Case Studies in Superconducting Magnets. Design and Operational Issues

Transcription

1 Case Studies in Superconducting Magnets Design and Operational Issues

2 SELECTED TOPICS IN SUPERCONDUCTIVITY Series Editor: Stuart Wolf Naval Research Laboratory Washington, D.C. CASE STUDIES IN SUPERCONDUCTING MAGNETS Design and Operational Issues Yukikazu Iwasa INTRODUCTION TO HIGH-TEMPERATURE SUPERCONDUCTIVITY Thomas P. Sheahen A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher.

3 Case Studies in Superconducting Magnets Design and Operational Issues Yukikazu Iwasa Francis Bitter National Magnet Laboratory and Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts Kluwer Academic Publishers NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

4 ebook ISBN Print ISBN Kluwer Academic / Plenum Publishers, New York 233 Spring Street, New York, N. Y Print 1994 KluwerAcademic / Plenum Publishers, New York All rights reserved No part of this ebook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's ebookstore at:

5 To the memory of my father, Seizaburo Iwasa

6 PREFACE This book is based on Superconducting Magnets, a graduate course I started teaching in the Department of Mechanical Engineering at the Massachusetts Institute of Technology, in 1989, shortly after the discovery of high-temperature superconductors. The book, intended for graduate students and professional engineers, covers the basic concepts of superconducting magnet technology, focusing on design and operational issues. My course consists of ten 3-hour lectures and eight homework sets, each set containing three to four tutorial problems to review lecture materials, to discuss topics in more depth than covered in the lecture, or to teach subjects not presented in the lecture at all. My colleague Emanuel Bobrov has helped me with the course, offering lectures on field computation and stress analysis. He has also created a few problems related to his lecture topics. Because the use of tutorial problems accompanied, a week later, by solutions has been successful in the course, I have decided to use the same format for this book. Most problems require many steps in their solution and through these steps it is hoped that the reader will gain deeper insight. About 75% of the problems are based on those specifically created for the course s homework or quiz problems; the remainder are based on lecture materials. Because the principal magnet projects at the Francis Bitter National Magnet Laboratory (FBNML) have been high-field solenoidal magnets, problems directly related to other applications are not represented. However, important topics covered in this book, particularly on field distribution, magnets, force, thermal stability, dissipation, and protection, are sufficiently basic and generic in concept that solenoidal magnets are suitable examples. In creating problems I have relied heavily on the magnet projects at FBNML and I am indebted to my colleagues in the Magnet Technology Division, specifically John Williams, Mat Leupold, Bob Weggel, and Emanuel Bobrov, with whom I have had the good fortune of working on these projects over a long period. Materials contributed by the other members of the Division, Alex Zhukovsky, Vlad Stejskal, Andy Szczepanowski, Dave Johnson, and Mel Vestal are also included and their contributions are acknowledged. I have also benefitted much through participation in the Technology Division of the Plasma Fusion Center (PFC) of MIT; I would particularly like to thank Bruce Montgomery from whom I have learned a great deal since my graduate student days. I would also like to thank Joe Minervini and Makoto Takayasu of the PFC, Dr. Larry Dresner of Oak Ridge National Laboratory, and Dr. Luca Bottura of Max-Planck Institut für Plasmaphysik, Garching, Germany, for advice on the creation of problems related to cable-in-conduit (CIC) conductors, and Dr. Ted Collings of the Battelle Memorial Institute, Ohio, for discussion on enabling technology vs replacing technology. In addition, I would like to thank many visiting scientists to FBNML, mostly from Japan really too many to cite individually here with whom I have collaborated with fruitful results, particularly in the areas of mechanical dissipation, magnet monitoring, and protection. vii

7 viii PREFACE I would like to thank Don Stevenson, the retired Assistant Director of the FBNML, who read several versions of the manuscript and offered helpful suggestions, and Albe Dawson of PFC for suggestions on early chapters. Many of my former and present students helped me on this project and I express my deepest gratitude to them. Philip Michael combed through the three last editions and offered many insightful suggestions. Rick Nelson painstakingly read early drafts, checked and corrected solutions, and offered many suggestions on the phrasing of the questions, writing, and equation style; he also assisted me in the preparation of early editions of the Glossary. Mamoon Yunus created beautiful field plots and graphs; Hunwook Lim produced most of the figures and prepared the Index; Jun Beom Kim rechecked several derivations, collected much of the data presented in the Appendices, and produced most of the graphs; Abraham Udobot also prepared many figures and laid out all the figures. I am also indebted to Dr. Hiroyasu Ogiwara of Toshiba Corporation for first suggesting a book based on my course materials, particularly on the problem sets. He has also arranged for me to offer lectures based on the course to magnet engineers at the Kanagawa Academy of Science and Technology, Kawasaki, Japan. Thanks are also due to the National Science Foundation (FBNML s sponsor); the Department of Mechanical Engineering; the Department of Energy Office of Fusion Energy; the Department of Energy Office of Renewable Energy; the Department of Energy Office of Basic Sciences; and Daikin Industries, Ltd. for their support of this book project. I have used D.E. Knuth s indispensable TEX in typesetting the entire text, equations, tables, and even some figures. Finally, I would express a word of appreciation to Kimiko who has made it possible for me to continue working on this project in the relaxed atmosphere of our home and thus to carry it forward to completion. Yukikazu Iwasa Weston, Massachusetts August, 1994 You know nothing till you prove it! FLY! Jonathan Livingston Seagull

8 CONTENTS CHAPTER 1 SUPERCONDUCTING MAGNET TECHNOLOGY Introductory Remarks Superconductivity Magnet-Grade Superconductors Magnet Design Class 1 and Class 2 Superconducting Magnets The Format of the Book CHAPTER 2 ELECTROMAGNETIC FIELDS Introduction Maxwell s Equations Quasi-Static Case Poynting Vector Field Solutions from the Scalar Potentials Problem 2.1: Magnetized sphere in a uniform field Problem 2.2: Type I superconducting rod in a uniform field Problem 2.3: Magnetic shielding with a spherical shell Problem 2.4: Shielding with a cylindrical shell Problem 2.5: The field far from a cluster of four dipoles Problem 2.6: Induction heating of a cylindrical shell Induction heating Part 1 (Field) Induction heating Part 2 (Power Dissipation) Problem 2.7: Eddy-current loss in a metallic strip Lamination to Reduce Eddy-Currrent Loss CHAPTER 3 MAGNETS, FIELDS, AND F ORCES Introduction Law of Biot and Savart Lorentz Force and Magnetic Pressure Problem 3.1: Uniform-current-density solenoids Bitter Magnet Problem 3.2: Bitter magnet Additional Comments on Water-Cooled Magnets Hybrid Magnet Parameters of Hybrid III Superconducting Magnet (SCM) Problem 3.3: Hybrid Magnet Problem 3.4: Helmholtz coil Problem 3.5: Spatially homogeneous fields Problem 3.6: Notched solenoid ix

9 x C ONTENTS Problem 3.7: Ideal dipole magnet Problem 3.8: Ideal quadrupole magnet Problem 3.9: Magnet comprised of two ideal racetracks Problem 3.10: Ideal toroidal magnet Nuclear Fusion and Magnetic Confinement Problem 3.11: Fringing field Problem 3.12: Circulating proton in an accelerator Particle Accelerators Problem 3.13: Magnetic force on an iron sphere Problem 3.14: Fault condition in hybrid magnets 1. Fault-mode forces Vertical Magnetic Force during Hybrid III Insert Burnout Problem 3.15: Fault condition in hybrid magnets 2. Mechanical support requirements Problem 3.16: Fault condition in hybrid magnets 3. Fault force transmission Problem 3.17: Stresses in an epoxy-impregnated solenoid Problem 3.18: Stresses in a composite Nb 3 Sn conductor CHAPTER 4 CRYOGENICS Introduction Cryogens Superfluidity Problem 4.1: Carnot refrigerator Joule-Thomson Process Problem 4.2: Cooling modes of a magnet Problem 4.3: Optimum gas-cooled leads Part Optimum gas-cooled leads Part Problem 4.4: Optimum leads for a vacuum environment Normal conductive metal vs HTS Wiedemann-Franz-Lorenz Law and Lorenz Number Problem 4.5: Gas-cooled support rods Structural Materials for Cryogenic Applications Problem 4.6: Subcooled 1.8-K cryostat Problem 4.7: Residual gas heat transfer into a cryostat Heat Input by Residual Gas: High Pressure Limit Heat Input by Residual Gas: Low Pressure Limit Vacuum Pumping System Vacuum Gauges Problem 4.8: Radiation heat transfer into a cryostat

10 C ONTENTS xi Radiation Heat Transfer: Applications to a Cryostat Effect of Superinsulation Layers Practical Considerations of Emissivity Problem 4.9: Laboratory-scale hydrogen (neon) condenser Problem 4.10: Carbon resistor thermometers Effects of a Magnetic Field on Thermometers C HAPTER 5 MAGNETIZATION OF H ARD S UPERCONDUCTORS Introduction Bean s Critical State Model Experimental Confirmation of Bean s Model A Magnetization Measurement Technique Problem 5.1: Magnetization with transport current 1. Field and then transport current Problem 5.2: Magnetization with transport current 2. Transport current and then field Use of SQUID for Magnetization Measurement Problem 5.3: Magnetization with transport current 3. Field and then current changes Magnetization Functions Summary Problem 5.4: Critical current density from magnetization Contact-Resistance Heating at Test Sample Ends Problem 5.5: Magnetization measurement Problem 5.6: Criterion for flux jumping Problem 5.7: Flux jumps Problem 5.8: Filament twisting Problem 5.9: Magnetization of conductors Filament Twisting in Composite Superconductors Problem 5.10: Flux jump criterion for HTS tapes C HAPTER 6 STABILITY Introduction Stability Theories and Criteria Cable-in-Conduit (CIC) Conductors Problem 6.1: Cryostability 1. Circuit model Peak Nucleate Boiling Heat Transfer Flux: Narrow Channels Problem 6.2: Cryostability 2. Temperature dependence Problem 6.3: Cryostability 3. Stekly criterion

11 xii C ONTENTS Discussion of Stekly Cryostability Criterion Problem 6.4: Cryostability 4. Nonlinear cooling curves Composite Superconductors: Monolithic and Built-up Problem 6.5: Dynamic stability for tape conductors 1. Magnetic and thermal diffusion Problem 6.6: Dynamic stability for tape conductors 2. Criterion for edge-cooled tapes Problem 6.7: Equal-area criterion Problem 6.8: The MPZ concept Problem 6.9: V vs I traces of a cooled composite conductor Problem 6.10: Stability analyses of Hybrid III SCM Cryostable vs Quasi-Adiabatic (QA) Magnets Problem 6.11: Stability of CIC conductors Problem 6.12: Ramp-rate-limitation in CIC conductors Problem 6.13: MPZ for a composite tape conductor Problem 6.14: Stability of HTS magnets C HAPTER 7 AC, SPLICE, AND M ECHANICAL L OSSES Introduction AC Losses Splice Resistance Mechanical Disturbances Acoustic Emission Technique Problem 7.1: Hysteresis loss basic derivation 1. Without transport current Problem 7.2: Hysteresis loss basic derivation 2. With transport current Problem 7.3: Hysteresis loss (no transport current) 1. Small" amplitude cyclic field Problem 7.4: Hysteresis loss (no transport current) 2. Large amplitude cyclic field Problem 7.5: Coupling time constant Problem 7.6: Hysteresis loss of an Nb3Sn strand Problem 7.7: AC losses in Hybrid III SCM Burst Disk and Diffuser for Hybrid III Cryostat Problem 7.8: AC losses in the US-DPC Coil Problem 7.9: Splice dissipation in Hybrid III Nb-Ti coil Mechanical Properties of Tin-Lead Solders Problem 7.10: A splice for CIC conductors Stability of a CIC Splice in a Time-Varying Magnetic Field

12 C ONTENTS xiii Problem 7.11: Loss due to "index number Experimental Determination of Index Number Problem 7.12: Frictional sliding Problem 7.13: Source location with AE signals Acoustic Emission Sensor for Cryogenic Environment Problem 7.14: Conductor-motion-induced voltage pulse Problem 7.15: Disturbances in HTS magnets Field Orientation Anisotropy in BiPbSrCaCuO (2223) Tapes C HAPTER 8 PROTECTION Introductory Remarks Protection for Class 2 Magnets Computer Simulation Problem 8.1: Active protection Comments on Z Functions for Magnet Protection Problem 8.2: Hot-spot temperatures in Hybrid III SCM Problem 8.3: Quench-voltage detection (QVD) 1. Basic technique using a bridge circuit Problem 8.4: Quench-voltage detection (QVD) 2. An improved technique Voltage Attenuation in Magnet Protection Circuit Problem 8.5: Quench-induced pressure in CIC conductors 1. Analytical approach Problem 8.6: Quench-induced pressure in CIC conductors 2. CIC coil for the NHMFL s 45-T hybrid Problem 8.7: Normal-zone propagation (NZP) 1. Velocity in the longitudinal direction Problem 8.8: Normal-zone propagation (NZP) 2. Transverse (turn-to-turn) velocity Problem 8.9: Passive Protection of "isolated magnets 1. Basic concepts Problem 8.10: Passive Protection of "isolated magnets 2. Two-section test coil Problem 8.11: Passive Protection of isolated magnets 3. Multi-coil NMR magnet Problem 8.12: NZP velocity in HTS magnets Dry High-field HTS magnets operating at 20 K C HAPTER 9 CONCLUDING R EMARKS Enabling Technology vs Replacing Technology Outlook for the HTS

13 xiv C ONTENTS A PPENDIX I PHYSICAL C ONSTANTS AND C ONVERSION F ACTORS Table A1.1 Selected Physical Constants Table A1.2 Selected Conversion Factors A PPENDIX II T HERMODYNAMIC P ROPERTIES OF C RYOGENS Table A2.1 Helium at 1 Atm Table A2.2 Helium at Saturation Figure A2.1 Isochoric P(T) curves for helium at two densities Figure A2.2 Isochoric u(t) curves for helium at two densities Table A2.3 Selected Properties of Cryogens at 1 Atm Table A2.4 Heat Transfer Properties of Cryogen Gases at 1 Atm A PPENDIX III PHYSICAL P ROPERTIES OF M ATERIALS Figure A3.1 Thermal conductivity vs temperature plots Figure A3.2 Heat capacity vs temperature plots Figure A3.3 Volumetric enthalpy vs temperature plots Table A3.1 Mechanical Properties of Materials Table A3.2 Mean Linear Thermal Expansion of Materials A PPENDIX IV ELECTRICAL P ROPERTIES OF N ORMAL M ETALS Figure A4.1 Normalized zero-field electrical resistivity vs temperature plots Figure A4.2 Kohler plots Figure A4.3 Copper Residual Resistivity Ratio (RRR) vs magnetic induction plots Table A4.1 Electrical Resistivity of Heater Metals A PPENDIX V P ROPERTIES OF S UPERCONDUCTORS Table A5.1 B c 2 vs T Data for Nb-Ti Table A5.2 B c 2 vs T Data for Nb 3 Sn Figure A5.1 J c vs B plots for Nb-Ti at 1.8 and 4.2K Figure A5.2 J c vs B plots for Nb 3 Sn at 1.8, 4.2, 10, and 12K Table A5.3 Parameters of BiPbSrCaCuO (2223) Figure A5.3 J c vs B plots for BiPbSrCaCuO (2223) at 4.2 and 27K Table A5.4 Selected Physical Properties of YBCO and BSCCO A PPENDIX VI GLOSSARY A PPENDIX VII Q UOTATION S OURCES AND C HARACTER IDENTIFICATION 413 INDEX