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Title: Exact and variational calculations of eigenmodes for three-dimensional free electron laser interaction with a warm electron beam

Abstract

I present an exact calculation of free-electron-laser (FEL) eigenmodes (fundamental as well as higher order modes) in the exponential-gain regime. These eigenmodes specify transverse profiles and exponential growth rates of the laser field, and they are self-consistent solutions of the coupled Maxwell-Vlasov equations describing the FEL interaction taking into account the effects due to energy spread, emittance and betatron oscillations of the electron beam, and diffraction and guiding of the laser field. The unperturbed electron distribution is assumed to be of Gaussian shape in four dimensional transverse phase space and in the energy variable, but uniform in longitudinal coordinate. The focusing of the electron beam is assumed to be matched to the natural wiggler focusing in both transverse planes. With these assumptions the eigenvalue problem can be reduced to a numerically manageable integral equation and solved exactly with a kernel iteration method. An approximate, but more efficient solution of the integral equation is also obtained for the fundamental mode by a variational technique, which is shown to agree well with the exact results. Furthermore, I present a handy formula, obtained from interpolating the numerical results, for a quick calculation of FEL exponential growth rate. Comparisons with simulation code TDA willmore » also be presented. Application of these solutions to the design and multi-dimensional parameter space optimization for an X-ray free electron laser driven by SLAC linac will be demonstrated. In addition, a rigorous analysis of transverse mode degeneracy and hence the transverse coherence of the X-ray FEL will be presented based on the exact solutions of the higher order guided modes.« less

Authors:
 [1]
  1. Lawrence Berkeley Lab., CA (United States)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
OSTI Identifier:
238624
Report Number(s):
BNL-61982-Absts.; CONF-9508156-Absts.
ON: DE96002729; TRN: 96:013113
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Conference
Resource Relation:
Conference: 17. international free electron laser conference, New York, NY (United States), 21-25 Aug 1995; Other Information: PBD: [1995]; Related Information: Is Part Of 17th international free electron laser conference and 2nd international FEL users` workshop. Program and abstracts; PB: 300 p.
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; 43 PARTICLE ACCELERATORS; FREE ELECTRON LASERS; PHOTON-ELECTRON COLLISIONS; CALCULATION METHODS; THREE-DIMENSIONAL CALCULATIONS; OSCILLATION MODES; ELECTRON BEAMS; WIGGLER MAGNETS; VARIATIONAL METHODS; X-RAY LASERS

Citation Formats

Xie, M. Exact and variational calculations of eigenmodes for three-dimensional free electron laser interaction with a warm electron beam. United States: N. p., 1995. Web.
Xie, M. Exact and variational calculations of eigenmodes for three-dimensional free electron laser interaction with a warm electron beam. United States.
Xie, M. 1995. "Exact and variational calculations of eigenmodes for three-dimensional free electron laser interaction with a warm electron beam". United States. https://www.osti.gov/servlets/purl/238624.
@article{osti_238624,
title = {Exact and variational calculations of eigenmodes for three-dimensional free electron laser interaction with a warm electron beam},
author = {Xie, M},
abstractNote = {I present an exact calculation of free-electron-laser (FEL) eigenmodes (fundamental as well as higher order modes) in the exponential-gain regime. These eigenmodes specify transverse profiles and exponential growth rates of the laser field, and they are self-consistent solutions of the coupled Maxwell-Vlasov equations describing the FEL interaction taking into account the effects due to energy spread, emittance and betatron oscillations of the electron beam, and diffraction and guiding of the laser field. The unperturbed electron distribution is assumed to be of Gaussian shape in four dimensional transverse phase space and in the energy variable, but uniform in longitudinal coordinate. The focusing of the electron beam is assumed to be matched to the natural wiggler focusing in both transverse planes. With these assumptions the eigenvalue problem can be reduced to a numerically manageable integral equation and solved exactly with a kernel iteration method. An approximate, but more efficient solution of the integral equation is also obtained for the fundamental mode by a variational technique, which is shown to agree well with the exact results. Furthermore, I present a handy formula, obtained from interpolating the numerical results, for a quick calculation of FEL exponential growth rate. Comparisons with simulation code TDA will also be presented. Application of these solutions to the design and multi-dimensional parameter space optimization for an X-ray free electron laser driven by SLAC linac will be demonstrated. In addition, a rigorous analysis of transverse mode degeneracy and hence the transverse coherence of the X-ray FEL will be presented based on the exact solutions of the higher order guided modes.},
doi = {},
url = {https://www.osti.gov/biblio/238624}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1995},
month = {12}
}

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