U.S. Particle Accelerator School
U.S. Particle Accelerator School
Education in Beam Physics and Accelerator Technology

Superconducting Dipole and Quadrupole Magnets for Particle Accelerators course

Sponsoring University:

University of Chicago


Superconducting Dipole and Quadrupole Magnets for Particle Accelerators


Arnaud Devred, CEA/Saclay

The quest for elementary particles has promoted the development of particle accelerators producing beams of increasingly higher energies. In a synchrotron, the particle energy is directly proportional to the product of the machine's bending radius times the bending magnets' field strength.  Present proton experiments at the TeV scale require facilities with circumferences ranging from a few to tens of kilometers and relying on a large number (several hundred to several thousand) high-field dipole magnets and high-field gradient quadrupole magnets. These electro-magnets use high-current-density, low-critical-temperature superconducting cables, and are cooled down at liquid helium temperature. They are among the most costly and the most challenging components of the machine. The course covers various types of accelerator magnets, parameters of existing superconducting particle accelerators, the superconducting materials that are available at industrial scale (chiefly, NbTi and Nb3Sn). We explain in details the manufacturing of NbTi wires and cables, and present the difficulties of processing and insulating Nb3Sn conductors, which so far have limited the use of this material in spite of its superior performances. We continue by discussing the two-dimensional current distributions which are the most appropriate for generating pure dipole and quadrupole fields and we explain how these ideal distributions can be approximated by so-called cosine-theta and cos2theta coils. We also present a few alternative designs which are being investigated and we describe the difficulties of realizing coil ends. Some of the toughest requirements on the performance of accelerator magnets are related to field quality, and we summarize the different sources of field errors. We present the mechanical design concepts that are used in existing accelerator magnets and we describe how the magnets are assembled; then a brief overview of the cooling schemes, which have been implemented in the various accelerator rings.  We discuss the issues related to quench performance and quench protection. The lectures are accompanied by practical exercises and problems to get a sense of the material properties at low temperatures and of the relevant parameters in the design of superconducting accelerator magnets.   Prerequisites: Basic electromagnetism.