Particle Acceleration and Detection Nb 3 Sn Accelerator Magnets Daniel Schoerling Alexander V. Zlobin Editors Designs, Technologies and Performance Particle Acceleration and Detection Series Editors Alexander Chao, SLAC, Stanford University, Menlo Park, CA, USA Frank Zimmermann, BE Department, ABP Group, CERN, Genève, Switzerland Katsunobu Oide, KEK, High Energy Accelerator Research Organization, Tsukuba, Japan Werner Riegler, Detector group, CERN, Genève, Switzerland Vladimir Shiltsev, Accelerator Physics Center, Fermi National Accelerator Lab, Batavia, IL, USA Kenzo Nakamura, Kavli IPMU, University of Tokyo, Kashiwa, Chiba, Japan The series Particle Acceleration and Detection is devoted to monograph texts dealing with all aspects of particle acceleration and detection research and advanced teaching. The scope also includes topics such as beam physics and instrumentation as well as applications. Presentations should strongly emphasize the underlying physical and engineering sciences. Of particular interest are • contributions which relate fundamental research to new applications beyond the immeadiate realm of the original fi eld of research • contributions which connect fundamental research in the aforementionned fi elds to fundamental research in related physical or engineering sciences • concise accounts of newly emerging important topics that are embedded in a broader framework in order to provide quick but readable access of very new material to a larger audience. The books forming this collection will be of importance for graduate students and active researchers alike More information about this series at http://www.springer.com/series/5267 Daniel Schoerling • Alexander V. Zlobin Editors Nb 3 Sn Accelerator Magnets Designs, Technologies and Performance Editors Daniel Schoerling CERN (European Organization for Nuclear Research) Meyrin, Genève, Switzerland Alexander V. Zlobin Fermi National Accelerator Laboratory (FNAL) Batavia, IL, USA ISSN 1611-1052 ISSN 2365-0877 (electronic) Particle Acceleration and Detection ISBN 978-3-030-16117-0 ISBN 978-3-030-16118-7 (eBook) https://doi.org/10.1007/978-3-030-16118-7 © The Editor(s) (if applicable) and The Author(s) 2019. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made. The images or other third party material in this book are included in the book ’ s Creative Commons licence, unless indicated otherwise in a credit line to the material. 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The publisher remains neutral with regard to jurisdictional claims in published maps and institutional af fi liations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Foreword Colliders of highly energetic particle beams are a crucial tool for fundamental research in high-energy physics (HEP), allowing for the investigation of highest mass particles and smallest length scales. Accelerator magnets are essential for steering and focusing such particle beams. The development and the practical implementation of superconducting (SC) accelerator magnets, in particular dipoles and quadrupoles, for the Fermilab Tevatron in the 1970s and 1980s enabled a breakthrough jump in technology and allowed for hitherto unprecedented particle- beam energies and collision rates. The Large Hadron Collider (LHC, in operation since 2008) at the European Organization for Nuclear Research (CERN) represents the current state of the art of large SC colliders. At present, CERN is preparing the high-luminosity LHC (HL-LHC) upgrade to increase the collision rate even further and to fully exploit the LHC potential. For the post-LHC era, various colliders are under study, including linear lepton colliders (Compact Linear Collider (CLIC) and International Linear Collider (ILC)), and circular colliders (for electron – positron and proton – proton collisions). At CERN, the long-term goal of the Future Circular Collider (FCC) Study is to push the energy frontier much beyond other proposed accelerators, so as to increase the discovery reach, in energy, by an order of magnitude with respect to LHC in an affordable and energy-ef fi cient manner. Two FCC options are currently under study, and, depending on the available time span, they can possibly be housed, succes- sively, in the same tunnel, as it had been the case for the Large Electron – Positron Collider (LEP) and LHC at CERN. The FCC hadron collider as second stage would provide a unique opportunity to probe the nature at the smallest distance scales ever explored by mankind; to discover, if existent, new particles with exceedingly tiny Compton wavelengths; to thoroughly examine the dynamics of electroweak sym- metry breaking; and to test the fundamental principles that have guided progress for decades. To enable highest energy hadron colliders, new, reliable, and cost-effective magnet technologies are indispensable. Currently, only Nb 3 Sn SC seem to be technically and commercially mature enough to be considered as candidate material v for the magnets of such a future collider, to be constructed in the coming decades. Although work on Nb 3 Sn magnets started already in the 1960s, a signi fi cant effort is still required to optimize both the SC material and the magnet designs to prepare for mass production. A major milestone will be the fi rst-time implementation of Nb 3 Sn dipole and quadrupole accelerator magnets in the HL-LHC. In parallel, a worldwide conductor and magnet R&D program has been launched, toward the challenging design goals for the FCC. This global effort is strongly supported by the FCC Study, the EuroCirCol Design Study co-funded by the European Commission, and the U.S. Magnet Development Program (MDP). This book provides a critical review of the existing worldwide experience in the area of Nb 3 Sn dipole magnets and will play a vital role in supporting this truly global effort toward the next generation of SC high- fi eld accelerator magnets. Genève, Switzerland Michael Benedikt FCC Study Leader Michael.Benedikt@cern.ch vi Foreword Preface The goal of this book is to summarize and review the vast experience with Nb 3 Sn accelerator dipole magnets accumulated in the United States, Europe, and Asia since the discovery and production of Nb 3 Sn composite conductors. Interest in Nb 3 Sn accelerator magnets is soaring, and their further development is rapidly gaining momentum worldwide, thanks to the growing maturity of this technology and its great potential for particle accelerators used in high-energy physics. This book is intended to contribute to the transfer of the accumulated experience with the design, technology, and performance of such magnets in view of the challenging require- ments set by the needs for ever-higher collision energies in future colliders. Engi- neers and physicists working in the fi eld of particle accelerators, as well as students studying courses in particle accelerator physics and technologies, may fi nd it an indispensable source of information on Nb 3 Sn accelerator magnets. Readers with a general interest in the history of science and technology may also fi nd useful information that was obtained over a long period of time, from the late 1960s to the present day. The book contains 16 chapters, structured within 5 sections. The fi rst section includes three introductory chapters. It starts with a brief description of the general problems of accelerator magnet design and operation (Chap. 1), followed by historical overviews of the research and development (R&D) of Nb 3 Sn wires and cables for accelerator magnets (Chap. 2), and the early period of Nb 3 Sn magnet R&D — a time during which this technology was competing with Nb-Ti magnets in the same fi eld range (Chap. 3). It took almost 25 years (1965 – 1990) to advance the performance of Nb 3 Sn accelerator magnets to fi elds above 10 T — a fi eld range beyond the limits of Nb-Ti accelerator magnets. The next three sections describe the period from the early 1990s to the present day. This period is characterized by the appearance of powerful numerical computer programs for the electromagnetic, mechanical, and thermal analysis of superconducting magnets, advanced superconducting and structural materials and fabrication techniques, and signi fi cant progress in magnet instrumentation and test methods. The great progress in these areas allowed signi fi cant advances in the vii magnet design process, improving the magnets ’ operating parameters and deepening the understanding of their performance. A key result of this progress is that the maximum fi eld in Nb 3 Sn accelerator magnets has approached at the present time 15 T. In this period, three main dipole designs (cos-theta, block type, and common coil) were thoroughly explored. Their design features, technologies, and perfor- mances are described in detail in Chaps. 4, 5, 6, 7, 8, and 9 (cos-theta), Chaps. 10, 11, and 12 (block type), and Chaps. 13, 14, and 15 (common coil). In each of the three sections, the chapters follow chronological order to demonstrate the progress made within each design approach. The structure of the material presented in the chapters follows the main theme of the book: magnet design, technology, and performance. This approach is used to ease the fi nding of appropriate information inside each chapter and to simplify the comparison of similar data presented in the various chapters. The last section of the book outlines the future needs and the target parameters of the next generation of Nb 3 Sn accelerator magnets and brie fl y summarizes the main open issues for their design and performance (Chap. 16). One of the main challenges in the next decade will be increasing the nominal operation fi eld in accelerator magnets towards 16 T. To provide suf fi cient operation margin, it will require raising the magnet maximum fi eld above 18 T and approaching the limit of the Nb 3 Sn accelerator magnet technology. New cost-effective materials and technology afford- able for the next generation of particle accelerators have to be also developed. The discussion presented in this session could be considered also as an invitation to the reader to take part in this new, exciting R&D phase of Nb 3 Sn accelerator magnet technologies. Genève, Switzerland Daniel Schoerling Batavia, IL, USA Alexander V. Zlobin viii Preface Acknowledgments The editors and authors thank the forefront experts from the research and develop- ment (R&D) projects, programs, and fi elds treated here for openly sharing with us their work and their enthusiastic engagement in the preparation of this book. We also thank the many other colleagues who have helped us in fi nding material spread over the archives of the laboratories involved in this fi eld over the last six decades and for providing their valuable insights and comments on the book ’ s content, in particular Daniel Dietderich (LBNL), Michael Fields (B-OST), René Flükiger (University of Genève and CERN), Eugeny Yu. Klimenko (Kurchatov Institute), David C. Larbalestier (ASC-FSU), Peter Lee (ASC-FSU), Clément Lorin (CEA-Saclay), Alfred D. McInturff (LBNL), Jean-Michel Rif fl et (CEA-Saclay), Tiina-Maria Salmi (UoT), William B. Sampson (BNL), Ronald M. Scanlan (LBNL), Manfred Thoener (B-EAS), Peter Wanderer (BNL), Akira Yamamoto (KEK), and Franz Zerobin (ELIN-UNION). We would also like to acknowledge the technical staff of BNL, CEA-Saclay, CERN, FNAL, KEK, LBNL, TAMU, and the University of Twente for their contributions to magnet design, fabrication, and testing. Most names are indicated in the corresponding references. Our thanks are also due to the copy editors from Sunrise Setting for editing and proofreading the text, Simon-Niklas Scheuring (Dreamlead Pictures) for image processing and coloring, and Pierre-Jean François and his team (Intitek) for drawing and sketch preparation. We thank Jens Vigen (Head of the CERN library) for his efforts toward publishing this book as an open access publication and Salomé Rohr (CERN library) for her great support in fi nding and archiving the references. Special thanks also go to Springer Nature and its editorial staff, in particular Hisako Niko, who supported this project from the beginning, and their valuable help in the publication process. Without the large effort and patience of all these people, this book would have not been possible. ix Contents Part I Introduction 1 Superconducting Magnets for Accelerators . . . . . . . . . . . . . . . . . . . 3 Alexander V. Zlobin and Daniel Schoerling 2 Nb 3 Sn Wires and Cables for High-Field Accelerator Magnets . . . . . 23 Emanuela Barzi and Alexander V. Zlobin 3 Nb 3 Sn Accelerator Magnets: The Early Days (1960s – 1980s) . . . . . . 53 Lucio Rossi and Alexander V. Zlobin Part II Cos-Theta Dipole Magnets 4 CERN – ELIN Nb 3 Sn Dipole Model . . . . . . . . . . . . . . . . . . . . . . . . . 87 Romeo Perin 5 The UT-CERN Cos-theta LHC-Type Nb 3 Sn Dipole Magnet . . . . . . 105 Herman H. J. ten Kate, Andries den Ouden, and Daniel Schoerling 6 LBNL Cos-theta Nb 3 Sn Dipole Magnet D20 . . . . . . . . . . . . . . . . . . 133 Shlomo Caspi 7 Cos-theta Nb 3 Sn Dipole for a Very Large Hadron Collider . . . . . . . 157 Alexander V. Zlobin 8 Nb 3 Sn 11 T Dipole for the High Luminosity LHC (FNAL) . . . . . . . 193 Alexander V. Zlobin 9 Nb 3 Sn 11 T Dipole for the High Luminosity LHC (CERN) . . . . . . . 223 Bernardo Bordini, Luca Bottura, Arnaud Devred, Lucio Fiscarelli, Mikko Karppinen, Gijs de Rijk, Lucio Rossi, Frédéric Savary, and Gerard Willering xi Part III Block-Type Dipole Magnets 10 Block-Type Nb 3 Sn Dipole R&D at Texas A&M University . . . . . . . 261 Peter McIntyre and Akhdiyor Sattarov 11 The HD Block-Coil Dipole Program at LBNL . . . . . . . . . . . . . . . . . 285 Gianluca Sabbi 12 CEA – CERN Block-Type Dipole Magnet for Cable Testing: FRESCA2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Etienne Rochepault and Paolo Ferracin Part IV Common-Coil Dipole Magnets 13 The LBNL Racetrack Dipole and Sub-scale Magnet Program . . . . . 343 Steve Gourlay 14 Common-Coil Nb 3 Sn Dipole Program at BNL . . . . . . . . . . . . . . . . 371 Ramesh Gupta 15 Common-Coil Dipole for a Very Large Hadron Collider . . . . . . . . . 395 Alexander V. Zlobin Part V Future Needs and Requirements 16 Nb 3 Sn Accelerator Dipole Magnet Needs for a Future Circular Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Davide Tommasini Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 xii Contents Glossary of Terms Accelerator magnet Accelerator magnets are a component of particle accelerators used to act on the beam properties. They typically have to meet stringent require- ments in terms of design, technologies, and performance to allow a reliable operation of the accelerator Arc Portion of a ring accelerator occupied by a regular structure of dipole, quad- rupole, sextupole and octupole magnets ARL Accelerator Research Laboratory (ARL) at the Texas Agricultural and Mechanical (A&M) University ASC-FSU Applied Superconductivity Center at the joint college of engineering of Florida A&M University (FAMU) and Florida State University (FSU) Beam pipe Ultrahigh vacuum chamber in which the beam is being transported Bi-2212 Bismuth strontium calcium copper oxide (Bi 2 Sr 2 CaCu 2 O 8 ), a high- temperature superconductor BICC Boundary-induced coupling currents Block type Dipole magnet type based on racetrack coils with fl ared ends BNL Brookhaven National Laboratory in Upton, Brookhaven, NY BSCCO Bismuth strontium calcium copper oxide, a family of high-temperature superconductors of which Bi-2212 is one variant CCT Canted-cosine-theta, a magnet type based on pairs of conductor layers wound and powered such that their transverse fi eld components sum and axial (solenoidal) fi eld components cancel. For dipoles, the single layers resemble tilted solenoids. CEA Saclay Commissariat à l ’ énergie atomique et aux énergies alternatives (CEA) de Saclay (English: French Alternative Energies and Atomic Energy Commission at Saclay) xiii CERN European Organization for Nuclear Research CLIC The Compact Linear Collider (CLIC) study is an international collaboration working on a concept for a machine to collide electrons and positrons (antielectrons) head on at energies up to several teraelectronvolts (TeV). CLIQ Coupling Loss Induced Quench (CLIQ), a system allowing to bring a superconducting magnet rapidly to the normal-conducting state Coldmass Assembly of superconducting magnet coils, a mechanical structure and a helium vessel Collider Particle accelerator for acceleration of charged particles which are brought to collision Common-Coil Dipole magnet type based primarily on fl at racetrack coils which are common to both apertures (twin-aperture magnets only) Copper-to-non-copper ratio Area ratio of the copper stabilizer to the non-copper in superconducting strands Cos-theta A magnet type with a winding scheme following a cosine current distribution: for a current distribution following cos θ , where θ is the angle around the aperture, a dipolar fi eld is generated; for a current distribution following cos 2 θ , a quadrupolar fi eld is generated and so on. Critical surface Graph of the critical current density J c as a function of the modulus of the magnetic fl ux density B and the operation temperature T Curing Process during coil production which is performed after winding to glue together the windings of a coil D20 Cos-theta Nb 3 Sn dipole magnet designed, manufactured, and tested at LBNL DESY Deutsches Elektronen-Synchrotron (English: German Electron Synchrotron) ELIN ELIN-UNION at Weiz, Austria, was an Austrian electric company FCC The Future Circular Collider (FCC) study develops options for potential high- energy frontier circular colliders at CERN for the post-LHC era FEM The fi nite element method (FEM) is a numerical method for approximating the solution of differential equations describing problems of engineering and math- ematical physics. FNAL Fermi National Accelerator Laboratory FRESCA2 Upgrade of the Facility for the Reception of Superconducting Cables (FRESCA2) xiv Glossary of Terms G-10 Grade G-10 is constructed from a continuous fi lament woven glass fabric with an epoxy resin binder. The epoxy resin is made from an epichlorohydrin/bisphenol A epoxy resin and contains no other halogenated compounds, except residuals from the manufacture of the base resin. This grade is not manufactured from a brominated epoxy resin and is not fl ame-retardant (NEMA Standards Publication LI 1-1998 (R2011), Speci fi cation Sheet – 21, NEMA Grade G-10) HD Helmholtz dipole series built at LBNL Heat treatment Process in which the precursors of Nb 3 Sn are reacted and the Nb 3 Sn phase forms HEP High Energy Physics HERA Hadron-Elektron-Ring-Anlage (HERA) (English: Hadron Electron Ring Facility) was a particle accelerator colliding leptons and protons at DESY, Germany. It was operated from 3 July 1983 until 29 September 2011 HFDA Series of cos-theta dipole magnets which were fabricated and tested at FNAL HL-LHC The High-Luminosity LHC (HL-LHC) is an upgrade of the LHC to achieve instantaneous luminosities, a factor of fi ve larger than the LHC nominal value Hot spot temperature Hottest spot after a quench in a superconducting coil IGC Intermagnetics General Corporation (IGC), a US company ILC The International Linear Collider is an international endeavor aiming at building a machine to collide electrons and positrons (antielectrons) head on at energies of up to 500 gigaelectronvolts (GeV) ISCC Interstrand Coupling Currents ITER ITER ( “ the way ” in Latin) is a project aiming to produce energy with fusion. KEK K ō -enerug ī kasokuki kenky ū kik ō (English: The High Energy Accelerator Research Organization) LBNL Lawrence Berkeley National Laboratory LEP The Large Electron-Positron Collider was operated from 14 July 1989 until 2 November 2000 at CERN LHC The Large Hadron Collider (LHC) is housed in the former LEP tunnel at CERN. It fi rst started up on 10 September 2008 LHe Liquid helium Magnet training Typical process in which superconducting magnets reach at an initial powering campaign after each quench a slightly higher current and magnetic fi eld Glossary of Terms xv Magnetic aperture Magnetic aperture of the magnet, contrary to the mechanical aperture, which is the minimum aperture of the storage ring MBH Abbreviation nominating the 11 T dipole magnets used for replacing a regular Nb-Ti bending magnet in a dispersion suppressor region of LHC MDP US Magnet Development Program, a US program to develop high- fi eld magnets for future circular colliders Mica tape Inorganic electric insulation material based on sheets of silicate minerals MIIT Heat load of the normal zone of a quenching magnet. MIIT 10 6 A 2 s Mirror coil Coil tested in a structure of iron which “ mirrors ” the missing coils to resemble the fi eld distribution in the magnet MJR Modi fi ed jelly-roll (MJR) process, a fabrication process of Nb 3 Sn multi fi lamentary wires MSUT Model Single of the University of Twente (MSUT) dipole n-Value of a superconductor Exponent obtained in a speci fi c range of electric fi eld or resistivity when the voltage/current curve is approximated by U ¼ I n OST Oxford Superconductor Technologies, a former US company which is now part of Bruker Corporation Persistent currents Induced eddy currents in the superconductors which are per- sistent, due to the fact that there is no resistivity PIT Powder-in-tube process, a fabrication process of Nb 3 Sn multi fi lamentary wires PMF Pressure Measurement Film Quench Transition from the superconducting to the normal-conducting state Quench heaters Heaters which are fi red to bring a superconducting magnet rapidly to the normal-conducting state RD Series of racetrack dipoles (RD) built at LBNL REBCO REBa 2 Cu 3 O 7 (REBCO), where RE stands for rare earth element, a group of high-temperature superconductors RHIC The Relativistic Heavy Ion Collider (RHIC) is a heavy-ion collider at BNL, USA. It fi rst started up in 2000 RRR Residual resistivity ratio: the ratio of the electrical resistivity at 273 K to that at 4.2 K Rutherford cable Multistrand fl at or slightly keystoned (trapezoidal) two-layer cable being identical to the Roebel bar xvi Glossary of Terms S2 glass S2 glass is a special glass used for insulation consisting out of 65 wt% SiO 2 , 25 wt% Al 2 O 3 , and 10 wt% MgO Short sample limit The short sample limit is the theoretical current and fi eld limit a superconducting magnet can reach, calculated based on test results in solenoidal background fi elds of short samples wound around normalized barrels which are heat treated together with the superconducting coils SSC Superconducting Super Collider was a particle accelerator complex under construction in the vicinity of Waxahachie, Texas, aiming at reaching a collision energy of 40 TeV. The project was cancelled in 1993 Strand Composite wire containing superconducting fi laments dispersed in a matrix with suitably small electrical resistivity properties Synchrotron A synchrotron is a type of particle accelerators in which the magnetic fi eld is synchronized to the beam energy, so that the particles travel on the same path while being accelerated TAMU Series of block type magnets being developed at the Accelerator Research Laboratory (ARL) at the Texas Agricultural and Mechanical (A&M) University (TAMU) Tevatron The Tevatron is a particle accelerator colliding protons and antiprotons at FNAL. It was operated from 3 July 1983 until 29 September 2011 Thermal cycle Cool down from room temperature (293 K) to cryogenic tempera- ture (4.2 K or 1.9 K), heat back to room temperature (293 K), and cool down again to cryogenic temperature (4.2 K or 1.9 K) of a superconducting magnet Transfer function Current-to- fi eld correspondence in accelerator magnets TWCA Teledyne Wah Chang Albany, a US company Twin-aperture magnet A magnet housing two apertures in the same yoke UNK Uskoritel ’ no Nakopitel ’ nyj Kompleks (UNK) (English: Accelerator and Storage Complex) was a particle accelerator complex under construction in Protvino, near Moscow, Russia, at the Institute for High Energy Physics, aiming at reaching a collision energy of 3 TeV. The project was cancelled VLHC Very Large Hadron Collider (VLHC) study Glossary of Terms xvii Part I Introduction Chapter 1 Superconducting Magnets for Accelerators Alexander V. Zlobin and Daniel Schoerling Abstract Superconducting magnets have enabled great progress and multiple fun- damental discoveries in the fi eld of high-energy physics. This chapter reviews the use of superconducting magnets in particle accelerators, introduces Nb 3 Sn superconducting accelerator magnets, and describes their main challenges. 1.1 Circular Accelerators and Superconducting Magnets Circular accelerators are the most important tool of modern high-energy physics (HEP) for investigating the largest mass and the smallest space scales. A key element of a circular accelerator is its magnet system (Wolski 2014). The magnet system is composed of large number of various magnets, mainly dipoles and quadrupoles, to guide and steer the particle beams. The main function of the majority of the magnets (the so-called arc magnets, which are periodically placed along a ring) is to keep the beam on a quasi-circular orbit and con fi ne them in a relatively small and well- de fi ned volume inside a vacuum pipe. Magnets are also used to transfer beams between accelerator rings in so-called transfer lines, to match beam parameters from the transfer line into the injection insertions or into extraction lines and beam dumps, to direct or separate beams for the accelerating radio frequency cavities, and to focus beams for collision at the interaction points where the experiments reside. One of the most important parameters of colliders is the beam energy, as it determines the physics discovery potential. The energy E in GeV of relativistic particles with a charge q in units of the electron charge in a circular accelerator is limited by the strength of the bending dipole magnets B in Tesla and the machine radius r in meters A. V. Zlobin ( * ) Fermi National Accelerator Laboratory (FNAL), Batavia, IL, USA e-mail: zlobin@fnal.gov D. Schoerling CERN (European Organization for Nuclear Research), Meyrin, Genève, Switzerland e-mail: Daniel.Schoerling@cern.ch © The Author(s) 2019 D. Schoerling, A. V. Zlobin (eds.), Nb 3 Sn Accelerator Magnets , Particle Acceleration and Detection, https://doi.org/10.1007/978-3-030-16118-7_1 3 E 0 : 3 qBr : Thus, high magnetic fi elds are an ef fi cient way towards higher energy machines for hadron and ion collisions. The value of the magnetic fi eld in a circular accelerator needs to be synchronized with the beam energy. It is achieved by using electromagnets that allow the fi eld strength to be varied by changing the electric current in the coil. The maximum fi eld of traditional electromagnets with copper or aluminum coils is limited, however, by Joule heating, which limits the current density in a magnet coil typically to ~10 A/mm 2 In 1911, the Dutch physicist H. Kamerlingh-Onnes discovered the phenomenon of superconductivity — the vanishing of electrical resistance in some metals at very low (<10 K) temperatures (Wilson 2012). This discovery inspired him 2 years later to propose a 100,000 Gauss (10 T) solenoid based on a superconducting coil cooled with liquid helium. He believed that superconductivity would allow the current in a coil to be increased and, thus, a larger magnetic fi eld to be generated. Yet, it took more than 50 years of hard work to realize this dream in practice. The design and construction of superconducting magnets have become possible only after the discovery and development in the early 1960s of technical supercon- ductors. Technical superconductors are de fi ned as a class of superconducting mate- rials that provide high current densities in the presence of high magnetic fi elds. Earlier attempts to use technical superconductors in superconducting magnets failed due to premature magnet transitions to the normal state, called quenches. These quenches were caused by the abrupt movement of magnetic fl ux inside a superconductor, the so-called fl ux jump effect. The analysis of fl ux jumps led to the development of stability criteria for technical superconductors (Wilson, 1983; Rogalla and Kes 2012). Stability of the superconducting state with respect to small fi eld or temperature perturbations can be guaranteed only if the superconductor transverse size does not exceed a maximum value proportional to the material ’ s speci fi c heat, and inversely proportional to its critical current density. For example, for a Nb-Ti superconductor at 5 T and 4.2 K the maximum fi lament size has to be smaller than 50 μ m. The other main concern was protection of the superconductor in the case of a quench. All superconductors in the normal state have high resistivity. In the case of a quench they are likely to be damaged by Joule heating due to the high current density they carry, if no adequate measures for protection are taken. To minimize heating after a quench, a superconductor should therefore be surrounded by a normal conductor with a low resistance. The two abovementioned conditions (stability and protection) have led to the concept of composite superconductors, in which small superconducting fi laments are embedded in a normal conducting matrix with low resistance and large thermal diffusivity. The matrix decreases the Joule heating when the superconductor becomes normal, conducts the heat away from the surface of the superconducting fi laments thanks to its high thermal conductivity, and absorbs a substantial fraction of heat due to its high speci fi c heat. To provide stability of a composite 4 A. V. Zlobin and D. Schoerling