Numerical modeling of superconductors is widely recognized as a powerful tool for interpreting experimental results, understanding physical mechanisms and predicting the performance of high-temperature superconductor (HTS) tapes, wires and devices. This is especially true for ac loss calculation, since a sufficiently low ac loss value is imperative to make these materials attractive for commercialization. In recent years, a large variety of numerical models, based on different techniques and implementations, have been proposed by researchers around the world, with the purpose of being able to estimate ac losses in HTSs quickly and accurately. This article presents a literature review of the methods for computing ac losses in HTS tapes, wires and devices. Technical superconductors have a relatively complex geometry (filaments, which might be twisted or transposed, or layers) and consist of different materials. As a result, different loss contributions exist. In this paper, we describe the ways of computing such loss contributions, which include hysteresis losses, eddy current losses, coupling losses, and losses in ferromagnetic materials. We also provide an estimation of the losses occurring in a variety of power applications.

Invisibility to electromagnetic fields has become an exciting theoretical possibility. However, the experimental realization of electromagnetic cloaks has only been achieved starting from simplified approaches (for instance, based on ray approximation, canceling only some terms of the scattering fields, or hiding a bulge in a plane instead of an object in free space). Here, we demonstrate, directly from Maxwell equations, that a specially designed cylindrical superconductor-ferromagnetic bilayer can exactly cloak uniform static magnetic fields, and we experimentally confirmed this effect in an actual setup.

A magnetic field harmonically varying in time (to probe the sample) and a lock-in technique (to register the sample response sensed by a pickup coil) are widely used for characterizing superconductors. Measuring the temperature dependence of the complex AC susceptibility is the most common procedure of this type. This paper reviews these techniques, introducing in addition the complex AC susceptibility, the so-called 'wide-band AC susceptibility'. The latter quantity refers to the magnetic flux and often offers an easier meeting between theory and experiment. Starting from models for linear flux diffusion, reversible screening, volume and surface flux pinning and the intermediate regime in a type II superconductor, the expressions for the complex AC susceptibility in different cases are presented and compared with those derived for the wide-band AC susceptibility. Derivation of the basic physical properties of high-T c superconducting materials from the AC data (resistivity, critical temperatures and fields, London and Campbell penetration depths, critical current density, granularity and content of superconducting phase, irreversibility line, pinning potential) is then thoroughly discussed.

Many superconductor applications require cables with a high current capacity. This is not feasible with single-piece coated conductors because their ac losses are too large. Therefore, it is necessary to develop superconducting cables with a high current capacity and low ac losses. One promising solution is given by ROEBEL cables. We assembled three ROEBEL cables from commercial YBCO coated conductors. The cables have the same width but a different number of strands, which results in different aspect ratios and current capacities. We experimentally studied their ac losses under a transport current or a perpendicular magnetic field. In addition, we performed numerical calculations, which agree with the experiments, especially for the transport case. We found that in the cables there is good current sharing between the strands. We also found that stacking the strands reduces the magnetization losses. For a given critical current, thicker cables have lower magnetization ac losses. In addition, a conducting matrix is not required for a good current sharing between strands.

The case of ac transport at in-phase alternating applied magnetic fields for a superconducting rectangular strip with finite thickness has been investigated. The applied magnetic field is considered perpendicular to the current flow. We present numerical calculations assuming the critical state model of the current distribution and ac loss for various values of aspect ratio, transport current and applied field amplitude. A rich phenomenology is obtained due to the metastable nature of the critical state. We perform a detailed comparison with the analytical limits and we discuss their applicability for the actual geometry of superconducting conductors. We also define a loss factor which allow a more detailed analysis of the ac behavior than the ac loss. Finally, we compare the calculations with experiments, showing a significant qualitative and quantitative agreement without any fitting parameter.

The electromagnetic properties of a pancake coil in AC regime as a function of the number of turns is studied theoretically and experimentally. Specifically, the AC loss, the coil critical current and the voltage signal are discussed. The coils are made of Bi 2 Sr 2 Ca 2 Cu 3 O 10 /Ag (BiSCCO) tape, although the main qualitative results are also applicable to other kinds of superconducting tapes, such as coated conductors. The AC loss and the voltage signal are electrically measured using different pick up coils with the help of a transformer. One of them avoids dealing with the huge coil inductance. Besides, the critical current of the coils is experimentally determined by conventional DC measurements. Furthermore, the critical current, the AC loss and the voltage signal are simulated, showing a good agreement with the experiments. For all simulations, the field dependent critical current density inferred from DC measurements on a short tape sample is taken into account. 1 In fact, this condition is not strictly sufficient. The external field must be much larger than the self field of a stack made of as many tapes as those in the radial direction when the radial field dominates the AC loss (and equivalent with the axial direction when the dominant is the axial field).

A calibration free measurement method for determination of the magnetization loss of superconducting samples exposed to the external AC magnetic field is presented. The idea is based on the measurement of the part of the power which is supplied by the AC source to the AC magnet generating the magnetic field, in which the sample is located. It uses a coil wound in parallel to the AC field magnet as the measurement coil. To achieve the necessary sensitivity, two identical systems are used, each consisting of an AC magnet and a measurement coil, one of them containing the sample and the other left empty. No measurement and/or calculation of the calibration constant is required. To confirm the suitability of this method, the loss of a Cu sample with known dissipation was measured. The applicability to the AC magnetization loss measurements of superconducting tapes is presented.

Future use of coated conductors in electric power applications like transmission cables, transformers or fault current limiters is sensitive to the amount of dissipation in the AC regime. This paper analyses factors controlling AC loss of coated conductors in typical configurations: the self-field case when transport current generates the magnetic field, and the case of AC applied field where the orientation of magnetic field with respect to the superconducting layer plays a significant role.We illustrate that a high-quality CC tape with non-magnetic substrate follows rather well the models developed for a thin strip. However, to meet an excellent agreement between experiment and theoretical prediction a detailed knowledge of the superconductor properties is necessary and a numerical method must be involved.In the case of a superconducting layer deposited on a ferromagnetic substrate theoretical predictions give only basic directions and one must rely on numerical simulations entirely. We demonstrate that, with the help of a dedicated analysis of experimental data, very good AC loss prediction is also possible for superconductor-ferromagnetic composites. Novel designs of coated conductor architectures can be developed in this way.