Introduction to impedance for short relativistic bunches

The main purpose of this paper is to give an introduction to the jargon used in discussing wake fields excited by a short bunch of particles passing through a structure. Often, terms such as the inductive or resistive part of the wake are used to describe the characteristics of the field or voltage which acts on the particles in the bunch. We have tried to illustrate how some of these terms relate to the common parallel circuit of a cavity. Many people will refer to a resistive portion of the total wake voltage shown in Fig. 3.6 when a portion of the wake voltage is in phase with the beam density profile. This is because the wake voltage for a resistive impedance is in phase with the beam density as shown in Fig. 3.2. Of course, we know that this portion of the wake in Fig. 3.6 comes from the capacitive part of the impedance. To the particles in the beam, however, this portion of the impedance has a resistive effect, since it produces a net energy loss. If, after reading this paper, the student has a more physical feel for the wake field in different regimes and finds the more advanced papers easier to read, then this paper has fulfilled its purpose.