Impact on Spin Tune From Horizontal Orbital Angle Between Snakes and Orbital Angle Between Spin Rotators

To keep the spin tune in the spin depolarizing resonance free region is required for accelerating polarized protons to high energy. In RHIC, two snakes are located at the opposite side of each accelerator. They are configured to yield a spin tune of 1/2. Two pairs of spin rotators are located at either side of two detectors in each ring in RHIC to provide longitudinal polarization for the experiments. Since the spin rotation from vertical to longitudinal is localized between the two rotators, the spin rotators do not change the spin tune. However, due to the imperfection of the orbits around the snakes and rotators, the spin tune can be shifted. This note presents the impact of the horizontal orbital angle between the two snakes on the spin tune, as well as the effect of the vertical orbital angle between two rotators at either side of the collision point on the spin tune.