Magnetic design in coil-dominated superconducting quadrupole magnets based on racetrack coil model

the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented. The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density. Then, a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10-4. Finally, considering the practical engineering needs of the accelerator interaction region, electromagnetic design examples of racetrack quadrupole magnets with high gradients, large apertures, and small apertures are described, and the application prospects of racetrack quadrupole coils are analyzed.