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.

Many large-scale applications require electromagnetic modelling with extensive numerical computations, such as magnets or 3-dimensional (3D) objects like transposed conductors or motors and generators. Therefore, it is necessary to develop computationally time-efficient but still accurate numerical methods. This article develops a general variational formalism for any E(J) relation and applies it to model coated-conductor coils containing up to thousands of turns, taking magnetization currents fully into account. The variational principle, valid for any 3D situation, restricts the computations to the sample volume, reducing the computation time. However, no additional magnetic materials interacting with the superconductor are taken directly into account. Regarding the coil modelling, we use a power law E(J) relation with magnetic field-dependent critical current density, Jc, and power law exponent, n. We test the numerical model by comparing the results to analytical formulas for thin strips and experiments for stacks of pancake coils, finding a very good agreement. Afterwards, we model a magnet-size coil of 4000 turns (stack of 20 pancake coils of 200 turns each). We found that the AC loss is mainly due to magnetization currents. We also found that for an n exponent of 20, the magnetization currents are greatly suppressed after 1 hour relaxation. In addition, in coated conductor coils magnetization currents have an important impact on the generated magnetic field; which should be taken into account for magnet design. In conclusion, the presented numerical method fulfills the requirements for electromagnetic design of coated conductor windings. * Final version published as E Pardo, JŠouc and L Frolek 2015 Supercond. Sci. Technol. 28 044003, doi:10.1088/0953-2048/28/4/044003. Several minor typos have been corrected in the published version. 1 ReBCO stands for ReBa 2 Cu 3 O 7−x , where Re is a rare earth, typically Y, Gd or Sm. the flux creep exponent and the AC loss. Critial current density and flux-creep exponentIn this article, we use a ReBCO coated conductor tape from SuperPower [49] for all experiments. This tape is 4 mm wide, with a total of 40 µm copper stabilizer layers, a 1 µm thick superconducting layer, and a self-field critical current at 77 K of 128 A.We measured the dependence of the critical current density J c on the magnetic field magnitude |B| ≡ B and its orientation θ (see sketch in figure 3) at 77 K, as detailed in [50]. In order to extract J c from measurements of the tape critical current, I c , we corrected the spurious effects of the self-field, following the method in [50]. The reader can find the I c measurements and extracted J c for the tape used in this article in [30]. For completeness, we include the extracted J c (B, θ) relation, being J c (B, θ, J) = [J c,ab (B, θ, J) m + J c,c (B) m ] 1/m (60) with J c,ab (B, θ, J) = J 0,ab 1 + Bf (θ,J) B 0,ab β ab ,J c,c (B) = J 0,c

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.

Many applications of ReBCO coated conductors contain stacks of pancake coils. In order to reduce their high AC loss, it is necessary to understand the loss mechanisms. In this article, we measure and simulate the AC loss and the critical current, Ic, in stacks of pancake coils ("pancakes"). We construct stacks of up to 4 pancakes and we measure them by electrical means. We also obtain the anisotropic field dependence of Jc from Ic measurements of the tape. This Jc is the only input to the simulations, together with the coil dimensions. After validating our computations with the measurements, we simulate stacks of many pancakes, up to 32. We found that the AC loss in a stack of (four) pancakes is very high, two orders of magnitude larger than for a single tape. A double pancake behaves as a single one with double width but a stack of more pancakes is very different. Finally, we found that a 2-strand Roebel cable reduces the AC loss in a stack of pancakes but not in a single pancake. In conclusion, our simulations are useful to predict the ac loss of stacks of coated conductor pancake coils and to reduce the ac loss by optimizing the coil design.

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.

Many applications of ReBCO-coated conductors operate at low magnetic fields in the superconductor (below 200 mT). In order to predict the critical current and AC loss in these applications, it is necessary to know the anisotropy and field dependence of the critical current density at low magnetic fields. In this paper, we obtain a formula for the critical current density in a coated conductor as a function of the local magnetic field and its orientation. Afterwards, we apply this formula to predict the critical current of a pancake coil that we constructed. We extract the critical current density of the tape from measurements of the in-field critical current at several orientations. Numerical simulations correct the effect of the self-field in the measurements and successfully predict the critical current in the pancake coil. We found that a simple elliptical model is not enough to describe the anisotropy of the critical current density. In conclusion, the analytical fit that we present is useful to predict the critical current of actual coils. Therefore, it may also be useful for other structures made of coated conductor, like power-transmission cables, Roebel cables and resistive fault current limiters.