Introduction to wakefields and wake potentials

What are wakefields and wake potentials, and why are these concepts useful in the physics of linear accelerators and storage rings? We approach this question by first reviewing the basic physical concepts which underlie the mathematical formalism. We then present a summary of the various techniques that have been developed to make detailed calculations of wake potentials. Finally, we give some applications to current problems of interest in accelerator physics. No attempt at completeness can be made in an introductory article of modest length. Rather, we try to give a broad overview and to list key references for more detailed study. It will also be apparent that the last chapter on this subject, with all the loose ends neatly tied up, has yet to be written. There are subtle points, there are controversial questions, and active calculations to resolve these questions are continuing at the time of this writing