Impedance of Small-Angle Collimators in High-Frequency Limit

We consider round an rectangular-aperture tapered collimators with a small taper angle fi. Depending on the angle, aperture, and the frequency difierent parameter regimes are found with spe- ciflc scalings of the impedance. The physical mechanism involved in formation of the beam wake fleld is discussed. Analytical for- mulas are derived for the limiting case of the difiraction regime for round collimators. For rectangular geometry with a large width to height ratio, two new regimes | difiraction 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 difiraction regime for both round and rectangular geometries.