Electromagnetic design of superconducting quadrupoles

We study how the critical gradient depends on the coil layout in a superconducting quadrupole for particle accelerators. We show that the results relative to a simple sector coil are well representative of the coil layouts that have been used to build several quadrupoles in the past 30 years. Using a semianalytical approach, we derive a formula that gives the critical gradient as a function of the coil cross-sectional area, of the magnet aperture, and of the superconducting cable parameters. This formula is used to evaluate the efficiency of several types of coil layouts (shell, racetrack, block, open midplane).