TRACKING ALGORITHM FOR THE STABLE SPIN POLARIZATION-FIELD IN STORAGE-RINGS USING STROBOSCOPIC AVERAGING

Polarized protons have never been accelerated to more than about 25 Ge V. To achieve polarized proton beams in the Relativistic Heavy Ion Col lider (RHIC, 250 GeV), the Hadron Electron Ring Accelerator (HERA, 820 GeV), and Fermilab's TeV accelerator (TEVATRON, 900 GeV), ideas and t echniques applicable to accelerator physics are needed. In this public ation we will stress an important aspect of very high energy polarized proton beams, namely, the fact that the equilibrium polarization dire ction can vary substantially across the beam in the interaction region of a high energy experiment when no countermeasure is taken. Such a d ivergence of the polarization direction would not only diminish the av erage polarization available to the particle physics experiment, but i t would also make the polarization involved in each collision analyzed in a detector strongly dependent on the phase space position of the i nteracting particle. In order to analyze and compensate for this effec t, methods for computing the equilibrium polarization direction are ne eded. In this paper we introduce the method of stroboscopic averaging, which computes this direction in a very efficient way. Since only tra cking data are needed, our method can be implemented easily in existin g spin tracking programs. Several examples demonstrate the importance of the spin divergence and the applicability of stroboscopic averaging .