H-Formulation FEM Modeling of the Current Distribution in 2G HTS Tapes and Its Experimental Validation Using Hall Probe Mapping

One of the most widespread mathematical formulations applied to simulate the electromagnetic phenomena of coated conductor in the recent literature is the H one. However, the only validation of the model has been indirect by using measurements taken from the applications, as measurements of the energy losses in ac fields, forces developed in levitation systems or any other parameter related to a specific application. Direct validation of the calculation requires the observation of the local out of plane magnetic field over the surface of the sample and this is only accessible under magneto-optical observations and, in a larger scale and better dynamic range, by the Hall scanning microscopy. We propose here the experimental validation of the H-formulation by comparing the simulated results with measurements made by a Hall probe mapping in a second generation (2G) tape sample for several DC transported currents at 77 K. The paper presents a methodology to simulate the 2G tape by using only measured data obtained from a sample and its normalized J(B) experimental curves. Some boundary conditions that allow a faster convergence of the problem are investigated. Simulated results of the 2G tape modelled considering only the 1 μm HTS layer were compared with other that represent the most important layers of the coated conductor structure in the calculations. The simulated and measured results present a good agreement, proving that this model can calculate precisely the magnetic field and, hence, the current distribution in HTS samples.This work was supported in part by the followings grants: “Science Without Borders” from the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); by the European Agency (EU) through the Factories of the Future Resources, Technology, Infrastructure and Services for Simulation and Modelling (FORTISSIMO) Project under Grant EU FP7-2013-ICT-609029, the European Development of Superconducting Tapes (EUROTAPES) Project under Grant EU-FP7 NMP-LA-2012- 280432, the European Consortium for the Development of Fusion Energy (EUROfusion, PPPT-WPMAG 2014), and EU COST ACTIONS MP1201 and MP1014; by the Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa” Programme for Centres of Excellence in R&D under Grant SEV-2015-0496, CONSOLIDER Excellence Network under Grant MAT2015- 68994-REDC, COACHSUPENERGY project under Grant MAT2014-56063- C2-1-R, co-financed by the European Regional Development Fund; by the Catalan Government under Grant 2014-SGR-753 and Xarmae

Proposal of a novel design for linear superconducting motor using 2G tape stacks

This paper presents a new design for a su- perconducting linear motor (SLM). This SLM uses stacks of second-generation (2G) superconducting tapes, which are responsible for replacing yttrium barium copper oxide bulks. The proposed SLM may operate as a synchronous motor or as a hysteresis motor, depending on the load force magnitude. A small-scale linear machine prototype with 2G stacks was constructed and tested to investigate the proposed SLM topology. The stator traveling magnetic field wave was represented by several Nd-Fe-B permanent magnets. A relative movement was produced between the stator and the stack, and the force was measured along the displacement. This system was also simulated by the finite element method, in order to calculate the induced currents in the stack and determine the electromagnetic force. The H-formulation was used to solve the problem, and a power law relation was applied to take into account the intrin- sically nonlinearity of the superconductor. The simulated and measured results were in accordance. Simulated re- sults were extrapolated, proving to be an interesting tool to scale up the motor in future projects. The proposed motor presented an estimated force density of almost 500 N/kg, which is much higher than any linear motor.This work was supported in part by the following agencies: CNPq/CAPES/INERGE, CNPq—Ci ˆ encias sem Fronteiras, FAPERJ, Catalan Government 2014- SGR-753, CONSOLIDER Excellence Network MAT2014-56063-C2-1-R and MAT2015-68994-REDC, Eurofusion EU COST ACTIONS MP1201/ MP1014/PPPT-WPMAG 2014, EUROTAPES FP7-NMP-Large-2011- 280432, FORTISSIMO FP7-2013-ICT-609029, and Spanish Govern- ment Agencies—Severo Ochoa Programme Centres of Excellence in R&D. (Corresponding author: Guilherme G. Sotelo.

Current distribution in wide YBCO tapes

The need of a better mechanical behaviour and the stabilization of coated conductors for applications, as Magnets, cables or Fault Current Limiters, has motivated the lamination of tapes with stainless steel or copper alloys, increasing so the elastic modulus of the conductors and their mechanical performance. Some of the stainless steels used are magnetic, thus introducing some perturbations of the current flow when energizing the conductor. In order to detect these possible perturbations, the magnetic self field in the surface of the tape has been explored by Hall mapping technique at several current loads in a monotonically driven cyclic sequence. By increasing current steps when loading up, crossing the critical field threshold, and decreasing down to remanent state. Deviation from the expected magnetic map has been observed. In this work, we will report on the resulting measurements, and the current flow is calculated by solving the inverse problem for a 12 mm wide stainless steel reinforced Coated Conductor tape. We discuss on the likely origin of the observed perturbations.We would like to acknowledge the support of Nanoselect project of the CONSOLIDER program, and EU-FP7-ECCOFLOW project, and Xermae

Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems

We provide a Biot–Savart inversion scheme that, for any two-dimensional, or bulk with planar crystallization, high-temperature superconducting (HTS) sample, determines current density maps with a higher resolution and accuracy than previous procedures and at a fraction of its computational cost. The starting point of our scheme is a Hall scanning microscopy map of the out-of-plane component of the magnetic field generated by the current. Such maps are noisy in scans of real samples with commercial-grade equipment, and their error is the limiting factor in any Biot–Savart inversion scheme. The main innovation of our proposed scheme is a singular spectrum analysis (SSA) filtering of the Hall probe maps, which cancels measurement errors such as noise or drifts without introducing any artifacts in the field map. The SSA filtering of the Hall probe data is so successful in this task that the resulting magnetic field map does not require an overdetermined QR inversion, allowing Fourier inversion of the Biot–Savart problem. Our implementation of SSA filtering of the Hall scan measurements, followed by Biot–Savart inversion using the fast Fourier transform (FFT), is applied to both simulations and real samples of HTS tape stacks. The algorithm works in cases where ill conditioning ruled out the application of Fourier inversion, and achieves a finer resolution for a fraction of the cost of the QR inversion used to date. The computation passes physical and statistical validity tests in all cases, and in three-dimensional samples it is shown to yield the average, with a depth-dependent weight, of the current density circulating in the different layers of the sample.We acknowledge the financial support from the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa Programme (SEV-2015-0496), CONSOLIDER Excellence Network (MAT2015-68994-REDC), COACHSUPENERGY project (MAT2014-51778-C2-1-R, co-financed by FEDER), GAP project (MTM2015-69135-P) and SUPERINKS project (RTC-2015-3640-3, co-financed by FEDER); the European Union for the FASTGRID project (H2020-NMBP-18-2016-IA-72109) and WPMAG 5 (H2020-EUROfusion); and the Catalan Government with 2017-SGR-932, 2014-SGR-753 and Xarmae

H-Formulation FEM Modeling of the Current Distribution in 2G HTS Tapes and Its Experimental Validation Using Hall Probe Mapping

One of the most widespread mathematical formulations applied to simulate the electromagnetic phenomena of coated conductor in the recent literature is the H one. However, the only validation of the model has been indirect by using measurements taken from the applications, as measurements of the energy losses in ac fields, forces developed in levitation systems or any other parameter related to a specific application. Direct validation of the calculation requires the observation of the local out of plane magnetic field over the surface of the sample and this is only accessible under magneto-optical observations and, in a larger scale and better dynamic range, by the Hall scanning microscopy. We propose here the experimental validation of the H-formulation by comparing the simulated results with measurements made by a Hall probe mapping in a second generation (2G) tape sample for several DC transported currents at 77 K. The paper presents a methodology to simulate the 2G tape by using only measured data obtained from a sample and its normalized J(B) experimental curves. Some boundary conditions that allow a faster convergence of the problem are investigated. Simulated results of the 2G tape modelled considering only the 1 μm HTS layer were compared with other that represent the most important layers of the coated conductor structure in the calculations. The simulated and measured results present a good agreement, proving that this model can calculate precisely the magnetic field and, hence, the current distribution in HTS samples