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 E z 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.

Upper limit for the accelerating gradient in the collinear wakefield accelerator as a function of the transformer ratio

“…Another important parameter to be considered is the magnitude of the accelerating field which is strictly defined by the product of the total bunch charge and the loss factor, i.e., Qκ ∥ (see, e.g., [19,20]). Evidently, these are not free parameters because the limitations on both are given by considerations of stability of the drive bunch propagating the wake field creating environment and gradually decelerating (possible tradeoffs are discussed for example in [21] In the first case we consider a single mode Green's function GðsÞ ¼ 2κ ∥ cosðksÞ.…”

Compact and powerful THz source investigation on laser plasma wakefield injector and dielectric lined structure

“…In principle, the waveguide can be of any cross section but a translational symmetry along z is imposed in order to make the analytical analysis feasible. The waveguide with other cross geometries can be analyzed with conformal mapping [45].…”

Analytic model of 3D beam dynamics in a wakefield device

“…It was shown in Ref. [8] (see Section 3 and Appendix B of the Ref. [8] for the details) that the upper limit of the Green's function G ⊥ for an arbitrary cross section of longitudinally homogenous vacuum channel could be written in terms of a conformal mapping function f (ω, ω 0 ) that maps the cross sectional area onto a unit disk (see Fig.2).…”