Transverse Resistive Wall Wakefunction with Inductive Bypass

Charged particle beams in circular accelerators couple with their surroundings through induced electromagnetic fields. This interaction can be described by so-called coupling impedances. In the frequency domain the impedance in connection with the bunch spectrum allows for stability analysis and estimates. However, for simulation codes one usually needs the wakefunction, the equivalent of the impedance in time domain. Recently the transverse impedance of a cylindrical pipe with arbitrary surface impedance was given by L. Vos. An expression for the wakefunction of this transverse resistive wall impedance with inductive bypass is derived here.