Analytical Formulae for the Loss Factors and Wakefields of a Rectangular Accelerating Structure

TL;DR

This paper derives analytical formulas for calculating loss factors and wakefields in rectangular accelerating structures, enabling better design and analysis for applications like flat beam acceleration in linear colliders.

Contribution

It provides the first explicit analytical expressions for loss factors and wakefields in rectangular structures, linking them to geometrical parameters.

Findings

Analytical formulas for loss factors are derived.

Relations between structure dimensions and wakefields are established.

Formulas applicable to single rectangular resonant cavities.

Abstract

Wakefields in a rectangular accelerating structure can be calculated in time domain by directly solving Maxwell's equations by a 3D code. In this paper, we will give analytical formulae to calculate the synchronous modes' loss factors. From these analytical formulae on can get the delta function wakefields. The relations between the loss factors (wakefields) and the structure geometrical dimensions are well established. These analytical expressions of loss factors can be used also in a single rectangular resonant cavity. It is shown that the potential application of a rectangular accelerating structure is to accelerate a flat beam in a linear collider.