Magnetic Design of Superconducting Magnets

In this paper we discuss the main principles of magnetic design for superconducting magnets (dipoles and quadrupoles) for particle accelerators. We give approximated equations that govern the relation between the field/gradient, the current density, the type of superconductor (Nb−Ti or Nb$_{3}$Sn), the thickness of the coil, and the fraction of stabilizer. We also state the main principle controlling the field quality optimization, and discuss the role of iron. A few examples are given to show the application of the equations and their validity limits.