High frequency energy generation through the interaction of a helical beam with the azimuthal electric field of a resonating structure

High frequency energy production from cyclotron electrons orbiting in a steady state magnetic field was studied, the major difficulties being the proper phasing of the electrons, necessary for the generation of the energy, and the perturbation caused by space charge, due to the presence of the electrons in the beam. Nevertheless, as the oscillating electric field present in the resonant cavity, field interacting with the electron beam consisting of cyclotron orbiting electrons, is azimuthal, the amplitude of the field rising with the distance from the axis of the electromagnetic cavity, the phasing of the electrons, permitting high frequency energy generation, is facilitated. A description is given of the physical mechanism resulting in the generation of high frequency energy, followed by a detailed theoretical development, without consideration of the perturbations caused by space charge, due to the electrons present in the beam, and, eventually, by the relativistic change in mass (subjects treated in a second part of this report). At long wave lengths, a pseudo-cavity, whose dimensions are less than the wave length of the generated energy, permits, by employing the same physical mechanism as described above, the production of energy in the decimetric and metric wave bands