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Title: Single-pass high-gain tapered free-electron laser with transverse diffraction in the postsaturation regime

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., |∇$$2\atop{⟂}$$ |~ k R/z R where k R is the resonant wave number and z R 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 Moreover, in this regime the gain guiding decreases and the simple constant detune is no longer valid.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. In conclusion 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.

Authors:
; ; ; ;
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1457579
Alternate Identifier(s):
OSTI ID: 1461480
Grant/Contract Number:  
AC02-76SF00515; FWP-2013-SLAC-100164
Resource Type:
Journal Article: Published Article
Journal Name:
Physical Review Accelerators and Beams
Additional Journal Information:
Journal Name: Physical Review Accelerators and Beams Journal Volume: 21 Journal Issue: 6; Journal ID: ISSN 2469-9888
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS

Citation Formats

Tsai, Cheng-Ying, Wu, Juhao, Yang, Chuan, Yoon, Moohyun, and Zhou, Guanqun. Single-pass high-gain tapered free-electron laser with transverse diffraction in the postsaturation regime. United States: N. p., 2018. Web. doi:10.1103/PhysRevAccelBeams.21.060702.
Tsai, Cheng-Ying, Wu, Juhao, Yang, Chuan, Yoon, Moohyun, & Zhou, Guanqun. Single-pass high-gain tapered free-electron laser with transverse diffraction in the postsaturation regime. United States. doi:10.1103/PhysRevAccelBeams.21.060702.
Tsai, Cheng-Ying, Wu, Juhao, Yang, Chuan, Yoon, Moohyun, and Zhou, Guanqun. Thu . "Single-pass high-gain tapered free-electron laser with transverse diffraction in the postsaturation regime". United States. doi:10.1103/PhysRevAccelBeams.21.060702.
@article{osti_1457579,
title = {Single-pass high-gain tapered free-electron laser with transverse diffraction in the postsaturation regime},
author = {Tsai, Cheng-Ying and Wu, Juhao and Yang, Chuan and Yoon, Moohyun and Zhou, Guanqun},
abstractNote = {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., |∇$2\atop{⟂}$ |~ 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. In conclusion 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.},
doi = {10.1103/PhysRevAccelBeams.21.060702},
journal = {Physical Review Accelerators and Beams},
issn = {2469-9888},
number = 6,
volume = 21,
place = {United States},
year = {2018},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevAccelBeams.21.060702

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