Transverse impedance of a conducting cylindrical pipe with discontinuous cross section

A bunch of charged particles travelling in an linear or circular accelerating machine interacts with the surrounding structure inducing electromagnetic fields which, acting back on the bunch, influence its dynamics. The knowledge of these fields is necessary for the predictions of the energy lost by the beam and for the analysis of the instability phenomena. In this paper, the authors study the fields induced by a dipole charge distribution crossing a discontinuity. An exact analytical expression of the longitudinal and transverse dipole impedance is derived by extending the analysis developed for the longitudinal case