New method of calculating the wakefields of a point charge in a waveguide of arbitrary cross section

Abstract

A new method for calculating the Cherenkov wakefield acting on a point charged particle passing through a longitudinally homogeneous structure lined with layer(s) of an arbitrary retarding (dielectric, resistive, or corrugated) material has been developed. In this paper we present a rigorous derivation of the expressions for the fields that are valid at the cross section of the particle on the basis of a conformal mapping method. This new formalism allows reduction of the loss factor calculation to a simple derivation of a conformal mapping function from the arbitrary cross section onto a circular disc. We generalize these results to the case of a bunch with an arbitrary transverse distribution by deriving a two-dimensional Green function at the cross section of the particle. Consequently, for the first time analytical expressions for the transverse distributions of the electric field Ez for the most commonly used cylindrical, planar and elliptical cross section geometries are found. The proposed approach significantly decreases simulation time and opens new possibilities in optimizing wakefield effects resulting from short charged particle bunches for FEL and Linear Collider applications.