Longitudinal wakefield for an axisymmetric collimator

Abstract

We consider the longitudinal point-charge wakefield, wðsÞ, for an axisymmetric collimator having inner radius b, outer radius d, inner length g, and taper length L. The taper angle is defined by tan ¼ ðd À bÞ=L. Using the electromagnetic simulation code ECHO, we explore the dependence of the wakefield on a collimator's geometric parameters over a wide range of profiles: from small-angle tapers to stepfunction transitions. The point-charge wakefield is determined using an approximation introduced by Podobedov and Stupakov. We have found it useful to exhibit the wakefield as a function of the scaled variable s=d. For small taper angles, our results illustrate the satisfaction of the longitudinal scaling found by Stupakov, Bane, and Zagorodnov; and for larger taper angles, the breaking of this longitudinal scaling is clearly depicted. The use of the scaled variable s=d turns out to be especially well suited to describing the wakefield for a collimator with step-function profile ( ¼ =2).

Preservation of low slice emittance in bunch compressors

“…The wakefield induced effect on the bunch depends on the geometry of the system and the properties of the beam (bunch size, pulse length, charge and trajectory). Analytical formulas can be found in the literature to calculate these effects [5,6]. Other known sources of projected emittance degradation are coherent synchrotron radiation (CSR), and space charge forces.…”