Higher Order Spin Resonances in High Energy Electron Storage Rings

Abstract

It was predicted by Sokolov and Ternov [1] that when electron and positrons circulate in a high energy storage ring, the particle spins become polarized by the emission of synchrotron radiation. In practice, the equilibrium degree of polarization is strongly affected by so-called depolarizing spin resonances. A formula for the equilibrium degree of polarization, including the resonances, was given by Derbenev and Kondratenko [2]. An algorithm to evaluate their formula was given by Mane, and coded into a computer program called SMILE [3]. The so-called SMILE algorithm treats arbitrary resonances, subject to the approximation of treating only linear orbital dynamics. Numerous formalisms for calculating synchrotron sideband resonances have also been published [4,5,6,7,8], and were all shown to be equivalent by Mane [8], However, all of the above formalisms employ perturbation theory in one form or another, and the convergence of the various formalisms is still unresolved. The SMILE algorithm employs an expansion in powers of the orbital action variables, which becomes an expansion in powers of the beam emittances after averaging over the beam distribution. The other formalisms express the spin integrals of the resonances as a sum of Bessel functions, rather than a sum of powers of action variables.