# Obliquely Incident Laser and Electron Beam Interaction in an Undulator

## TL;DR

This paper investigates how oblique laser-electron interactions in an undulator affect beam modulation, revealing energy and angular effects that differ from normal incidence, with implications for free-electron laser applications.

## Contribution

It provides a systematic analysis of oblique laser-electron interactions in undulators, highlighting their impact on beam modulation and potential applications in laser-electron manipulation.

## Key findings

- Oblique incidence causes energy and angular modulations on the electron beam.
- Oblique interaction reduces the bunching factors of HGHG and EEHG.
- Multi-dimensional modulation techniques may enhance laser-electron manipulation.

## Abstract

The angular drift of a laser beam is of particular concern in applications such as seeded free-electron lasers. A systematical study of the obliquely incident laser and electron beam interaction in an undulator is presented in this paper. Theoretical analysis and numerical simulations demonstrate that the interaction would imprint energy and angular modulations on the electron beam simultaneously. Compared with the normally incident pattern, the obliquely incident laser-electron interaction leads to reductions in the bunching factors of HGHG and EEHG. In the meanwhile, proactive applications of this multi-dimensional modulation technique may bring vitality to the field of laser-electron manipulation