sustSUSTEFSuperconductor Science and TechnologySUSTSupercond. Sci. Technol.0953-20481361-6668IOP Publishingsustabae0410.1088/1361-6668/abae04abae04SUST-104001.R1PaperA new benchmark problem for electromagnetic modelling of superconductors: the high-T c superconducting dynamo0000-0003-0466-3680AinslieMark1mark.ainslie@eng.cam.ac.uk0000-0003-0108-7235GrilliFrancesco20000-0003-3934-4372QuévalLoïc30000-0002-6375-4227PardoEnric40000-0001-7980-9539Perez-MendezFernando10000-0003-0892-5430MatairaRatu50000-0002-1845-4006MorandiAntonio60000-0001-9907-4509GhabeliAsef40000-0001-8555-2469BumbyChris5BrambillaRoberto7 Department of Engineering, University of Cambridge, United Kingdom Institute for Technical Physics, Karlsruhe Institute of Technology, Karlsruhe, Germany Group of Electrical Engineering Paris (GeePs), CentraleSupélec, University of Paris-Saclay, France Institute of Electrical Engineering, Slovak Academy of Sciences, Slovakia Robinson Research Institute, Victoria University of Wellington, New Zealand University of Bologna, Bologna, Italy Retired; Ricerca sul Sistema Elettrico, Milano, Italy (formerly) 011020203182020318202033101050091962020217202011820202072020© 2020 The Author(s). Published by IOP Publishing Ltd2020 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Abstract

The high-T c superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. Finally, a critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom, tolerance settings and the approximate time taken per cycle for each model. This benchmark and the results contained herein provide researchers with a suitable framework to validate, compare and optimise their own methods for modelling the HTS dynamo.

HTS dynamoflux pumpcoated conductornumerical simulationHTS modellinghigh temperature superconductorsConsejo Nacional de Ciencia y Tecnologia and Secretaria de Energia de Mexico541016/439167Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266 Early Career FellowshipEP/P020313/1NZ Royal Society Marsden GrantMFP-VUW1806ccc1361-6668/20/105009+13$33.00printedPrinted in the UKcrossmarkyes