Bounds on geometric wakefields in collimators and step transitions of arbitrary cross sections

TL;DR

This paper introduces a conformal mapping technique to analytically estimate bounds on wakefields in collimators and step transitions, aiding design and optimization of accelerator components.

Contribution

It presents a novel analytical method for bounding wake potentials, simplifying the analysis and optimization of accelerator beamline components.

Findings

Derived simple bounds for wake potentials in various geometries

Validated bounds against known formulas in example cases

Facilitates shape optimization of collimators and transitions

Abstract

We present the wakefield conformal mapping technique that can be readily applied to the analysis of the radiation generated by an ultra-relativistic particle in the step transition and a collimator. We derive simple analytical expressions for the lower and upper bounds of both longitudinal and transverse wake potentials. We test the derived expressions against well-known formulas in several representative examples. The proposed method can greatly simplify the optimization of collimating sections, as well as become a useful tool in the shape optimization problems.