Theoretical computation of the polarization characteristics of an X-ray Free-Electron Laser with planar undulator

TL;DR

This paper provides a theoretical analysis of the polarization suppression in X-ray Free-Electron Lasers with planar undulators, showing that vertical polarization components are significantly reduced compared to horizontal ones.

Contribution

It introduces an analytical model quantifying the suppression of vertical polarization in XFELs with planar undulators, considering resonance effects and steady state operation.

Findings

Vertical polarization is suppressed by at least a factor of   in power.

Resonance terms dominate, non-resonance terms are negligible.

Qualitative suppression effects are observable despite quantitative comparison challenges.

Abstract

We show that radiation pulses from an X-ray Free-Electron Laser (XFEL) with a planar undulator, which are mainly polarized in the horizontal direction, exhibit a suppression of the vertical polarization component of the power at least by a factor $\lambda_w^2/(4 \pi L_g)^2$, where $\lambda_w$ is the length of the undulator period and $L_g$ is the FEL field gain length. We illustrate this fact by examining the XFEL operation under the steady state assumption. In our calculations we considered only resonance terms: in fact, non resonance terms are suppressed by a factor $\lambda_w^3/(4 \pi L_g)^3$ and can be neglected. While finding a situation for making quantitative comparison between analytical and experimental results may not be straightforward, the qualitative aspects of the suppression of the vertical polarization rate at XFELs should be easy to observe. We remark that our exact results can potentially be useful to developers of new generation FEL codes for cross-checking their results.