Theory of Microwave Emission by Velocity-Space Instabilities of an Intense Relativistic Electron Beam

The stability of waveguide modes in a waveguide along which is propagated an unneutralized, intense beam of relativistic electrons guided by an applied axial magnetic field is considered. It is found that the waveguide mode can interact unstably with the beam by resonating with the Doppler shifted cyclotron frequency of the beam. This instability appears to be the mechanism by which microwaves are produced in some recent experiments which are discussed.