COUPLING IMPEDANCES OF SMALL DISCONTINUITIES FOR NON-ULTRARELATIVISTIC BEAMS ∗

The beam coupling impedances of small discontinuities of an accelerator vacuum chamber have been calculated (e.g., [1]) for ultrarelativistic beams using Bethe’s diffraction theory. Here we extend the results for an arbitrary beam velocity. The vacuum chamber is assumed to have an arbitrary, but fixed, cross section. The impedance dependence on the beam velocity exhibits some unusual features. For example, the reactive impedance, which dominates in the ultrarelativistic limit, can vanish at a certain beam velocity, or its magnitude can exceed the ultrarelativistic value many times.