Abstract
So far, polarized proton beams have never been accelerated to energies higher than 25 GeV. During the acceleration process, the beam polarization is quite undisturbed, when the accelerator is well adjusted, except at first-order depolarizing spin orbit resonances. At some accelerators other effects have been observed but first-order resonances have always been dominant. At these resonances the spin tune plus or minus one of the orbit tunes is an integer. These beams have usually been investigated by theories which correspondingly lead to an undisturbed polarization during acceleration, except at such resonances. Therefore we speak of ``first-order theories.'' The first frequently used first-order theory is the single resonance model, which is usually used for simulating the acceleration process. Here the equation of spin motion is simplified drastically by dropping all but the dominant Fourier component of the driving term of that differential equation. The second frequently used first-order theory, the linearized spin-orbit motion theory, is also quite crude. It is based on a linearization of the spin and orbit equation of motion with respect to the phase space coordinates and two suitably chosen spin coordinates. Because of linearization this method cannot be used close to resonances but at fixed energies it is a useful tool. It will be shown that the validity of these first-order theories is restricted at Hadron Electron Ring Accelerator (HERA) energies of up to 820 GeV. An overview of the available theories which go beyond the first-order resonances is given and we explain which of these approaches are applicable for the analysis of polarization in the HERA proton ring. Since these theories include more than one Fourier harmonic in the driving term of the equation of motion, we refer to them as ``non-first-order'' or ``higher-order'' theories. Finally, the higher-order effects observed while simulating polarized beams in HERA with these advanced methods are illustrated.
Highlights
The Hadron Electron Accelerator Ring (HERA) is the only circular accelerator which utilizes longitudinally polarized high energy electrons
Before introducing the techniques which include non-firstorder effects, we demonstrate that the single resonance model (SRM) and SLIM
The mathematical concepts involved in the three adiabatic methods are very similar. These three methods are implemented in the code SPRINT and we show examples of the higher-order effects which were observed with these methods while studying polarized proton beams at high energy in HERA
Summary
The Hadron Electron Accelerator Ring (HERA) is the only circular accelerator which utilizes longitudinally polarized high energy electrons. Accelerating protons up to 820 GeV in HERA would be achieved by the following acceleration chain: a 19 keV H2 source, a 750 keV radio frequency quadrupole, a 50 MeV proton linear accelerator, the 8 GeV proton synchrotron DESY III, the 39 GeV proton synchrotron PETRA, and the 820 GeV storage ring HERA In each of these accelerators depolarizing effects have to be avoided. The imperfection resonances occur when the spin of a proton performs an integer number of complete rotations around some rotation axis while the particle travels once around the closed orbit of the accelerator. These resonances can be avoided by using so-called partial snakes [4,5]. We have described such measures in other papers [1,6,7]
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