Numerical studies of Siberian snakes and spin rotators for RHIC

For the program of polarized protons in RHIC, two Siberian snakes and four spin rotators per ring will be used. The Snakes will produce a complete spin flip. Spin Rotators, in pairs, will rotate the spin from the vertical direction to the horizontal plane at a given insertion, and back to the vertical after the insertion. Snakes, 180 degrees apart and with their axis of spin precession at 90 degrees to each other, are an effective means to avoid depolarization of the proton beam in traversing resonances. Classical snakes and rotators are made with magnetic solenoids or with a sequence of magnetic dipoles with fields alternately directed in the radial and vertical direction. Another possibility is to use helical magnets, essentially twisted dipoles, in which the field, transverse the axis of the magnet, continuously rotates as the particles proceed along it. After some comparative studies, the authors decided to adopt for RHIC an elegant solution with four helical magnets both for the snakes and the rotators proposed by Shatunov and Ptitsin. In order to simplify the construction of the magnets and to minimize cost, four identical super conducting helical modules will be used for each device. Snakes will be built with four right-handed helices. Spin rotators with two right-handed and two left-handed helices. The maximum field will be limited to 4 Tesla. While small bore helical undulators have been built for free electron lasers, large super conducting helical magnets have not been built yet. In spite of this difficulty, this choice is dictated by some distinctive advantages of helical over more conventional transverse snakes/rotators: (i) the devices are modular, they can be built with arrangements of identical modules, (ii) the maximum orbit excursion in the magnet is smaller, (iii) orbit excursion is independent from the separation between adjacent magnets, (iv) they allow an easier control of the spin rotation and the orientation of the spin precession axis