Electron-spin polarization in high-energy storage rings. I. Derivation of the equilibrium polarization

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Abstract
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.