Gyrotron theory

The gyrotron or electron-cyclotron-resonance-maser is a high-power microwave source in which the microwave field gains energy from a beam of relativistic electrons. At present time, the development is being stimulated by the demand for high-power microwave radiation to heat tokamak plasmas to fusion temperatures and by new radar applications. The heart of the device is a resonant cavity in a steady magnetic field. A hallow cylindrical beam of electrons gyrating about the magnetic field direction with relativistic energies enters the cavity and interacts with the microwave there. The microwave field gain energy from the electrons and a fraction of this energy leaves the cavity via the output waveguide. In this work, some general properties of relativistic coherent states of electrons moving in a steady and homo-geneous magnetic are presented and three types of eigenfunctions as solutions of the Klein-Gordon-Equation are considered. These eigenstates are multipletts. The multipletts are constructed as eigenstates of Johnson-Lippmann-Operators and the influence of the microwave field is investigated by perturbation theory. The resulting stability problem for perturbation theory is solved and the Floquet-Exponent is calculated to second order. By coupling the Klein-Gordon current with the wavefunction of photons, selections rules for the Redmond-Field can be derived. The expection values of light-emission are determined by using Fermis Golden Rule. A further purpose of this article is to show, that quantum theory is needed to derive correct results. (author)