A General Approach for Calculating Coupling Impedances of Small Discontinuities

A general theory of the beam interaction with small discontinuities of the vacuum chamber is developed taking into account the reaction of radiated waves back on the discontinuity. The reactive impedance calculated earlier is reproduced as the first order, and the resistive one as the second order of a perturbation theory based on this general approach. The theory also gives, in a very natural way, the results for the trapped modes due to small discontinuities obtained earlier by a different method.