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Accelerating polarized proton beams and storing them for many turns can lead to a loss of polarization when accelerating through energies where a spin rotation frequency is in resonance with orbit oscillation frequencies. First-order resonance effects can be avoided by installing Siberian snakes in the ring, devices which rotate the spin by 180° around the snake axis while not changing the beam’s orbit significantly. For large rings, several Siberian snakes are required. Here a criterion will be derived that allows one to find an optimal choice for the orientation of the snake axes. Rings with superperiod four are analyzed in detail, and the HERA proton ring is used as an example for approximate fourfold symmetry. The proposed arrangement of Siberian snakes matches their effects so that all spin-orbit coupling integrals vanish at all energies and therefore there is no first-order spin-orbit coupling at all for this choice, which I call snake matching. It will be shown that in general at least eight Siberian snakes are needed and that there are exactly four possibilities to arrange their axes. When the betatron phase advance between snakes is chosen suitably, four Siberian snakes can be sufficient. Since the spin motion depends on a particle’s trajectory, protons at different phase space positions generally have different spin directions. The time averaged polarization at each phase space point is parallel to the invariant spin field, and the spread of this spin field limits the polarization that can be stored. By the here presented choice of Siberian snakes this limit is completely eliminated up to first order in the transverse phase space coordinates. The invariant spin field and the amplitude-dependent spin tune are also computed without linearization to show the advantages of this choice of snakes. Ultimately, the goal of snake matching is to reduce the loss of polarization during the acceleration of the beam. To show that a favorable choice of snakes has been found, polarized protons are tracked for part of HERA-p’s acceleration cycle which shows that polarization is preserved best for the here proposed arrangement of Siberian snakes

Optimal axes of Siberian snakes for polarized proton acceleration