Electromagnetic Design of Superconducting Quadrupoles

We study how the critical gradient depends on the coil lay-out in a superconducting quadrupole for particle accelerators. We show that the results relative to a simple sector coil are well representative of the coil lay-outs that have been used to build several quadrupoles in the past 30 years. Using a semi-analytical approach we derive a formula that gives that 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 lay-outs (shell, racetrack, block, open mid-plane).