Analytical field calculation of helical coils

Various helical coils such as helical dipole magnets, multifilamentary superconductors and superconducting strands have something in common with the helical structure. In this paper, we discuss the analytical calculation for the magnetic field of helical coils. In addition, the comparison between the analytical and numerical calculations is presented for simple helical coils. In particular, the helical multipole coefficients are introduced for helical dipole magnets, which are essential components of Siberian Snakes and spin rotators for polarized proton acceleration at Relativistic Heavy-Ion Collider (RHIC). The relation between the field homogeneity and helical multipoles is also studied. Finally, the analytically and numerically calculated and measured results of the magnetic field at the middle of the slotted helical dipole prototypes with the half-length for RHIC are compared. In this paper, the end effects of helical dipoles is not treated.