A CANONICAL 8-DIMENSIONAL FORMALISM FOR CLASSICAL SPIN-ORBIT MOTION IN STORAGE-RINGS .1. A NEW PAIR OF CANONICAL SPIN VARIABLES

In this paper we present a classical symplectic treatment of linear an d nonlinear spin-orbit motion for storage rings using a fully coupled eight-dimensional formalism which generalizes earlier investigations o f coupled synchro-betatron oscillations [1, 2] by introducing two new real canonical spin variables which behave, in a small-angle limit, li ke those already used in linearised spin theory. Thus in addition to t he usual x-z-s couplings, both the spin to orbit and orbit to spin cou pling are described canonically. Since the spin Hamiltonian can be exp anded in a Taylor series in canonical variables, the formalism is conv enient for use in 8-dimensional symplectic tracking calculations with the help, for example, of Lie algebra or differential algebra [3, 4], for the study of chaotic spin motion, for construction of spin normal forms and for studying the effect of Stern-Gerlach forces [5].