A unified theory of magnetic bremsstrahlung, electrostatic bremsstrahlung, Compton-Raman scattering, and Cerenkov-Smith-Purcell free-electron lasers

Abstract

This paper discusses in a comparative way the main operating parameters of various free-electron lasers (FEL's), providing a useful tool for laser design and a comparative evaluation of the various lasers. We show that the various kinds of FEL's satisfy the same gain-dispersion relation and differ only in a single coupling parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> . The different gain regimes which are common to all FEL's are delineated. We find the small signal gain in all the gain regimes (warm and cold beam, low- or high-gain, single electron, collective or strong coupling interaction). The laser gain parameter, radiation extraction efficiency, maximum power generation, and spectral width are given and compared in the various kinds of FEL's and gain regimes. The maximum power generation of all FEL's (except Compton-Raman scattering) is shown to be limited by an interaction region width parameter. This parameter and, consequently, the laser power are larger in the highly relativistic limit by a factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim \gamma_{0}</tex> in all bremsstrahlung FEL's, in comparison to Cerenkov-Smith-Purcell FEL's. Some expressions which were derived earlier for the magnetic bremsstrahlung FEL, like the expression for gain in the low-gain regime with the space charge effect correction and the low-gain expression for efficiency, are shown to be special cases of more general expressions.