Thermal effects on the linear gain in free-electron lasers

The authors develop a self-consistent formulation of the linear gain in both helical and planar wiggler configurations in the presence of an axial energy spread derived from a beam pitch-angle spread. Such a beam may be thought of as monoenergetic but with a non-vanishing emittance. The analysis includes collective Raman effects for both the helical and planar wiggler systems, and describes the gain at harmonics in the case of a planar wiggler. General dispersion equations are derived, and solved numerically, for each wiggler configuration which includes a general thermal function which describes the effect of the pitch-angle spread