High-Gain FEL Theory, Introduction

  • An HeEmail author
  • Lingyun Yang
  • Lihua Yu
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This chapter provides a detailed introduction to the 1D theory of high-gain free electron laser (FEL) and a brief overview of the 3D scaling function for FEL gain. For 1D theory, we start from the resonance condition and energy exchange between electron and radiation field. Their dynamics are then derived as the coupled Maxwell-Vlasov equations using a fluid model. In solving these coupled equations, we introduce some important FEL parameters and concepts, such as the dispersion relation, the FEL parameter ρ, the power gain length L G 1 D , the saturation power P s , and the undulator saturation length L s . We also discuss two operating modes of FEL, the amplifier and SASE (self-amplified spontaneous emission), as two typical cases of the initial value problem of the coupled Maxwell-Vlasov equations. We also discuss the radiation power, intensity fluctuations, bandwidth, and coherent length for SASE. In the last section, without further derivation, we briefly mention some results from the 3D FEL theory, e.g., the scaled power gain function G, the scaling parameter ρ and D, the energy spread, and the gain length calculation with scaling function. We assume the readers are familiar with classical mechanics and electrodynamics in the graduate level. Knowledge of integral transform and calculus of residues from mathematical physics are helpful but not essential.


High-gain free electron laser 1D theory Coupled Maxwell-Vlasov equations The dispersion relation FEL parameter The power gain length The saturation power The saturation length Amplifier SASE Radiation power Intensity fluctuations Bandwidth Coherent length 3D FEL theory The scaled power gain function The scaling parameter 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Photon Science DivisionBrookhaven National LaboratoryUptonUSA

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