A canonical 8-dimensional formalism for classical spin-orbit motion in storage rings. II. Normal forms and the n-axis

The two real canonical spin variables α and β introduced in an earlier paper to describe spin motion in storage rings [1] are combined with the six canonical variables of coupled synchro-betatron motion to form a system of eight canonical spin-orbit variables in which spin and orbital motion are treated on the same level. In these variables on turn maps are origin preserving and the usual techniques of canonical perturbation theory can be applied. By writing the Hamiltonian in normal form the spin detuning terms as well as the so calledn-axis, the semiclassical spin axis which is needed in the theory of radiative polarization, can be constructed. The equations derived are valid for arbitrary particle velocity (below and above transition energy)