Modulated Electron Bunch with Amplitude Front Tilt in an Undulator

TL;DR

This paper investigates how a modulated electron bunch with amplitude front tilt affects the spatiotemporal properties of X-ray pulses in an undulator, extending previous steady-state analysis to time-dependent SASE mode.

Contribution

It introduces a detailed analysis of spatiotemporal distortions caused by electron bunch front tilt in SASE mode, providing exact results applicable to XFEL simulations.

Findings

Bunch front tilt induces pulse front tilt and angular dispersion.

Spatiotemporal coupling arises naturally from bunch deflection.

Results can help improve XFEL simulation accuracy.

Abstract

In a previous paper we discussed the physics of a microbunched electron beam kicked by the dipole field of a corrector magnet by describing the kinematics of coherent undulator radiation after the kick. We demonstrated that the effect of aberration of light supplies the basis for understanding phenomena like the deflection of coherent undulator radiation by a dipole magnet. We illustrated this fact by examining the operation of an XFEL under the steady state assumption, that is a harmonic time dependence. We argued that in this particular case the microbunch front tilt has no objective meaning; in other words, there is no experiment that can discriminate whether an electron beam is endowed with a microbunch front tilt of not. In this paper we extend our considerations to time-dependent phenomena related with a finite electron bunch duration, or SASE mode of operation. We focus our attention on the spatiotemporal distortions of an X-ray pulse. Spatiotemporal coupling arises naturally in coherent undulator radiation behind the kick, because the deflection process involves the introduction of a tilt of the bunch profile. This tilt of the bunch profile leads to radiation pulse front tilt, which is equivalent to angular dispersion of the output radiation. We remark that our exact results can potentially be useful to developers of new generation XFEL codes for cross-checking their results.