THE GENERATION OF HIGH MAGNETIC FIELDS THE INTERNATIONAL CRYOGENICS MONOGRAPH SERIES General Editors Dr. K. Mendelssohn, F. R. S. The Glarendon Laboratory Oxford, England Dr. K. D. Timmerhaus University of Colorado Bou/der, Colorado H. J. Goldsmid Thermoelectric Refrigeration, 1964 G. T. Meaden Electrical Resistance of Metals, 1965 E. S. R. Gopal Specific Heats at Low Temperatures, 1966 M. G. Zabetakis Safety with Cryogenic Fluids, 1967 D. H. Parkinsan and B. E. Mulhall The Generation of High Magnetic Fields, 1967 Volumes J. L. Olsen and S. Gygax in preparation Superconductivity jor Engineers A. J. Croft and P. V. E. McClintock Cryogenic Labaratory Equipment G. K. Gaule Superconductivity in Elements, Alloys, and Compounds F. B. Canfield Low-Temperature Phase Equilibria W. E. Keller Helium-3 and Helium-4 S. Ramaseshan Low-Temperature Crystallography P. E. Glaserand A. Wechsler Cryogenic Insularion Systems D. A. Wigley The Mechanical Properries of Materials at Low Temperatures S. A. Stern Cryopumping THE GENERATION OF HIGH MAGNETIC FIELDS David H. Parkinsen Deputy Chief Scientific Of}icer Head of Physics Group Royal Radar Establishment, Malvern and Honorary Professor of Physics University of Birmingham and Brian E. Mulhall Senior Scientific Of}icer Royal Radar Establishment, Malvern SPRINGER SCIENCE+BUSINESS MEDIA, LLC First Published in Great Britain in 1967 by Heywood Books, an imprint of Iliffe Books Ltd., Dorset House, Stamford Street, London, S.E. 1 Library of Congress Catalog Card Number 67-13568 ©Springer Science+Business Media New York 1967 Originally published by Plenum Press in 1967 Softcoverreprint ofthe hardcoverIst edition 1967 ISBN 978-1-4899-6992-7 ISBN 978-1-4899-7069-5 (eBook) DOI 10.1007/978-1-4899-7069-5 All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher Preface The present book occupies a natural place in the growth ofinterest in high magnetic fields. Over the last few years a nurober of large international laboratories have been discussed or planned, and one, the National Magnet Laboratory at M.I.T., is now in full operation. About five years ago we became involved in one such study. Particular attentionwas given to steady fields, ofwhich we already bad some experience. However, the field of interest covered the whole garout of the techniques which might be employed and also the whole range of possible fields up to the extreme Iimits. lt soon became evident that here was a mass of facts and experience which bad not previously been collated. Thus the idea oftbis book was born. Two particular problems have confronted us in the preparation. The first has been caused by the rapid advances in technology, especially those in superconductivity. Nevertheless, we feel that the present time is opportune for reviewing the situation. We have tried to present basic principles throughout as weil as to create a useful source book for those interested in the subject. As with many technical problems, those involved here have no unique solutions, and compromises must be sought. Wehave tried to pointout the conflicting factors in each case. Second is the perennial problern of units. lt is inevitable that a book of this type relies heavily on the literature. Some of the more recent papers have been written using rationalized mks units, many more using the cgs system, while those concerned with engineering practice are usually in the British (fps) system. We favor the mks system and have used it as widely as possible, particularly when discus sing general principles; nevertheless, where appropriate, we have tried to facilitate comparison with the Iiterature by using alternative systems. In all cases this is clearly stated. Writing has been necessarily a spare-time occupation to be indulged in between experiments on the one band and marshalling the V vi Preface resources of a solid state laboratory on the other. Much is based on first-band experience and much on discussion with friends and col leagues, too numerous to be mentioned individually here. We freely acknowledge the value of these interchanges of ideas. In gaining our own experience we have relied heavily on our colleagues at the Royal Radar Establishment. In particular we are indebted to Messrs. A. G. Harris and F. Mansfield, on whom the responsibility has rested for the organisation and engineering of the High Field Laboratory and to Dr. J. Hulbert for many useful discussions concerned with pulsed fields and superconducting solenoids. D. H. PARKINSON B. E. MULHALL September 1966 Contents Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter 1 Introducdon and General Survey 1.0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . I 1.1. Applications of High Fields . . . . . . . . . . . . . 2 1.2. Techniques of Magnetic Field Generation.. 5 1.3. Historical Review . . . . . . . . . . . . . . . . . . . . . . 8 1.4. Centers of High·Field Work . . . . . . . . . . . . . 9 Chapter 2 Solenoid Analysis 2.0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1. Analysis of Optimization . . . . . . . . . . . . . . . . 14 2.2. Extension of Analysis to Include Cooling.. 16 2.3. Field away from the Origin.............. 19 2.4. Electromagnetic Forces . . . . . . . . . . . . . . . . . 23 2.5. Inductance Calculations. . . . . . . . . . . . . . . . . 27 Appendix .......... , . . . . . . . . . . . . . . . . . . . 29 Chapter 3 Cooling 3.0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 .1. Theory of Cooling. . . . . . . . . . . . . . . . . . . . . . 33 3.2. Nucleate Boiling Heat Transfer. . . . . . . . . . . 39 3.3. Further Cooling Topics . . . . . . . . . . . . . . . . . 40 3.4. Coolant Fluids.... . . . . . . . . . . . . . . . . . . . . . 42 Chapter 4 Solenoid Construction and Instrumentation 4.0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4 .I. General Constructional Considerations. . . . 45 vii viii Contents 4.2. Solenoid Constructions. . . . . . . . . . . . . . . . . 47 4.3. Instrumentation. . . . . . . . . . . . . . . . . . . . . . . . 54 Chapter 5 Power Supplies 5.0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.1. Conventional Coils..................... 62 5.2. Cryogenic Systems . . . . . . . . . . . . . . . . . . . . . 69 5.3. Economic Considerations . . . . . . . . . . . . . . . 73 Chapter 6 Hard Superconductors 6.0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.1. Superconductivity . . . . . . . . . . . . . . . . . . . . . . 79 6.2. Flux-Pinning and Currents in Type II Super- conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.3. Further Properties and Limitations of Type II Superconductors. . . . . . . . . . . . . . . . . . . . . 90 6.4. Sponge Models . . . . . . . . . . . . . . . . . . . . . . . . 94 6.5. Type II Superconductors and Sponge Models............................... 95 6.6. Characteristics of Hard Superconducting Materials for Solenoid Construction. . . . . . 96 6. 7. Other Hard Superconductors and Future Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 03 Chapter 7 Superconducting Solenoids 7.0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7 .I. Theoretical Analysis . . . . . . . . . . . . . . . . . . . . 106 7.2. Degradation of Solenoid Performance, Training, and Other Effects . . . . . . . . . . . . . . I 08 7.3. Stabilization of Coils................... 113 7.4. Coil Construction...................... 121 7.5. Leads and Contacts in Superconducting Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 7.6. Power Supplies and Flux-Pumping . . . . . . . 123 7.7. Future Developments. . . . . . . . . . . . . . . . . . . 128 Chapter 8 Pulse Techniques and Flux Concentration 8.0. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 129 8 .I. Electromechanical Systems . . . . . . . . . . . . . . 130 8.2. Lead-Acid Cells........................ 133 8.3. Low-temperature Pulsed Solenoids........ 135 8.4. Condenser Discharges. . . . . . . . . . . . . . . . . . . 136 8.5. Flux Concentrators. . . . . . . . . . . . . . . . . . . . . 142 8.6. The Implosion Technique... . . . . . . . . . . . . 146 Contents ix Chapter 9 Future Prospects 9.1. Superconductors....................... 151 9.2. Orthodox Coils........................ 152 9.3. Pulsed Coils........................... 153 9.4. Force-Free Coils....................... 154 9.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 References.............................................. 157 Indexes Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Author Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163