Quantum and classical phase-space dynamics of a free-electron laser

TL;DR

This paper explores the transition from quantum to classical phase-space dynamics in free-electron lasers, highlighting conditions where quantum effects influence classical behavior and their impact on FEL gain.

Contribution

It identifies the specific initial conditions under which quantum and classical FEL dynamics converge or diverge in phase space.

Findings

Quantum signatures are observable when initial momentum spread exceeds recoil.

Classical behavior emerges when many momentum levels are involved and spread is large.

Quantum effects can be washed out in averaged FEL quantities under certain conditions.

Abstract

In a quantum mechanical description of the free-electron laser (FEL) the electrons jump on discrete momentum ladders, while they follow continuous trajectories according to the classical description. In order to observe the transition from quantum to classical dynamics, it is not sufficient that many momentum levels are involved. Only if additionally the initial momentum spread of the electron beam is larger than the quantum mechanical recoil, caused by the emission and absorption of photons, the quantum dynamics in phase space resembles the classical one. Beyond these criteria, quantum signatures of averaged quantities like the FEL gain might be washed out.