This volume lays down the foundations of a theory of rings based on finite maps. The purpose of the ring is entirely discussed in terms of the global properties of the one-turn map. Proposing a theory of rings based on such maps, this work offers another perspective on storage ring theory.
Table of Contents
A pictorial view in one degree of freedom; from the Hamiltonian to the map; classification of one-turn maps; from linear to nonlinear maps; vector fields and canonical transformations; the ring; floquet rings; a theoretical construct; power series and analytic/symbolic calculations; examples of the analytical normalization; the layout in the laboratory frame; symplectic integration; "small" rings - using the correct Hamiltonian; fringe effects in ring dynamics; large ring approximations and the rest; inclusion of radiation.