Longitudinal Coupling Impedance for a Beam Pipe with a Cavity

A method is presented for the computation of the longitudinal coupling impedance of an azimuthally symmetric obstacle of general shape in a long beam pipe. The method involves a numerical calculation of the fields at mesh points in the cavity alone, from which the additive contribution of the cavity to the coupling impedance of the beam pipe can be obtained as a surface integral confined to the cavity wall. Numerical work for obstacles of various geometries is in progress.