Description of modulated beam dynamics

TL;DR

This paper develops a spectral formalism for analyzing the dynamics of modulated electron beams in linear beamlines, simplifying the study of schemes for X-ray free electron laser seeding.

Contribution

It introduces a spectral distribution function approach that reduces complex beam dynamics to linear transformations of spectral parameters, aiding analysis of FEL seeding schemes.

Findings

Spectral parameters transform linearly during beamline propagation.

The approach simplifies analysis of various FEL seeding schemes.

Bandwidths of output bunching are calculated for multiple schemes.

Abstract

General formalism for describing dynamics of modulated beams along linear beamlines is developed. We describe modulated beams with spectral distribution function which represents Fourier transform of the conventional beam distribution function in the 6-dimensional phase space. The introduced spectral distribution function is localized in some region of the spectral domain for nearly monochromatic modulations and it can be characterized with a small number of typical parameters which we choose to be the lowest order moments of the spectral distribution. We study evolution of modulated beams in linear beamlines and find that characteristic spectral parameters transform linearly. The developed approach significantly simplifies analysis of various schemes proposed for seeding X-ray free electron lasers. We use this approach to study several recently proposed schemes and find the bandwidth of the output bunching in each case.