Introduction

An electron-storage ring consists of an assembly of deflecting bending magnets and focusing quadrupole magnets, called a lattice (Fig. 13.1). The bending magnets determine a closed equilibrium orbit for a particle having the nominal values for energy, initial position, and angle. Particles with small deviations from these nominal parameters are kept in the vicinity of the nominal orbit by the focusing quadrupoles. In addition a storage ring has magnet-free straight sections. These contain an acceleration system, which is usually called the radio-frequency system or just the RF system. It is used to replace the energy lost by the particles due to the emission of synchrotron radiation or to accelerate the electron beam to higher energy.

The straight sections also house insertion devices (undulator and wiggler magnets) and other equipment such as instruments necessary for the operation of the storage ring. The particles are made to circulate inside a vacuum chamber with a very low pressure of a few nTorr (0.13 μPa) in order to minimize the interaction between the particles and the residual gas.

We restrict ourselves to a plane storage ring and describe the beam dynamics in a coordinate system that follows the nominal equilibrium orbit as shown in Fig. 13.2. The longitudinal coordinate s is the path-length along this nominal equilibrium orbit.