## Abstract

We study the spontaneous emission in high-gain free-electron lasers operating in the quantum regime and its detrimental effect on coherent emission. A quantum model describing the coherent and spontaneous emission in free electron lasers has been recently proposed and investigated [G. R. M. Robb and R. Bonifacio, Phys. Plasmas 19, 073101 (2012)]. The model is based on a Wigner distribution describing the electron beam dynamics, coupled to Maxwell equations for the emitted radiation field. Here, we rephrase the model in a more rigorous way, considering a discrete Wigner distribution defined for a periodic space coordinate for which the electron momentum is discrete. From its numerical solution, we find good agreement with the approximate continuous model. In the quantum regime of the free-electron laser, we obtain a simple density matrix equation for two momentum states, where the role of the spontaneous emission has a clear interpretation in terms of coherence decay and population transfer.

Original language | English |
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Article number | 013111 |

Number of pages | 5 |

Journal | Physics of Plasmas |

Volume | 25 |

Issue number | 1 |

DOIs | |

Publication status | Published - 16 Jan 2018 |

## Keywords

- laser theory
- free
- Maxwell equations
- plasma physics
- synchrotron radiation