The Longitudinal Coupling Impedance of Step Discontinuities in a Circular Beam Tube

The longitudinal coupling impedance presented by a single wall discontinuity to the circulating beam in a circular accelerator or storage ring is usually analyzed by considering a "developed" periodic structure. However, the typical parameters are often such that it becomes adequate to treat the discontinuity as a nonperiodic problem. Using modal field matching methods, solutions were derived for the cases of a single as well as a double-step discontinuity in a circular beam tube. Numerical results are presented in this paper and the typical behavior at low frequency, at resonance, and above cut-off is discussed.