Abstract
The so-called spin response formalism, which is linear response theory applied to spin dynamics in storage rings, can calculate the resonance strengths for spin flippers in storage rings of arbitrary structure, including rings with Siberian Snakes and spin rotators. We calculate so-called spin response functions for a model of the RHIC lattice, for various scenarios of spin rotator settings.
Highlights
The program ASPIRRIN [1,2] is an ideal tool to calculate spin flip resonance strengths in storage rings
For rf dipole spin flippers, the spin response formalism encapsulates the contributions to the spin flip resonance strength from both the direct spin kick and from the spin-orbit coupling due to the induced coherent betatron oscillations, in so-called ‘‘spin response functions.’’ Much of the initial experimental and theoretical work on spin flippers was carried out at the Budker Institute of Nuclear Physics
In the absence of electric fields, the effects of the magnetic fields in the spin precession equation of motion (the Thomas–Bargmann-Michel-Telegdi (BMT) equation [11,12]) can be completely expressed using ðx; x0; z; z0Þ and solenoidal fields. This was done, for example, by Courant and Ruth [13], leading to a compact formula for the strengths of imperfection and intrinsic depolarizing spin resonances. (Imperfection resonances are driven by closed orbit imperfections and intrinsic resonances are driven by the free vertical betatron oscillations.) The Courant-Ruth formula treats only planar uncoupled rings, i.e., without Siberian Snakes and spin rotators, and it does not treat spin flippers
Summary
The program ASPIRRIN [1,2] is an ideal tool to calculate spin flip resonance strengths in storage rings. In a recent paper Shatunov and Mane [3] used ASPIRRIN to successfully calculate the spin flip resonance strengths of stored polarized proton [4] and deuteron [5] beams, where the data was taken using a radial field rf dipole spin flipper at the COSY storage ring. A spin flipper was used in an experiment to compare the ratio of the anomalous magnetic moments of electrons and positrons counterrotating in the same storage ring [6] This experiment set a world record for CPT invariance in a lepton system at the time it was published. A Siberian Snake is theoretically defined as any device which rotates the spin of a particle by 180 around an axis in the horizontal plane, but leaves the orbital motion unchanged.
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