Magneticresonant three dimensional kinetic theory of the free electron laser with waveguide cavity

Vlasov kinetic theory of the free electron laser employing waveguide frifting tube and helical pump is presented. Distinct from the former theories this theory has (1) taken into account the 3-d structure of the scattering field; (2) applied the plasma kinetic theory, which is more accurate than the other methods, to analysing the effect of the longitudinal. field; (3) taken account of the influence of the annular structure of the beam. The magnetic resonant effect appearing when the cyclotron frequency of electrons approaches the effective frequency of the magnetic pump is analysed and the growth rate formula in the linear regime derived. Results show that on taking into account the 3-d structure of the field and beam, one cannot arbitrarily choose the radius of the hollow beam, or else within certain range the instability may disappear altogether. Lastly, the equation for determination of the optimum beam radius is given and the possibility of raising growth rate by operating in high order modes shown.