  The concepts of wake fields and impedance are introduced to describe the
electromagnetic interaction of a bunch of charged particles with its
environment in an particle accelerator. The wake fields can act back on the
beam and lead to instabilities, which may limit the achievable current per
bunch, the total current, or even both. Some typical examples are used to
illustrate the wake function and its basic properties. Then the
frequency-domain view of the wake field or impedance is explained, and basic
properties of the impedance are derived. The impedance of a cavity mode is
illustrated using an equivalent circuit model. The relation of wake field
effects to important beam parameters is treated in the rigid beam
approximation. Several examples are employed to illustrate the impact of the
geometry and the material properties of the vacuum chamber on the impedance.
Finally, a basic introduction to beam instabilities based on a head tail model
of the beam is given.
