Abstract
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 degrees 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 to find an optimal choice of the snake axes. Rings with super-period four are analyzed in detail, and the HERA proton ring is used as an example for approximate four-fold 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 snakes 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. To show that favorable choice of snakes have 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.
Highlights
INTRODUCTION2l=L along a storage ring of length L describes the spin direction for the design orbit which is periodic from turn to turn, where l is the path length along the design orbit
The design orbit spin direction n~ 0 at some azimuth2l=L along a storage ring of length L describes the spin direction for the design orbit which is periodic from turn to turn, where l is the path length along the design orbit.The design orbit spin tune 0 describes the number of times a spin has rotated around n~ 0 during one turn around the ring.Spin-orbit resonances in high-energy accelerators arise when the electromagnetic fields on synchrobetatron trajectories cause disturbances of the spin’s motion which build up coherently from turn to turn.In a flat ring, for instance, an initially vertical spin of a particle traveling on the design orbit remains vertical during particle motion
Siberian snakes are indispensable if polarized proton beams are to be accelerated in a high-energy synchrotron
Summary
2l=L along a storage ring of length L describes the spin direction for the design orbit which is periodic from turn to turn, where l is the path length along the design orbit. Since each initial phase space position leads to a different particle trajectory with different spin motion, spin fields in general change from turn to turn. ~ k0 Pj kj Qj for integers kj , the spin motion can be strongly disturbed As another illustration of the benefits of the proposed choice of Siberian snakes it will be shown that they increase the orbital amplitudes for which low order resonance conditions occur. Invariant in a storage ring, but that it is an adiabatic invariant [7] when parameters of the accelerator, like the beam’s energy, change This means that a beam that is initially polarized parallel to the invariant spin field.
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