Small signal gain based on analytic models of thin intense electron beams
Abstract
The freeelectron laser theory of the effective energy distribution and the small signal gain for a thin electron beam was developed. The assumption of thinness allows us to treat various transverse locations and electron beam trajectory angles as introducing phase shifts that have the same effect as those introduced by a change in energy of the electron. We have extended these ideas in five important ways. The first is the ability to treat electron beams with three different classes of matching or symmetry conditions: (1) electron beams with separate betatron matching in each plane; (2) those with aspect ratio matching; and (3) crossed matched beams. Manifestations of these symmetries include elliptical cross sections and electron beams that have modulated spatial profiles. Second, two emittance parameters for the electron beam are shown to consolidate into a single parameter that describes most of the energy variation of the effective energy distributions. Third, these calculations extend to energy distributions, angular distributions, and spatial distributions that all follow Gaussian profiles. Fourth, this model incorporates the description of the incident Gaussian optical beam and the above electron beam dynamics into a single influence function kernal. Fifth, threedimensional profiles of the optical fields are computed. In this work the parameters of the incident optical beam are included. The resulting transverse dependence of the fields may be characterized by an optical beam radius. This optical beam width starts out large compared to the thin electron beam and then, in the example given, contracts to a size that becomes so small that the thin beam assumption is violated.
 Publication:

Presented at the 12th International Free Electron Laser Conference
 Pub Date:
 November 1990
 Bibcode:
 1990ifel.confQ..17E
 Keywords:

 Electron Beams;
 Energy Distribution;
 Free Electron Lasers;
 Laser Outputs;
 Mathematical Models;
 Power Gain;
 Angular Distribution;
 Aspect Ratio;
 Betatrons;
 Normal Density Functions;
 Spatial Distribution;
 Trajectories;
 Electronics and Electrical Engineering