Wake potentials and impedances of charged beams in gradually tapering structures

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