A new benchmark problem for electromagnetic modelling of superconductors: the high-T c superconducting dynamo

Mark Ainslie,Fernando Perez-Mendez,Antonio Morandi,Chris Bumby,Francesco Grilli,Roberto Brambilla,Ratu Mataira,Loïc Quéval,Asef Ghabeli,Enric Pardo

doi:10.1088/1361-6668/abae04

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.

Highlights

The high-Tc superconducting (HTS) dynamo [1,2,3] is a promising device that can inject large DC supercurrents into a closed superconducting circuit
We propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community
To adequately compare the performance of different modelling approaches, here we propose a new benchmark problem for the HTS modelling community [20]: the HTS dynamo

Summary

Introduction

The high-Tc superconducting (HTS) dynamo [1,2,3] is a promising device that can inject large DC supercurrents into a closed superconducting circuit. A number of different explanations have been proposed to explain this mechanism [6,7,8,9,10,11,12,13], but quantitatively accurate, predictive calculations have been difficult It was shown recently in Mataira et al [14, 15] that the behaviour of the HTS dynamo can be explained well—most importantly, with good quantitative agreement—using classical electromagnetic theory. In [18], it is shown that this voltage is independent of the critical current density, Jc, when the superconductor is fully penetrated by supercurrents Since these overcritical eddy currents must recirculate within the HTS wire, and can co-exist with a transport current, the wire width is a key parameter and [19] shows that this should be sufficiently large so that the eddy and transport currents do not drive the full width of the stator into the flux-flow regime

Results

Discussion

Conclusion