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Alamos amplifier amplitude angle average axial axis beam energy beam quality betatron bunch curvature devices diffraction dimensionless effects efficiency electric field electron beam electron energy Electron Laser electron phase electron pulse emittance energy spread experiments FELs focusing free-electron laser frequency gain medium harmonic helical high gain IEEE Instr interaction klystron Kramers-Kronig relations Lett light linac linear longitudinal Madey magnetic field Methods in Phys micropulse mode structure modulation Newnam Nucl operation optical beam optical field optical mode optical pulse optical wave optical wavelength outcoupling parameters pass peak current phase shift phase space phase velocity photon propagation Quantum Electronics radius Rayleigh range refractive guiding regime resonator rf linacs saturation short wavelength shown in Figure sideband sideband instability simulation slippage spontaneous emission Stanford storage ring synchrotron periods transverse mode typically UCSB undulator length undulator period W. B. Colson wave equation waveguide wavelength wiggler