When analytic solutions are not available, finite-element-based tools can be used to simulate hysteresis losses in superconductors with various shapes. A widely used tool for the corresponding magnetoquasistatic problem is based on the H-formulation, where H is the magnetic field intensity, eddy current model. In this paper, we study this type of tool in a threedimensional simulation problem. We consider a case where we simultaneously apply both a time-varying external magnetic field and a transport current to a twisted wire. We show how the modelling decisions (air has high finite resistivity and applied field determines the boundary condition) affect the current density distribution along the wire. According to the results, the wire carries the imposed net current only on the boundary of the modelling domain, but not inside it. The current diffuses to the air and back to the boundary. To fix this problem, we present another formulation where air is treated as a region with 0 conductivity. Correspondingly, we express H in the air with a scalar potential and a cohomology basis function which considers the net current condition. As shown in this paper, this formulation does not fail in these so-called AC-AC (time varying transport current and applied magnetic field) simulations.

This paper describes the standalone magnet cold testing of the high temperature superconducting magnet Feather-M2.1-2. This magnet was constructed within the European funded FP7-EUCARD2 collaboration to test Roebel type HTS cable, and is one of the first high temperature superconducting dipole magnets in the world. The magnet was operated in forced flow helium gas with temperatures ranging between 5 to 85 K. During the tests a magnetic dipole field of 3.1 T was reached inside the aperture at a current of 6.5 kA and a temperature of 5.7 K. These values are in agreement with the self-field critical current of the used SuperOx cable assembled with Sunam tapes (lowperformance batch), thereby confirming that no degradation occurred during winding, impregnation, assembly and cool-down of the magnet. The magnet was quenched many tens of times by ramping over the critical current and no degradation nor training was evident. During the tests the voltage over the coil was monitored in the micro-volt range. An inductive cancellation wire was used to remove the inductive component, thereby significantly reducing noise levels. Close to the quench current, drift was detected both in temperature and voltage over the coil. This drifting happens in a time scale of minutes and is a clear indication that the magnet has reached its limit. All quenches happened approximately at the same average electric field and thus none of the quenches occurred unexpectedly.

As is well known, the superconductor hysteresis loss modelling problem may be formulated as an eddy current (EC) problem in which the resistivity of the superconducting region is modelled with a power law. We compare three EC formulations suitable for the modelling of superconductor hysteresis losses. Namely, the a-v-j-, T-ϕand h-formulations are discussed. We review these formulations, and through simulation results the properties of these formulations are discussed and their suitabilities for different modelling situations are compared. Special attention is paid to the h-formulation: we investigate the effects of the modelling decisions related to resistivity of the air region in an h-formulation based EC solver. According to the results, these decisions affect the energy distribution of the field solution and may even lead to seemingly contradictory behaviour.

Articles you may be interested inMicrostructure dependence of the c-axis critical current density in second-generation YBCO tapes Singular current density in the planar superconductor/normal metal/superconductor junctionIn several superconducting applications, as, for example, in some supercondcuting generators, motors, and power transmission cables, the superconductor experiences a changing magnetic field in a DC background. Simulating the losses caused by this AC ripple field is an important task from the application design point of view. In this work, we compare two formulations, the H-formulation and the minimum magnetic energy variation-formulation, based on the eddy current model (ECM) and the critical state model (CSM), respectively, for simulating ripple field losses in a DC biased coated conductor tape. Furthermore, we compare our simulation results with measurements. We investigate the frequency-dependence of the hysteresis loss predictions of the power law based ECM and verify by measurements, that in DC use, ECM clearly over-estimates the homogenization of the current density profile in the coated conductor tape: the relaxation of the local current density is not nearly as prominent in the measurement as it is in the simulation. Hence, we suggest that the power law resistivity, used as the local relation between the electric field intensity E and current density J in ECM, is not an intrinsic property of high-temperature superconductors. The difference between the models manifests itself as discrepancies in ripple field loss simulations in very low AC fields with significant DC fields or currents involved. The results also show, however, that for many practical situations, CSM and ECM are both eligible models for ripple field loss simulations. V C 2014 AIP Publishing LLC. [http://dx.

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Currently, modelling hysteresis losses in superconductors is most often based on the H -formulation of the eddy current model (ECM) solved using the finite element method (FEM). In the H -formulation, the problem is expressed using the magnetic field intensity H and discretized using edge elements in the whole domain. Even though this approach is well established, it uses unnecessary degrees of freedom (DOFs) and introduces modelling error such as currents flowing in air regions due to finite air resistivity. In this paper, we present a modelling tool utilizing another H -oriented formulation of the ECM, making use of cohomology of the air regions. We constrain the net currents through the conductors by fixing the DOFs related to the so-called cohomology basis functions. As air regions will be truly non-conducting, DOFs and running times of these nonlinear simulations are reduced significantly as compared to the classical H -formulation. This fact is demonstrated through numerical simulations.

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