High Frequency Impedances in European XFEL

TL;DR

This paper estimates high frequency impedances of the European XFEL vacuum chamber transitions using optical approximation, providing analytical formulas and validating them against numerical solutions of Maxwell's equations.

Contribution

It introduces analytical expressions for high frequency impedances of XFEL vacuum chambers and compares them with numerical solutions, enhancing impedance estimation methods.

Findings

Analytical formulas for longitudinal impedances derived.

Closed-form expressions for transverse impedances provided.

Good agreement between analytical and numerical results achieved.

Abstract

The method of the optical approximation is used to estimate the high frequency impedances of different vacuum chamber transitions of the European XFEL beam line. The approximations of the longitudinal impedances are obtained in terms of simple one-dimensional integrals. The transverse impedances are written in analytical closed form. The analytical results are compared with the results obtained by numerical solution of Maxwell's equations.