Relativistic x-ray free-electron lasers in the quantum regime

Bengt Eliasson, Padma Shukla

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16 Citations (Scopus)
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We present a nonlinear theory for relativistic x-ray free-electron lasers in the quantum regime, using a collective Klein-Gordon (KG) equation (for relativistic electrons), which is coupled with the Maxwell-Poisson equations for the electromagnetic and electrostatic fields. In our model, an intense electromagnetic wave is used as a wiggler which interacts with a relativistic electron beam to produce coherent tunable radiation. The KG-Maxwell-Poisson model is used to derive a general nonlinear dispersion relation for parametric instabilities in three space dimensions, including an arbitrarily large amplitude electromagnetic wiggler field. The nonlinear dispersion relation reveals the importance of quantum recoil effects and oblique scattering of the radiation that can be tuned by varying the beam energy.
Original languageEnglish
Article number065401(R)
Number of pages5
JournalPhysical Review E
Issue number6
Publication statusPublished - 20 Jun 2012


  • x-ray
  • free electron laser
  • quantum
  • relativistic


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