Magnetic Resonant Three Dimensional Kinetic Theory of the Free Electron Laser with Waveguide Cavity

Vlasov kinetic theory of F E L employing waveguide laser cavity and helical pump is presented. Distinct from the former theories(1-5) this paper has taken into consideration theinfluence of the longitudinal magnetic field and the 3-d structure of the scattered field with the method of plasma kinetic theory. The spatial growth rate formula for the case of magnetic resonance is derived. The results show that the 3-d structure of the field has harmful influence on gain and would even cancel the instability altogether under certain conditions. A condition for eliminating the harmful effect and obtaining the maximum gain is derived and a suggestion employing hollow beams with small wall thickness is made. This theory is a generalization of that by P. Sprangle and R. A. Smith(5) in consideration of the longitudinal field and the 3-d structure of the scattered field.