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.

Highlights

  • An free-electron laser (FEL) is considered as a device that can be fully described within classical physics

  • An FEL is considered as a device that can be fully described within classical physics

  • We analyze the transition from quantum to classical in a low-gain FEL by contrasting the dynamics of an electron in phase space with the corresponding classical description

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Summary

INTRODUCTION

An FEL is considered as a device that can be fully described within classical physics. There exists a “quantum regime” [1,2,3] where quantum mechanics is mandatory for an accurate description of the FEL dynamics. We analyze the transition from quantum to classical in a low-gain FEL by contrasting the dynamics of an electron in phase space with the corresponding classical description. We find that the occurrence of quantum effects depends on the quantum mechanical recoil, caused by the absorption and emission of photons: A small recoil energy, compared to the coupling to the fields, and a small recoil momentum, compared to the initial momentum spread, are necessary to observe a classical evolution of the Wigner function. We study quantum corrections to the FEL gain

Historical overview
Wigner function
Quantum versus classical
Outline
EVOLUTION OF WIGNER FUNCTION
Longer times
Small-signal limit
CONCLUSIONS
Pendulum Hamiltonian
Laser field couples to electron current
Formulation with Wigner function
Structure of equation
First order
Connection to classical theory
Schrödinger equation and Mathieu functions
Findings
Full Text
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