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An analytical method is developed for calculating the geometric wakefield andimpedances of an ultrarelativistic beam propagating on- and off-axis through anaxially symmetric geometry with slowly varying circular cross-section, such asa transition. Unlike previous analytical methods, our approach considers a beamof arbitrary longitudinal profile and permits detailed perturbativeinvestigation of impedance as a function of frequency. We compare the accuracyof the results of our approach with numerical simulations performed using thecode ECHO and determine parameters in which there is good agreement with theasymptotic analysis.

Wake potentials and impedances of charged beams in gradually tapering structures