A thick beam free electron laser
Abstract
A 3D theory is presented for a free electron laser that employs an electron beam of a thickness comparable to both the wiggler wavelength and the waveguide radius. The timeindependent and the linearized timedependent cold fluid and Maxwell equations are expanded in a small parameter, which is the ratio of the perpendicular to parallel electron momentum. The stability problem is reduced to a nonlinear eigenvalue problem of a fourthorder system of linear ordinary differential equations. A perturbation method is justified and used to solve these equations. A dispersion relation is derived which results from the solvability condition for the firstorder equations in the perturbation. The orders of magnitude of the beam density and wave frequency, for which the growth rate of the instability scales as in the strongpump regime of the 1D analysis, are determined. An equation, which the beam energy radial profile has to satisfy, is also derived.
 Publication:

Physics of Fluids
 Pub Date:
 August 1987
 DOI:
 10.1063/1.866088
 Bibcode:
 1987PhFl...30.2496F
 Keywords:

 Electron Beams;
 Free Electron Lasers;
 Laser Modes;
 Laser Stability;
 Linear Equations;
 Differential Equations;
 Maxwell Equation;
 Perturbation Theory;
 Time Dependence;
 Wiggler Magnets;
 Lasers and Masers