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Proceedings Paper

Small-signal gain for parabolic profile beams in free-electron lasers
Author(s): C. James Elliott
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Paper Abstract

Three new types of free electron lasers (FELs) that are being examined in new ranges of parameter design space are: compact systems, XUV systems, and high power devices. Shorter wiggler wavelengths, shorter or longer lasers, higher currents, and higher quality electron beams are a few of the trends in the FEL community. The primary predictor of FEL oscillation is the small signal gain. We present 3-D small-signal calculations for more realistic parabolic-profile electron beams in the limit of moderately wide to wide electron beams. This limit complements the thin electron beam limit and needs be included in any analytical approximation that encompasses all 3-D effects. The system of equations for the optical modes are of Hamiltonian form and are solved as the analytical eigenmodes of the stationary quantum mechanical harmonic oscillator. We show the complete solution to the initial value problem in the special case of a cold, resonant electron beam, including the damped modes heretofore neglected. From this we derive the asymptotic solution as a superposition of Hermite [square symmetry] or Laguerre (circular symmetry) modes. We give expressions for the mode size, the spatial growth rate, and injection fraction for the dominant mode.

Paper Details

Date Published: 1 December 1991
PDF: 7 pages
Proc. SPIE 1552, Short-Wavelength Radiation Sources, (1 December 1991); doi: 10.1117/12.50603
Show Author Affiliations
C. James Elliott, Los Alamos National Lab. (United States)

Published in SPIE Proceedings Vol. 1552:
Short-Wavelength Radiation Sources
Phillip Sprangle, Editor(s)

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