Abstract
The use of iris loaded cavities to accelerate high current bunched beams makes it important to understand the impedance and wake fields caused by an iris in a beam pipe. In this paper we present a method to calculate both the longitudinal and transverse impedance of a circular iris of radius b and thickness g in a circular beam pipe of radius a for ultrarelativistic particles. An integral equation is derived for the transverse electric field at the junction between the iris and the beam pipe and a variational expression is obtained for the impedance, using the transverse field as a trial function. Accurate numerical results are obtained for the longitudinal and transverse impedances using a trial function with only a few adjustable parameters. By invoking causality we confirm the analytic behavior of the impedances in the complex frequency plane and obtain the corresponding wake functions. We particularly explore the limit b\ensuremath{\rightarrow}\ensuremath{\infty} to compare with previous studies of the impedance of a circular hole in a transverse metallic plane.
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