Theory of eigenmode amplification

For an infinite electron beam drifting with both transverse and axial velocities in a uniform axial dc magnetic field, the solution of Maxwell's equation yields a dispersion equation which predicts the existence of circularly polarized slow waves whose rotating rf fields are in synchronism with the cycloiding electrons, and also predicts the wave to be unstable with a gain which is independent of the frequency. Therefore this mechanism, referred to as "Whistler mode","Weibel mode" or "Eigenmode", has application at millimeter wave lengths because the potential bandwidth was found to be very large and low dc magnetic fields are required. This paper analyzes the eigenmode interaction by small and large signal theories and by a kinematic model.