Longitudinal coupling impedance of a hole in an accelerator beam pipe at finite frequencies.

摘要

The penetration of electric and magnetic fields through a hole in a metallic wall plays an important role in many devices. In an accelerator, such holes in the beam pipe serve to allow access for pumping, devices for beam current and beam position measurement, coupling between cavities, etc. Finding an analytic or semianalytic expression for the impedance of a hole of different geometry in a broad frequency range is highly desirable in the design of high intensity storage rings.; In much of the early work the hole dimensions were considered to be very small compared to the wavelength, which permitted the use of the static approximation for the fields. The main purpose of this work is to extend the analyses to include the effects of finite frequencies, including the possibility of resonant effects in the hole. The frequency corrections are important for long slots since the static approximation loses its validity when the length of the slot becomes comparable with the wavelengths contained in the beam spectrum.; We develop the analysis and find frequency corrections for the coupling impedance of a circular hole in the wall of a beam pipe of both zero and finite thickness. We develop a similar analysis for the frequency corrections to the coupling impedance of an elliptical hole in a metallic wall of zero thickness. Of great importance is a hole of a rectangular shape, which enters into the designs of modern high-energy super-conducting colliders as the shape of pumping slots in a special beam screen (liner). We therefore develop an analysis for such a slot valid at any frequency. We also take into account the cross-sectional curvature of the beam pipe as well as the coaxial structure of the beam pipe and the liner. We perform a detailed study of the coupling impedance of an annular cut, square hole, and transverse and longitudinal slots in the liner surface in a broad frequency range. We also discuss in detail the effect of the outer wall of the beam pipe on the impedance of a slot in the liner surface as well as the possibility of the resonant behavior of a long rectangular slot.