## Wakefields in a pillbox cavity

The wakefields due to a bunch in a pillbox cavity can be found by mode-expansion of the fields given by the wave-equation. Usually one considers first the wakefield due to an infinitely short pulse and then integrates over the current distribution. Since the series for the delta function pulse converge rather poorly, it is preferable to use the wakefield due to a step-function current, which can also be integrated to give the result for an arbitrary current distribution. For the most important case of fields with azimuthal symmetry, the results are expressed as double series over the radial mode numbermore »