Threedimensional theory of the smallsignal highgain freeelectron laser including betatron oscillations
Abstract
We have developed a threedimensional freeelectron laser (FEL) theory in the smallsignal highgain regime based upon the MaxwellVlasov equations including the effects of the energy spread, the emittance, and the betatron oscillations of the electron beam. The radiation field is expressed in terms of the Green's function of the inhomogeneous wave equation and the distribution function of the electron beam. The distribution function is expanded in terms of a set of orthogonal functions determined by the unperturbed electron distributions. The coupled MaxwellVlasov equations are then reduced to a matrix equation, from which a dispersion relation for the eigenvalues is derived. The growth rate for the fundamental mode can be obtained for any initial beam distribution including the hollowbeam, the waterbag, and the Gaussian distribution. Comparisons of our numerical solutions with simulation results and with other analytical approaches show good agreements except for the onedimensional limit. We present a handy interpolating formula for the FEL gain of a Gaussian beam, as a function of the scaled parameters, that can be used for a quick estimate of the gain. The present theory can be applied to the beamconditioning case by a few modifications.
 Authors:

 Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (United States)
 Publication Date:
 OSTI Identifier:
 7010632
 DOE Contract Number:
 AC0376SF00098
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review A. General Physics; (United States)
 Additional Journal Information:
 Journal Volume: 46:10; Journal ID: ISSN 10502947
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; FREE ELECTRON LASERS; BOLTZMANNVLASOV EQUATION; BEAM EMITTANCE; BETATRON OSCILLATIONS; DISTRIBUTION FUNCTIONS; ELECTRONS; GAIN; SERIES EXPANSION; THREEDIMENSIONAL CALCULATIONS; AMPLIFICATION; BEAM DYNAMICS; DIFFERENTIAL EQUATIONS; ELEMENTARY PARTICLES; EQUATIONS; FERMIONS; FUNCTIONS; LASERS; LEPTONS; OSCILLATIONS; PARTIAL DIFFERENTIAL EQUATIONS; 426002*  Engineering Lasers & Masers (1990)
Citation Formats
Chin, Y H, Kim, K, and Xie, M. Threedimensional theory of the smallsignal highgain freeelectron laser including betatron oscillations. United States: N. p., 1992.
Web. doi:10.1103/PhysRevA.46.6662.
Chin, Y H, Kim, K, & Xie, M. Threedimensional theory of the smallsignal highgain freeelectron laser including betatron oscillations. United States. https://doi.org/10.1103/PhysRevA.46.6662
Chin, Y H, Kim, K, and Xie, M. 1992.
"Threedimensional theory of the smallsignal highgain freeelectron laser including betatron oscillations". United States. https://doi.org/10.1103/PhysRevA.46.6662.
@article{osti_7010632,
title = {Threedimensional theory of the smallsignal highgain freeelectron laser including betatron oscillations},
author = {Chin, Y H and Kim, K and Xie, M},
abstractNote = {We have developed a threedimensional freeelectron laser (FEL) theory in the smallsignal highgain regime based upon the MaxwellVlasov equations including the effects of the energy spread, the emittance, and the betatron oscillations of the electron beam. The radiation field is expressed in terms of the Green's function of the inhomogeneous wave equation and the distribution function of the electron beam. The distribution function is expanded in terms of a set of orthogonal functions determined by the unperturbed electron distributions. The coupled MaxwellVlasov equations are then reduced to a matrix equation, from which a dispersion relation for the eigenvalues is derived. The growth rate for the fundamental mode can be obtained for any initial beam distribution including the hollowbeam, the waterbag, and the Gaussian distribution. Comparisons of our numerical solutions with simulation results and with other analytical approaches show good agreements except for the onedimensional limit. We present a handy interpolating formula for the FEL gain of a Gaussian beam, as a function of the scaled parameters, that can be used for a quick estimate of the gain. The present theory can be applied to the beamconditioning case by a few modifications.},
doi = {10.1103/PhysRevA.46.6662},
url = {https://www.osti.gov/biblio/7010632},
journal = {Physical Review A. General Physics; (United States)},
issn = {10502947},
number = ,
volume = 46:10,
place = {United States},
year = {1992},
month = {11}
}