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

S S Baturin,A D Kanareykin

doi:10.1103/physrevaccelbeams.19.051001

S S Baturin, A D Kanareykin

Open Access

https://doi.org/10.1103/physrevaccelbeams.19.051001

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Abstract

Recently, a new method for calculating the Cherenkov field acting on a point-like electron bunch passing through longitudinally homogeneous structures lined with arbitrary slowdown layers was proposed, where the formalism was obtained though consideration of a general integral relation that allows calculation of the fields at the vicinity of a point-like bunch. It demonstrates that the Cherenkov field at the point of the short relativistic bunch does not depend on the waveguide system material and is a constant for any given transverse dimensions and cross-section shapes of waveguides. With this paper we present a strict derivation of the fields formulas valid at the cross-section of a bunch on the basis of a conformal mapping method. We generalize the results of the previous paper to the case of transversely distributed bunch by deriving a two-dimensional Green function at the cross-section of a bunch. Comparison of the results proving validity of the method is given in the appendix.

Highlights

Wakefields excited when very short bunches pass through accelerating structures or other longitudinally extended components of a beam line, are of major concern for linear colliders (ILC [1], CLIC [2]), and FEL (LCLS-II, X-FEL, etc.) [3,4] and other accelerator projects
The results were obtained by using formula (31) and found to be in full agreement with those obtained using the mode decomposition method [14,23,24], where dielectric was considered as a retarding layer
We provide formulas for the loss factor and transverse Ez field distribution for the case of an elliptical cross section

Summary

Introduction

Wakefields excited when very short bunches pass through accelerating structures or other longitudinally extended components of a beam line (pipes, collimators, bellows), are of major concern for linear colliders (ILC [1], CLIC [2]), and FEL (LCLS-II, X-FEL, etc.) [3,4] and other accelerator projects. Analysis of the short-range wakefields in the longitudinally extended components, especially in undulator vacuum chambers, is needed to control the energy spread and emittance of the short bunches [5,6]. Theoretical analysis of Cherenkov radiation commonly considers a “short bunch” approach [7,8,9,10].

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