On Free-Electron Laser Growing Modes and their Bandwidth

TL;DR

This paper provides an analytical understanding of free-electron laser modes, showing that typically only one mode grows for a bell-shaped electron energy distribution and deriving an expression for the laser's bandwidth.

Contribution

It analytically demonstrates the existence of a single growing mode in typical free-electron lasers and derives a formula for their amplification bandwidth.

Findings

Only one growing mode exists for typical bell-shaped energy distributions.

An analytical expression for the free-electron laser bandwidth is derived.

The results enhance understanding of mode competition and bandwidth in free-electron lasers.

Abstract

Free-electron lasers play an increasing role in science, from generating unique femtosecond X- ray pulses for single short recording of the protein structures to amplifying feeble interactions in advanced cooling systems for high-energy hadron colliders. While modern Free-electron laser codes can describe their amplification mechanism, a deep analytical understanding of the mechanism is of extreme importance for a number of applications. Mode competition, their growth rates and amplification bandwidth are among the most important parameters of a free-electron laser. A dispersion relation, which defines these important characteristics, can be solved analytically only for a very few simple cases. In this letter we show that for a typical bell-shape energy distribution in electron beam there is no more that one growing mode. We also derive an analytical expression which determines the bandwidth of the free-electron laser.