Analytical Formulas for Short Bunch Wakes in a Flat Dechirper

TL;DR

This paper presents analytical formulas for short bunch wakes in a flat dechirper, improving accuracy over previous models and validated by numerical comparisons, with practical implications for beam energy chirp and transverse kicks.

Contribution

Develops first-order analytical models for longitudinal and transverse wakes in a flat dechirper, enhancing accuracy over zeroth-order formulas and validated against numerical calculations.

Findings

16% droop in energy chirp at bunch tail

3 MV transverse kick differential over 30 μm

Good agreement between analytical and numerical results

Abstract

We develop analytical models of the longitudinal and transverse wakes, on and off axis for realistic structures, and then compare them with numerical calculations, and generally find good agreement. These analytical "first order" formulas approximate the droop at the origin of the longitudinal wake and of the slope of the transverse wakes; they represent an improvement in accuracy over earlier, "zeroth order" formulas. In example calculations for the RadiaBeam/LCLS dechirper using typical parameters, we find a 16\% droop in the energy chirp at the bunch tail compared to simpler calculations. With the beam moved to 200~$\mu$m from one jaw in one dechiper section, one can achieve a 3~MV transverse kick differential over a 30~$\mu$m length.