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Title: Sideband instability analysis based on a one-dimensional high-gain free electron laser model

Abstract

When an untapered high-gain free electron laser (FEL) reaches saturation, the exponential growth ceases and the radiation power starts to oscillate about an equilibrium. The FEL radiation power or efficiency can be increased by undulator tapering. For a high-gain tapered FEL, although the power is enhanced after the first saturation, it is known that there is a so-called second saturation where the FEL power growth stops even with a tapered undulator system. The sideband instability is one of the primary reasons leading to this second saturation. In this paper, we provide a quantitative analysis on how the gradient of undulator tapering can mitigate the sideband growth. The study is carried out semianalytically and compared with one-dimensional numerical simulations. The physical parameters are taken from Linac Coherent Light Source-like electron bunch and undulator systems. The sideband field gain and the evolution of the radiation spectra for different gradients of undulator tapering are examined. It is found that a strong undulator tapering (~10 % ) provides effective suppression of the sideband instability in the postsaturation regime.

Authors:
 [1];  [1];  [1];  [1];  [1]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1416368
Grant/Contract Number:
AC02-76SF00515; FWP-2013-SLAC-100164
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review Accelerators and Beams
Additional Journal Information:
Journal Volume: 20; Journal Issue: 12; 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. Sideband instability analysis based on a one-dimensional high-gain free electron laser model. United States: N. p., 2017. Web. doi:10.1103/physrevaccelbeams.20.120702.
Tsai, Cheng-Ying, Wu, Juhao, Yang, Chuan, Yoon, Moohyun, & Zhou, Guanqun. Sideband instability analysis based on a one-dimensional high-gain free electron laser model. United States. doi:10.1103/physrevaccelbeams.20.120702.
Tsai, Cheng-Ying, Wu, Juhao, Yang, Chuan, Yoon, Moohyun, and Zhou, Guanqun. 2017. "Sideband instability analysis based on a one-dimensional high-gain free electron laser model". United States. doi:10.1103/physrevaccelbeams.20.120702. https://www.osti.gov/servlets/purl/1416368.
@article{osti_1416368,
title = {Sideband instability analysis based on a one-dimensional high-gain free electron laser model},
author = {Tsai, Cheng-Ying and Wu, Juhao and Yang, Chuan and Yoon, Moohyun and Zhou, Guanqun},
abstractNote = {When an untapered high-gain free electron laser (FEL) reaches saturation, the exponential growth ceases and the radiation power starts to oscillate about an equilibrium. The FEL radiation power or efficiency can be increased by undulator tapering. For a high-gain tapered FEL, although the power is enhanced after the first saturation, it is known that there is a so-called second saturation where the FEL power growth stops even with a tapered undulator system. The sideband instability is one of the primary reasons leading to this second saturation. In this paper, we provide a quantitative analysis on how the gradient of undulator tapering can mitigate the sideband growth. The study is carried out semianalytically and compared with one-dimensional numerical simulations. The physical parameters are taken from Linac Coherent Light Source-like electron bunch and undulator systems. The sideband field gain and the evolution of the radiation spectra for different gradients of undulator tapering are examined. It is found that a strong undulator tapering (~10 % ) provides effective suppression of the sideband instability in the postsaturation regime.},
doi = {10.1103/physrevaccelbeams.20.120702},
journal = {Physical Review Accelerators and Beams},
number = 12,
volume = 20,
place = {United States},
year = 2017,
month =
}

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  • The nonlinear evolution of a helical wiggler, free-electron laser is investigated within the framework of a macroclump model for the trapped electrons. The model describes the nonlinear evolution of a right-circularly polarized electromagnetic wave with frequency {omega}{sub {ital s}} and wave number {ital k}{sub {ital s}}, and slowly varying amplitude {ital {cflx a}}{sub {ital s}}({ital z},{ital t}) and phase {delta}{sub {ital s}}({ital z},{ital t}) (eikonal approximation). The model further assumes that the trapped electrons can be treated as tightly bunched macroclumps that interact coherently with the radiation field. The analysis is carried out in the ponderomotive frame, which leads tomore » a substantial simplification in both the analytical and numerical studies. As a first application, the nonlinear evolution of the primary signal is examined when {partial derivative}/{partial derivative}{ital l}{prime}=0 (no spatial variation of the wave amplitude and phase). The evolution equations are reduced to quadrature, and the maximum excursion of the wave amplitude {ital {cflx a}}{sub {ital s},max} is calculated analytically. Subsequently, the nonlinear evolution of the sideband instability is investigated, making use of the equations describing the self-consistent evolution of the wave amplitude {ital {cflx a}}{sub {ital s}} and phase {delta}{sub {ital s}}, which vary slowly with both space and time, together with the macroclump orbit equation.« less
  • Use is made of the single-particle orbit equations together with Maxwell's equations and appropriate statistical averages to investigate detailed properties of the sideband instability for a helical-wiggler free-electron laser with wiggler wavelength lambda/sub 0/ = 2..pi../k/sub 0/ = const and normalized wiggler amplitude a/sub w/ = eB-italic-circumflex/sub w//mc/sup 2/k/sub 0/ = const. The model describes the nonlinear evolution of a right-circularly polarized primary electromagnetic wave with frequency ..omega../sub s/, wavenumber k/sub s/, and slowly varying amplitude a-italic-circumflex/sub s/(z,t) and phase delta/sub s/(z,t) (eikonal approximation). The orbit and wave equations are analyzed in the ponderomotive frame (''primed'' variables) moving with velocitymore » v/sub p/ = ..omega../sub s//(k/sub s/+k/sub 0/) relative to the laboratory. Detailed properties of the sideband instability are investigated for small-amplitude perturbations about a quasisteady equilibrium state characterized by a-italic-circumflex/sup 0//sub s/ = const (independent of z' and t'). Two cases are treated. The first case assumes constant equilibrium wave phase delta/sup 0//sub s/ = const, which requires (for self-consistency) both untrapped- and trapped-electron populations satisfying = 0.« less
  • A kinetic formalism based on the Vlasov-Maxwell equations is used to investigate properties of the sideband instability for a tenuous, relativistic electron beam propagating through a constant-amplitude helical wiggler magnetic field (wavelength lambda/sub 0/ -- 2..pi../k/sub 0/ and normalized amplitude a/sub w/ -- eB-circumflex/sub w//mc/sup 2/k/sub 0/). The analysis is carried out for perturbations about an equilibrium Bernstein-Greene-Kruskal state in which the distribution of beam electrons G/sub s/(..gamma..') and the wiggler magnetic field coexist in quasisteady equilibrium with a finite-amplitude, circularly polarized, primary electromagnetic wave (..omega../sub s/,k/sub s/) with normalized amplitude a/sub s/ -- eB-circumflex/sub s//mc/sup 2/k/sub s/ and constantmore » equilibrium wave phase.« less
  • Here, the use of a transverse gradient undulator (TGU) is viewed as an attractive option for free-electron lasers (FELs) driven by beams with a large energy spread. By suitably dispersing the electron beam and tilting the undulator poles, the energy spread effect can be substantially mitigated. However, adding the dispersion typically leads to electron beams with large aspect ratios. As a result, the presence of higher-order modes in the FEL radiation can become significant. To investigate this effect, we study the eigenmode properties of a TGU-based, high-gain FEL, using both an analytically-solvable model and a variational technique. Our analysis, whichmore » includes the fundamental and the higher-order FEL eigenmodes, can provide an estimate of the mode content for the output radiation. This formalism also enables us to study the trade-off between FEL gain and transverse coherence. Numerical results are presented for a representative soft X-ray, TGU FEL example.« less