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

Fares, H. and Piovella, N. and Robb, G. R. M. (2018) The detrimental effect of spontaneous emission in quantum free electron lasers : a discrete Wigner model. Physics of Plasmas, 25 (1). 013111. ISSN 1070-664X

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    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.