution that is influenced by the aspect ratio of the conductor and the material properties in E=f(J,B) is calculated numerically. The numerical results are compared with the experimental results for the AC loss of a tape driven by a transport current. Finally, a total AC loss factor is given for two cases in magnetic field direction, perpendicular and parallel to the conductor broad side.     

Heat diffusion characteristics of magnetite nanoparticles dispersed hydro-gel in alternating magnetic field

Heat diffusion characteristics of a spherical heat source dispersing magnetite nanoparticles (MNPs) in hydro-gel were investigated numerically and experimentally to evaluate the conditions required for magnetic fluid hyperthermia (MFH). Numerical estimation assumed one-dimensional spherical model and constant heat evolution. Experimental observation was carried out by exposing the magnetite-dispersed hydro-gel in an AC magnetic field with strength and frequency of 3.2 kA/m and 600 kHz, respectively. The temperature distribution observed along the radial axis of the spherical heat source agreed well with the theoretical estimation quantitatively and qualitatively. However, the minor difference existed between the theory and experiment was due to the variation in experimentally determined and actual particle size distributions. Thus, we could conclude that the proposed algorithm could be extended to be used in the estimation of the temperature distribution in intravital conditions with blood flow, metabolism etc., to arrive at biologically significant conclusions helpful for MFH cancer treatment.     

AC transport and magnetic characterisation of multifilamentary Ag-BSCCO(2223) tapes with different filament arrangements

AC losses in multifilamentary tapes depend on various parameters. Among them, geometrical factors such as overall tape width and thickness as well as the precise arrangement of the filaments are expected to have an important influence. Several theoretical models describe this dependency. In order to study these geometrical effects experimentally, we prepared a series of Bi(2223)/Ag tapes with gradually changing filament arrangements and tape aspect ratio, and characterised them by AC transport and magnetic measurements. The results are compared to model predictions.     

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.     

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.     

Electronic transport of Lorentz plasma with collision and magnetic field effects

The electronic transverse transport of Lorentz plasma with collision and magnetic field effects is studied by solving the Boltzmann equation for different electron density distributions. For the Maxwellian distribution, it is shown that transport coefficients decrease as ? increases, ? is the ratio of an electron's magneto-cyclotron frequency to plasma collision frequency. It means that the electrons are possible to be highly collimated by a strong magnetic field. For the quasimonoenergetic distribution with different widths, it is found that the transport coefficients decrease greatly as εˉ decreases.In particular when the width approaches to zero the transverse transport coefficients are hardly affected by the magnetic field and the minimal one is obtained. Results imply that the strong magnetic field and quasi-monoenergetic distribution are both beneficial to reduce the electronic transverse transport. This study is also helpful to understand the relevant problems of plasma transport in the background of the inertial confinement fusion.     

用费曼模型求截面为任意形状的无限长载流螺线管的磁场

利用载流线圈的费曼模型，根据截面为圆形的无限长载流螺线管的磁场分布和场叠加原理，求出截面为任意形状的无限长载流螺线管的磁场分布．     

Heat generation ability in AC magnetic field and their computer simulation for Ti tube filled with ferrite powder

The heat generation ability of needle-type materials was studied for the application of thermal coagulation therapy in an AC magnetic field. Although the Ti tube without the MgFe₂O₄ powder or Ti rod showed poor heat generation abilities in an AC magnetic field, the temperature was significantly increased by the presence of ferrite powder in the Ti tube. We confirmed using a computer simulation that the eddy loss of the Ti tube was increased by the enhanced magnetic flux density due to the ferrite powder in the Ti tube. The heat generation of the ferrite filled Ti tube was increased by utilization of the quenched MgFe₂O₄ powder from elevated temperature. The relative magnetic permeability of the quenched ferrite was enhanced with the decrease in the inverse ratio of the cubic spinel structure. The heat generation ability was increased with the increase in the relative magnetic permeability of the Ti tube with ferrite powder. The calculated joule loss based on the experimental results showed an agreement with those using the computer simulation.     

强磁场中氢分子离子H2^＋能级的绝热及绝热变分计算

采用绝热近拟和绝热变分近似两种方法,计算了均匀强磁场（１０≤β≤１０００）中Ｈ２＾＋的σｇ,πｕ,δｇ,Φｕ,γｇ,ηｕ态的能有有原子核间的平衡距离,并与前人的结果进行了比较。     

Synthesis and antibody conjugation of magnetic nanoparticles with improved specific power absorption rates for alternating magnetic field cancer therapy

Bionized nanoferrite (BNF) particles with high specific power absorption rates were synthesized in the size range of 20–100 nm by high-pressure homogenization for targeted cancer therapy with alternating magnetic fields. Several strategies were used to conjugate antibodies to the BNF particles. These strategies were compared using an immunoassay to find optimal conditions to reach a high immunoreactivity of the final antibody–particle conjugate.