1,721,014 research outputs found

    Loops and Meshes Formulations for 3-D Eddy-Current Computation in Topologically Non-Trivial Domains with Volume Integral Equations

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    The volume integral equation method based on the current vector potential approximated by means edge element basis function is a well-established approach for 3-D eddy currents computation. The application of the method is straightforward when simply connected geometries and no connection with external circuits are involved. In this case, in fact, the solving system is easily obtained based on tree-cotree decomposition of the primal graph. However, when multiply connected geometries or external generators are considered, 'additional' degrees of freedom, not related to interior cotree edges of the primal graph, need to be identified and involved to assure the consistency of the numerical solution. In this article, the link between the volume integral equation method and the circuit is investigated in detail, and the circuit view is used as a guide for systematically finding the additional degrees of freedom arising in case of multiply connected geometries and/or external circuits. In particular, the dual graph is introduced as the support of the circuit and it is shown that this is the natural frame for taking the topology into account. For multiply connected geometries, the additional degrees of freedom are related to loop currents crossing one only time (or an odd number of times) any cutting surface making the domain simply connected, and are found by applying a minimum path algorithm on the dual graph forming the circuit. In case of conducting domain connected to an external generator, an extended dual graph is introduced for finding the further additional degrees of freedom. This article also researches into the possibility to replace the usual current density of the elements, obtained via facet-element shape functions and exactly matching the current of the faces, with a uniform current density obtained by means of a minimum error procedure and approximately matching the current of the faces. The use of this uniform current density, besides improving the calculation time and the accuracy of the coupling coefficients, also allows the extension of the volume integral equation method to discretizations of the problem domain made of arbitrarily shaped polyhedral elements

    Combined modeling of cables and joints/terminations for the electromagnetic analysis of superconducting cables

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    The electromagnetic models developed in the recent years to study current distribution and ac losses in superconducting magnets have focussed on detailed descriptions of either cables or joints/terminations, usually considered separately. A more accurate physical description of the magnet system requires to model simultaneously the different parts of cable, the joints between them and the cable terminations. In this work we present the coupling of a distributed parameters circuit model of the cable with a simple lumped parameters resistive model of the joints and terminations. The principles and results of the coupling strategy are illustrated and validated by means of a comparison with the analytical solution of the problem found for triplex cables

    The possible effect of surface barriers on the magnetic levitation of cylindrical superconductors

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    Superconducting magnetic levitation force measurements on large field cooled cylindrical MgB2 bulks with different diameters and thicknesses are reported. For these experiments, a special set-up permitting one to measure forces up to 500 N was used. In contradiction to previous measurements, the obtained force hysteresis cycles could not be reproduced with the analytical mean field model proposed by Bernstein et al (2017 Supercond. Sci. Technol. 30 065007). The failure of the model has been attributed to surface barriers effects which were not taken into account in the model. This last one was accordingly modified in order that the measured force cycles could be reproduced. Contrary to most other models describing surface barriers effects, the modified model suggests that above a threshold field anti-vortices and not vortices enter the superconductor. This behaviour is related to the storage by the superconductor of the mechanical work done by the operator. In addition, it has turned out that the threshold field is a decreasing function of the critical surface current density of the samples. As a consequence, the surface barriers effects occur only if this quantity and the critical current density are large enough. Otherwise, the internal magnetic field of the superconductor could be computed and was seen to be a decreasing function of the thickness of the superconductors
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