Spin-orbit motion in a storage ring in the presence of synchrotron radiation using a dispersion formalism

In this report we investigate the spin-orbit motion of particles in storage rings. Having summarized the fully six-dimensional description of the orbital motion with coordinates (x, px, z, pz, σ, η = ΔE/E0) we introduce the dispersion. Since the dispersion function is introduced via a canonical transformation, the symplectic structure of the equations of motion (and thus of all the transfer matrices) in the absence of radiation effects is completely preserved. In this formulation the coupling between transverse and longitudinal motion only appears in the cavities. As physical applications of this approach we calculate the damping constants, the beam emittance matrix and the depolarization time. (orig.)