Analytical treatment of the wakefields driven by transversely shaped beams in a planar slow-wave structure

TL;DR

This paper presents an analytical model demonstrating how transversely elliptical beams can effectively suppress transverse wakefields in planar structures, offering insights into beam shaping for improved accelerator performance.

Contribution

It introduces a simple analytical model that reveals the geometric basis of wakefield suppression by elliptical beams and derives scaling laws for wake potentials based on beam ellipticity.

Findings

Highly elliptical beams reduce transverse wakefields effectively.

Scaling laws relate beam ellipticity to wake potential amplitudes.

Using elliptical beams benefits wakefield acceleration by mitigating transverse forces.

Abstract

The suppression of transverse wakefield effects using transversely elliptical drive beams in a planar structure is studied with a simple analytical model that unveils the geometric nature of this phenomenon. By analyzing the suggested model we derive scaling laws for the amplitude of the longitudinal and transverse wake potentials as a function of the Gaussian beam ellipticity - $\sigma_x/a$. We explicitly show that in a wakefield accelerator application it is beneficial to use highly elliptical beams for mitigating transverse forces while maintaining the accelerating field. We consider two scaling strategies: 1) aperture scaling, where we keep a constant charge to have the same accelerating gradient as in a cylindrical structure and 2) charge scaling, where aperture is the same as in the cylindrical structure and charge is increased to match the gradient.