Generation of intense oscillations by a relativistic electron beam interacting with a rippled magnetic field

The relativistic electron beam (REB) passing through a rippled field produces high-frequency oscillations due to the magneto-cyclotron resonance [1] and parametric instability [2]. Devices based on either of these mechanisms are called “gyrotrons” or “ubitrons” respectively. The REB is injected into a circular waveguide of the radius R, placed into the external magnetic field Ho. The beam is instable as the regular Doppler branch (equation) is crossed by the fast branch of the dispersion, curve of a circular waveguide (equation), and periodic modulation with equation results in a parametric relation between the charge density wave (equation) and the cyclotron wave (equation). The generation frequency is determined by the expression equation. The frequency increase in a factor of ∼ 2 γ² if the electromagnetic wave is reflected by REB.