A fundamental theorem on the maximum frequency of coherent oscillations by Robert S. Elliott

Summary form only given. Elliott (J. Appl. Phys. 23, 812-18, 1952) enunciated an important theorem on the maximum frequency limit for electron beam oscillators. The theorem is based on several physical laws. The first law states that the average power supplied by an electron beam to the field must be equal to the total average power lost by the resonant structure, including the useful output power and the ohmic loss. The second law states that the product of the frequency of oscillation and the average stored energy of the device must be greater than the average output power. The third law invokes the quantum theory of radiation. It implies that the minimum stored energy should be at least equal to the average noise energy level. With these laws at his disposal, Elliott was able to formulate his theorem. The author reviews Elliott´s paper, showing the key formulation, and the proof of the theorem and its application to the design of klystrons and magnetrons. The author points out the inherent limitations of these devices in generating coherent oscillations in the optical spectra.<>