Calculation of wakefields in 2D rectangular structures

TL;DR

This paper introduces a new numerical method for calculating electromagnetic wakefields in 2D rectangular vacuum chamber structures, enabling efficient and accurate analysis of wake potentials with variable height cross-sections.

Contribution

A novel Fourier-based approach and the ECHO(2D) code for computing wakefields in rectangular structures with variable height are developed and validated.

Findings

The new method provides accurate wakefield calculations with moderate computational resources.

Numerical examples demonstrate the effectiveness of the approach.

The approach is comparable in efficiency to methods for rotationally symmetric structures.

Abstract

We consider the calculation of electromagnetic fields generated by an electron bunch passing through a vacuum chamber structure that, in general, consists of an entry pipe, followed by some kind of transition or cavity, and ending in an exit pipe. We limit our study to structures having rectangular cross-section, where the height can vary as function of longitudinal coordinate but the width and side walls remain fixed. For such structures, we derive a Fourier representation of the wake potentials through one-dimensional functions. A new numerical approach for calculating the wakes in such structures is proposed and implemented in the computer code ECHO(2D). The computation resource requirements for this approach are moderate and comparable to those for finding the wakes in 2D rotationally symmetric structures. Numerical examples obtained with the new numerical code are presented.