Magnetic design study of coil-dominated superconducting quadrupole magnets based on racetrack coils

Several coil structures have been used in accelerator superconducting quadrupole magnets, and cos2{\theta} quadrupole magnets are the most mature in theoretical research and engineering applications. However, the cos2{\theta} quadrupole magnet has a complicated coil structure, especially at the end of the coil, which makes it difficult to apply strain-sensitive high-temperature superconductors. Racetrack quadrupole magnets are friendly to high-temperature superconductors. Field strength of iron-dominated racetrack magnets is limited by the magnetic saturation of the iron poles. Therefore, coil-dominated racetrack quadrupole magnets with simple geometry have become the focus of our research. In this paper, analytical expressions of the magnetic field harmonics related to racetrack quadrupole coil parameters are obtained. These expressions are used to find the solution of coil geometry parameters with field harmonics on the order of 10-4. Then, examples are given to build ideal quadrupole model and verify the theoretical formulas. Next, the design and optimization of example racetrack quadrupole magnets are completed in ROXIE. Finally, the advantages and disadvantages of the racetrack coils and the cos2{\theta} coils are compared and discussed.