AC Loss and Macroscopic Theory of Superconductors

227 Pages·2001·74.825 MB·\227

by  W.J. Carr Jr. (Author)

AC LOSS AND MACROSCOPIC
THEORY OF SUPERCONDUCTORS

AC LOSS AND MACROSCOPIC
THEORY OF SUPERCONDUCTORS
Second Edition
W. J. CARR, Jr.
Consulting Scientist
Retired from Westinghouse Science and Technology Center
Pittsburgh, Pennsylvania, USA
lCTi CRC Press
Taylor &. Francis Group
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
First published 2001
by Taylor & Francis
11 New Fetter Lane, London EC4P 4EE
Simultaneously published in the USA and Canada
by Taylor & Francis Inc
29 West 35th Street, New York, NY 100(11
Taylor & Francis is an imprint of the Taylor & Francis Group
©2001 Taylor & Francis
Typeset by Scientifik Graphics (Singapore) Pte Ltd
Printed and bound in Great Britain by MPG Books Ltd, Bodmin
All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form
or by any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying and recording, or in any information storage or retrieval system, without
permission in writing from the publishers.
Every elTort has been made to ensure that the advice and information in this book is true and
accurate at the time of going to press. However, neither the publisher nor the authors can accept
any legal responsibility or liability for any errors or omissions that may be made. In the case of
drug administration, any medical procedure or the use of technical equipment mentioned within
this book, you are strongly advised to consult the manufacturer's guidelines.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging in Publication Data
A catalogue record has been applied for
ISBN: 0-415-26797.-8
To Winifred, James and Robert
and
to Kathy, Jennifer and Matthew

Contents
Preface to Second Edition xiii
Part I Introduction to Applied Superconductivity and
Macroscopic Theory
1 Introduction 3
1.1 Focus of the Book 3
1.2 Applications of Superconductors and their Limitations 3
1.3 High T Superconductors 4
c
1.4 Loss in a Superconductor 4
1.5 Critical Current Density 5
1.6 The Bean Model and its History 7
1.7 Hysteresis Loss in the Bean Model 8
1.8 Magnitude of the Electric Field 8
1.9 Multifilament Conductors, Stability and Eddy Current
Loss 9
1.10 Viewpoint and Scope of the Book 12
I. II The "Magic" of Volume Averaging 13
1.12 Units 14
References 14
2 Survey of Type-II Superconductivity 17
2.1 Type-I and Type-II Superconductors 17
2.2 Vortex Magnetization 20
2.3 Flux Penetration and Bulk Current Density in a Hard
Superconductor 21
2.4 Extended Bean Models 24
2.5 Flux Pinning and Critical Current Density 25
2.6 Origin of the Internal Heat 26
References 27
3 Macroscopic Description of Type-II Superconductors 29
3.1 The Macroscopic Equations in Superconductors and
Normal Materials 29
3.2 The Maxwell-Lorentz Equations 30
3.3 Derivation of Maxwell's Equations 30
3.4 Calculation of the Average Charge and Current Density 32
3.5 Maxwell's Equations in SI Units 34
3.6 The Family of Maxwell Equations 34
vii
VIII Contents
3.7 True Magnetization and Effective Magnetization 35
3.8 The Magnetic Moment Under Static Conditions 36
3.9 The Magnetic Moment of a Long Wire 37
3.10 Constitutive Equations 38
3.11 Summary of the Meaning of the Maxwell Variables in
Normal Materials and Superconductors 38
Notation 40
References 40
4 Expressions for the Loss Per Cycle 41
4.1 The Various Ways of Computing Cyclic Loss 41
4.2 The Microscopic Applied Field Loss 41
4.3 The Macroscopic Applied Field Loss 42
4.4 Loss Per Cycle in SI Units and Approximation for
Ordinary Superconductors 42
4.5 Loss in Terms of the Poynting Vector 43
4.6 Calculation of the Loss From the Effective
Magnetization and Applied Magnetic Field 44
4.7 Computation of Loss From the Flux for a
One-Dimensional Problem 44
4.8 Loss in a Superconducting Wire with External Leads
Attached 45
4.9 Loss Density 46
4.10 The Electric Field at a Discontinuity in Tangential
Current Density 47
4.11 Summary 47
Part II Hysteresis in Ordinary Bulk Superconductors
5 Instantaneous Power Loss in a Sheet in the Bean
Approximation 51
5.1 Introduction 51
5.2 Solution of Maxwell Equations 53
5.3 Electric Field Near the Surface 55
5.4 Field Penetration into a Flux-Free Sheet Due to
Establishment of a Transport Current and Transverse
Applied Field 56
5.5 Instantaneous Power Loss 57
5.6 Partial Penetration Power Loss for a Virgin and a
Cyclic State 58
5.7 Above Complete Penetration 61
5.8 Field Profiles 62
Contents ix
5.9 Summary of the More Important Loss Expressions 64
Notation 65
6 Cyclical Hysteresis in a Sheet 67
6.1 Loss Per Cycle for No Transport Current 67
6.2 Effect of a DC Transport Current 68
6.3 Alternating Current Loss with No Applied Magnetic
Field 70
6.4 Combined Alternating Current and Transverse Field 70
6.5 Loss Due to a Field Applied Normal to a Strip 71
6.6 Calculation of H 72
6.7 Effect of a Constant Bias Field 72
6.8 Improved Loss Expressions 73
6.9 Summary 74
Notation 77
References 77
7 Hysteresis Loss in Circular Wires in the Bean
Approximation 79
7.1 Introduction 79
7.2 Transverse Field Loss for Weak Partial Penetration 79
7.3 Loss for Full Penetration 83
7.4 Approximations for the Transverse Field Loss Over
the Complete Range of Field 84
7.5 Longitudinal Field Loss 84
7.6 Alternating Current Loss 87
7.7 Dynamic Resistance for Full Penetration 89
7.8 Dynamic Resistance for Modified Bean Models 94
7.9 Cyclic Lu<-s for a Combined Alternating Transverse
Field and Transport Current 94
7.10 Transverse Field Loss in Hollow and Concentric
Cylinders 97
7.1 I Loss for a Large Transverse Rotating Field 101
7.12 Loss for a Field Having Both Transverse and
Longitudinal Components and the Problem of
Critical-Current Anisotropy 101
7.13 Summary of Loss Formulas 102
Notation 105
References 106
Part III Multifilament Superconductors
8 Theory of Filamentary Superconductors 109