J un 2 00 0 1 Polarized Protons in HERA
Polarized proton beams at HERA can currently only be produced by extracting a beam from a polarized source and then accelerating it in the three synchrotrons at DESY. In this paper, the processes which can depolarize a proton beam in circular accelerators are explained, devices which could avoid this depolarization in the DESY accelerator chain are described, and specific problems which become important at the high energies of HERA are mentioned. At HERA’s high energies, spin motion cannot be accurately described with the isolated resonance model which has been successfully used for lower energy rings. To illustrate the principles of more accurate simulations, the invariant spin field is introduced to describe the equilibrium polarization state of a beam and the changes during acceleration. It will be shown how linearized spin motion leads to a computationally quick approximation for the invariant spin field and how to amend this with more time consuming but accurate non-perturbative computations. Analysis with these techniques has allowed us to establish optimal Siberian Snake schemes for HERA.
Possibilities for Polarized Protons at HERA
This article explores the implications of obtaining polarized protons at high energy in HERA.
Electron-spin polarization in high-energy storage rings. I. Derivation of the equilibrium polarization.
A detailed exposition on the origin and buildup of polarization in high-energy electron storage rings is presented. Fundamental, but not clearly understood, theoretical results are rederived and clarified (Ya. S. Derbenev and A. M. Kondratenko, Zh. Eksp. Teor. Fiz. 64, 1918 (1973) (Sov. Phys.: JETP 37, 968 (1973))). It is explained how to diagonalize the Hamiltonian of a storage ring, in particular the spin-dependent terms, to the first order in Planck's constant. Relevant perturbations, their time scales, and the various ensemble averages, are elucidated: the use of statistical concepts is shown to be essential to the calculation. Semiclassical techniques are used to derive, and extend to first order in g-2, the equilibrium degree of polarization (the Derbenev-Kondratenko formula). In so doing, some aspects of the polarization mechanism not previously recognized are uncovered. Because Derbenev and Kondratenko use a different mathematical approach, a proof is given of the equivalence between their formalism and the one used here.