Small-signal gain for parabolic profile beams in free-electron lasers

C. James Elliott

doi:10.1117/12.50603

1 December 1991 Small-signal gain for parabolic profile beams in free-electron lasers

C. James Elliott

Proceedings Volume 1552, Short-Wavelength Radiation Sources; (1991) https://doi.org/10.1117/12.50603
Event: San Diego, '91, 1991, San Diego, CA, United States

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.

Citation Download Citation

C. James Elliott "Small-signal gain for parabolic profile beams in free-electron lasers", Proc. SPIE 1552, Short-Wavelength Radiation Sources, (1 December 1991); https://doi.org/10.1117/12.50603

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KEYWORDS

Electron beams

Free electron lasers

Diffraction

Transform theory

Oscillators

Superposition

Bessel functions

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