The detrimental effect of spontaneous emission in quantum free electron lasers: a discrete Wigner model

H. Fares, N. Piovella, G. R. M. Robb

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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 languageEnglish
Article number013111
Number of pages5
JournalPhysics of Plasmas
Issue number1
Publication statusPublished - 16 Jan 2018


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

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