Electron-spin polarization in high-energy storage rings. II. Evaluation of the equilibrium polarization

A new algorithm is presented to evaluate the equilibrium degree of polarization in a high-energy electron storage ring (the Derbenev-Kondratenko formula). The algorithm includes all modes of orbital motion, to arbitrary orders in principle, thus facilitating the calculation of so-called ‘‘spin resonances,’’ especially higher-order resonances. The algorithm is applicable to storage rings of arbitrary geometry and energy, and, in particular, is able to deal with overlapping resonances. Precautions are described to ensure stability of the algorithm. In the approximation of linear orbital dynamics, a computer program has been written to implement this algorithm, and sample results are presented.