The effects of betatron motion on the preservation of FEL microbunching

TL;DR

This paper investigates how betatron motion affects the preservation of microbunching in X-ray FELs, providing analytical formulas, numerical validation, and simulation comparisons to improve understanding of polarization control schemes.

Contribution

It develops an analytical expression for debunching due to betatron motion in a FODO lattice and validates it with numerical studies and Genesis simulations.

Findings

Analytical formula accurately predicts microbunching debunching.

Numerical results confirm the formula's validity beyond the asymptote.

Simulation comparisons support the analytical and numerical findings.

Abstract

In some options for circular polarization control at X-ray FELs, a helical radiator is placed a few ten meters distance behind the baseline undulator. If the microbunch structure induced in the baseline (planar) undulator can be preserved, intense coherent radiation is emitted in the helical radiator. The effects of betatron motion on the preservation of micro bunching in such in-line schemes should be accounting for. In this paper we present a comprehensive study of these effects. It is shown that one can work out an analytical expression for the debunching of an electron beam moving in a FODO lattice, strictly valid in the asymptote for a FODO cell much shorter than the betatron function. Further on, numerical studies can be used to demonstrate that the validity of such analytical expression goes beyond the above-mentioned asymptote, and can be used in much more a general context. Finally, a comparison with Genesis simulations is given.