ABSTRACT
This chapter introduces the theory of transverse and longitudinal beam motion in accelerators. Beam motion is also affected by the electromagnetic fields generated by the beam itself, directly or through the interactions with the environment. The study of beam motion under the influence of electromagnetic fields in accelerators is called beam dynamics. The transverse motion of a beam in accelerators is determined by the magnetic fields in the various types of magnets. Particles in a beam tend to diverge from each other as they travel along the orbit due to their slightly different directions of motion. In an accelerator the particles in a beam are expected to closely follow the design path. Drift spaces, dipole magnets, and quadrupole magnets are the basic building blocks of accelerator lattices. The placement of these components in a beam line determines the transformation of the phase space coordinates to the linear order.
