Transverse Impedances of Cavities

,).I' (0) (ID)-1 , Fig. 1. Cylindrically symmetric structures considered *'inthe present work: a) a cavity and b) a collimator.- .-:. Wewill briefly describe our method and present some early results. More details will be forthcoming in a future paper.-_ The Current Sources Consider an ultra-relativistic particle of charge Q moving at speed /3c parallel to the z axis of a cylindrically symmetric t Work supported by the US Department of Energy, contract DE-AC03-76SF00515.. Introduction structure. Let the transverse position of the particle be at r = h and B f 0. The current density is then given as When an ultra-relativistic'charge moves past a discontinu-ity in an accelerator vacuum chamber, electromagnetic fields are excited. A test charge following behind the exciting charge will, in. general, experience a longitudinal kick (affecting its energy) and a transverse kick from these fields. The interaction can be characterized by the wakefield or the impedance of the structure. Either of these functions are useful for studying the current dependent behavior of a bunch of particles in an accelerator.