# Traveling wave method for simulating geometric beam coupling impedance of a beamscreen with pumping holes

## TL;DR

This paper introduces a traveling wave decomposition method to accurately simulate the broadband coupling impedance caused by pumping holes in accelerator vacuum chambers, especially for complex designs like HE-LHC and FCC-hh.

## Contribution

It presents a novel traveling wave-based approach combined with numerical solvers to improve impedance estimation over traditional methods.

## Key findings

- Traveling wave method shows higher sensitivity to small impedances.
- Compared with direct wakefield calculations, the new method offers improved accuracy.
- Applicable to complex chamber geometries like HE-LHC and FCC-hh.

## Abstract

In particle accelerators, pumping holes in a vacuum chamber can be a source of unwanted broadband coupling impedance, leading to beam instabilities. Analytical methods have been previously developed to estimate the impedance of holes in circular-like chambers e.g. the beamscreen of the Large Hadron Collider (LHC). More sophisticated chamber designs like that of the High Energy LHC (HE-LHC) and the Future Circular Collider (FCC-hh) call for a different way to calculate the impedance. We propose using decomposition of the wakefield into synchronous traveling waves and employing a numerical solver to find the impedance of each wave. This method is compared to the direct time domain wakefield calculation method and its greater sensitivity to small impedances is shown.