Longitudinal coupling impedance of an abrupt junction in a vacuum chamber

The paper deals with the evaluation of the longitudinal coupling impedance due to a charged particle traveling at a constant but otherwise arbitrary velocity on the symmetry axis of an abrupt junction joining two semi-infinite circular waveguides. Modal expansions are used to match the electric and magnetic fields on the junction, and noteworthy attention is given to the truncation of the infinite matrices. The optimum finite size for these matrices is found by imposing the edge condition. The asymptotic value of the longitudinal coupling impedance, valid in the case beta = 1, is finally compared with the numerical results.