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Numerical Modelling of Bulk Superconductor Magnetisation

Dr Mark Ainslie, Hiroyuki Fujishiro


This book provides readers with numerical analysis techniques to model the magnetisation of bulk superconductors based on the finite element method. Applications of magnetised bulk superconductors are wide ranging in engineering due to their greatly enhanced magnetic field compared to conventional magnets. Their uses include rotating electric machines, magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR) systems and magnetic separation. Numerical modelling is a particularly important and cost-effective method to guide both superconducting material processing and practical device design. It has been used successfully to interpret experimental results and the physical behaviour and properties of bulk superconductors during their various magnetisation processes, to predict and propose new magnetisation techniques and to design and predict the performance of bulk superconductor-based devices.

The necessary fundamentals of bulk superconducting materials, how to model these and their various magnetisation processes are presented along with an in-depth summary of the current state-of-the-art in the field, and example models, implemented in the software package COMSOL Multiphysics®, are provided so that readers may carry out modelling of their own.

About Editors

Mark Ainslie is an Engineering and Physical Sciences Research Council (EPSRC) Early Career Fellow in the Bulk Superconductivity Group at the University of Cambridge, UK. His research interests cover a broad range of topics in applied superconductivity in electrical engineering, including superconducting electric machine design, bulk superconductor magnetisation, numerical modelling, and interactions between conventional and superconducting materials.

Hiroyuki Fujishiro is the Vice President/Executive Director of research, revitalization and regional development at Iwate University, Japan. His research interests cover a broad range of topics in applied superconductivity, including experiments on bulk superconductor magnetisation (mainly pulsed field magnetisation and field-cooled magnetisation), and the numerical simulation of electromagnetic, thermal and mechanical behaviours during these magnetising processes.

Table of Contents


CHAPTER 1:       Foreword/introduction

CHAPTER 2:       Fundamentals of bulk superconducting materials

2.1                          Bulk superconductors
2.2                          Magnetic properties of bulk superconductors
2.2.1                      Superconducting material classifications                  Low- and high-temperature superconducting materials                  Type I and II superconductivity                  Irreversibility field
2.2.2                      Flux pinning and field trapping
2.2.3                      Flux creep
2.3                          Fabrication processes
2.3.1                      Bulk (RE)BCO superconductors
2.3.2                      Bulk MgB2 superconductors
2.3.3                      Bulk iron-pnictide superconductors
2.4                          Magnetisation of bulk superconductors
2.4.1                      Pulsed field magnetisation
2.5                          Bulk superconductor applications
2.5.1                      Flux pinning applications                  Levitation                  Magnetic bearings, flywheel energy storage and superconducting mixers
2.5.2                      Flux trapping applications                  Magnetic separation                  Rotating machines                  Portable NMR/MRI systems                  Lorentz force velocimetry                  Other applications
2.5.3                      Flux shielding applications
2.5.4                      Magnetic lens
2.5.5                      Conductor alternative

CHAPTER 3:        Numerical modelling of bulk superconducting materials

3.1                          Modelling of bulk superconductors
3.1.1                      Analytical techniques
3.1.2                      Numerical techniques
3.2                          Finite element method
3.2.1                      Modelling bulk superconductors using FEM                  Geometry, including magnetisation fixture                  Electromagnetic formulation              H-formulation                  Electrical properties              Critical current density, Jc(B, T)              E-J power law              Electromagnetic boundary conditions                  Thermal properties & electromagnetic-thermal coupling

CHAPTER 4:        Modelling magnetisation of bulk superconductors

4.1                          Magnetisation of bulk superconductors
4.1.1                      Zero-field-cooled (ZFC) & field-cooled (FC) magnetisation                  Simulation of ZFC magnetisation                  Simulation of FC magnetisation                  Case study #1: MgB2 bulks                  Case study #2: Iron-pnictide bulks
4.1.2                      Pulsed field magnetisation                  Basic model                  Influence of PFM parameters on trapped fields                  Case study #3: PFM of bulk HTS materials using a split coil with an iron yoke

CHAPTER 5:        Demagnetisation & novel, hybrid bulk superconductor structures

5.1                          Demagnetisation effects & AC losses
5.2                          Novel & hybrid bulk superconductor structures
5.2.1                      Composite structures with improved thermal conductivity
5.2.2                      Hybrid ferromagnet-superconductor structures
5.2.3                      Hollow bulk cylinders & tubes for shielding
5.2.4                      Hybrid trapped field magnet lens

APPENDIX A:      Thermal properties of bulk superconductors

A.1                        Introduction
A.2                        Experimental procedure
A.2.1                      Thermal conductivity
A.2.2                      Thermal dilatation
A.3                        Typical results
A.3.1                      Bulk (RE)BCO
A.3.1.1                  Thermal conductivity
A.3.1.2                  Thermal conductivity in magnetic fields
A.3.1.3                  Thermal dilatation
A.3.2                      Bulk MgB2
A.3.2.1                  Thermal conductivity
A.3.2.2                  Thermal dilatation


Hardback ISBN: 9780750313339

Ebook ISBN: 9780750313322

DOI: 10.1088/978-0-7503-1332-2

Publisher: Institute of Physics Publishing


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