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.
Highlights
The corrugated, metallic beam pipe has been proposed as a “dechirper” for linac-based X-ray free electron lasers (FELs) [1]
The RadiaBeam/Linac Coherent Light Source (LCLS) dechirper has recently become the first one that has been tested at high energies and short bunch lengths (10’s of microns) [7]
Using the RadiaBeam/LCLS dechirper nominal parameters (Table I), for the case with the beam on axis, we compare wlðs; y 1⁄4 0Þ from Eq (15) with the numerical result obtained by taking the inverse Fourier transform of the general impedance equation, Eq (10), with no approximations
Summary
The corrugated, metallic beam pipe has been proposed as a “dechirper” for linac-based X-ray free electron lasers (FELs) [1]. We make an assumption about the form of the wakes that we check by comparing with two numerical methods: (1) we numerically perform the inverse Fourier transform of generalized expressions for the impedance found in [16] to obtain the (point charge) wake, and (2) we obtain the bunch wake for a short Gaussian bunch using the time-domain, wakefield solving program for rectangular geometry, ECHO(2D) [15]. This report is organized as follows: The first section concerns the case of a dechirper in round geometry This is followed by the derivation of analytical expressions for longitudinal wakes in flat geometry, both on and off axis. We calculate the dipole and quad wakes away from the axis This is followed by a short section estimating some wake effects for example LCLS machine and beam parameters. The wakes and impedances in this report are given per unit length of structure
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