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 v elocity on the symmetry axis of an abrupt junction joining two semi-infinit e circular waveguides. Modal expansions are used to match the electric and magnetic fields on the junction, and noteworthy attention is given to the t runcation of the infinite matrices. The optimum finite size for these matri ces is found by imposing the edge condition. The asymptotic value of the lo ngitudinal coupling impedance, valid in the case beta = 1, is finally compa red with the numerical results.