Abstract
Quadruple magnet is an essential component for the accelerator, and the field uniformity in the good field region reflects the quality of quadruple magnet. In this paper, the total magnetic field B was separated into the coil-induced magnetic field $B_s$ and the iron-induced magnetic field $B_c$ to explain why the total magnetic field B has some inhomogeneity. Using Fourier analysis, harmonic components of $B_s$, $B_c$ and B have been analyzed at good field region, respectively. The harmonics of multipole magnet and Fourier analysis are helpful to show the uniformity of magnetic field. Several geometries of yoke and coils were defined to analyze the effect on field uniformity of an HTS quadruple magnet. By the analysis, it was found that the sixth harmonics which is the main factor of field inhomogeneity can be reduced to zero. It means that the sixth harmonics of the magnetic field B can be removed by adjusting the geometry of the magnet pole and the position of coils. We expect that this result can effectively improve the uniformity of an HTS quadruple magnet.