Impedance of Small-Angle Collimators in High-Frequency Limit∗

We consider round an rectangular-aperture tapered collimators with a small taper angle α. Depending on the angle, aperture, and the frequency different parameter regimes are found with spe-cific scalings of the impedance. The physical mechanism involved in formation of the beam wake field is discussed. Analytical for-mulas are derived for the limiting case of the diffraction regime for round collimators. For rectangular geometry with a large width to height ratio, two new regimes — diffraction and intermediate – are found and the impedance is calculated for each regime. In addition to consideration based on solution of Maxwell’s equa-tions, a simple recipe is given for calculation of the impedance in the diffraction regime for both round and rectangular geometries. ∗Work supported by Department of Energy contract DE–AC03–76SF00515.