Abstract
It has been well known that the resonant interaction of an ultrarelativistic electron beam and the radiation field in the single-pass high-gain free electron laser (FEL) amplifier leads to the optical gain guiding. The transverse Laplacian term of the slowly varying wave equation in the linear regime can be approximated as a constant detuning parameter, i.e., |∇⊥2|∼kR/zR where kR is the resonant wave number and zR is the Rayleigh range of the laser. In the post-saturation regime, the radiation power begins to oscillate about an equilibrium for the untapered case while continues to grow by undulator tapering. Moreover, in this regime the gain guiding decreases and the simple constant detune is no longer valid. In this paper we study the single-pass high-gain FEL performance in the post-saturation regime with inclusion of diffraction effect and undulator tapering. Our analysis relies upon two constants of motion, one from the energy conservation and the other from the adiabatic invariant of the action variable. By constructing a two-dimensional axisymmetric wave equation and the coupled one-dimensional electron dynamical equations, the performance of a tapered FEL in the postsaturation regime can be analyzed, including the fundamental mode profile, the power efficiency and the scaled energy spread. We begin the analytical investigation with two different axisymmetric electron beam profiles, the uniform and bounded parabolic ones. It is found that the tapered FEL power efficiency can be smaller but close to the taper ratio provided the resonant phase remains constant and the beam-wave is properly matched. Such a tapered efficiency is nearly independent of transverse electron beam size before significant electron detrapping occurs. This is essentially different from the untapered case, where the power extraction efficiency is around the essential FEL gain bandwidth (or ρ, the Pierce or FEL parameter) and depends on the beam size. It is also found that the power enhancement due to undulator tapering is attributed more by the field increase outside the transverse electron beam than that inside the transverse electron beam. Several scaling properties on the taper ratio and the transverse electron beam size are also discussed in this paper.3 MoreReceived 29 January 2018DOI:https://doi.org/10.1103/PhysRevAccelBeams.21.060702Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsSynchrotron radiation & free-electron lasersAccelerators & Beams
Highlights
The requirements will correspond to an output laser consisting of 1013 to 1014 1-keV photons within a several tens of fs pulse duration, i.e., the target output power of 1 TW or higher
II A we briefly review the one-dimensional (1-D) free electron laser (FEL) dynamics and the associated two constants of motion that will be employed in our subsequent analysis
By taking advantage of two integrals of the motion, one from the energy conservation and the other from the action variable based on the adiabatic invariance of the undulator tapering, we have studied two cases that allow analytical solutions of the radiation field: the uniform and the bounded parabolic transverse electron beam profiles
Summary
Generating an intense high-power x-ray free electron laser (FEL) can be of great interest, e.g., the peak power at the level of terawatt (TW) or sub-TW, since such power level of. The resonant interaction of ultrarelativistic electron beam and radiation field in the single-pass high-gain exponential regime of the FEL amplifier has been intensively studied, for example, the longitudinal microbunching dynamics associated with the exponential growth of the dominant modes and the SASE FEL statistical properties The transverse Laplacian term in the slowly varying wave equation in the exponential-growth regime can be well approximated as a constant detuning parameter, i.e., j∇2⊥j ∼ kR=zR where kR is the resonant wave number and zR is the corresponding Rayleigh range of the laser This diffractive effect becomes more important for singlepass FELs at shorter wavelengths with ever-increasing undulator lengths, because the corresponding Rayleigh length can usually be only about 10–20 m and the shortwavelength radiation beam is difficult to confine by a waveguide structure.
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