Gyrotron and peniotron modes in rotating-beam devices

Abstract

Abstract Several authors have assumed the existence of the (s + 1), s and (s − 1) harmonic interactions in the electron beam immersed in an axial magnetic field (Dohler et al. 1982, Ono et al. 1983). This paper examines the interaction between a relativistically rotating electron layer and electromagnetic fields with exp (jωt − Γz − jsθ) variation. The linearized relativistic Lorentz force equation is used to evaluate the RF displacement due to harmonic fields. It can be shown from this analysis that in the non-relativistic case, the beam waves are one at the (s + 1), one at the (s − 1) and two at the s harmonic of the cyclotron frequency. These modes may be identified as the fast (s + 1) and slow (s − 1) peniotron modes. This result is consistent with existing theories. The gyrotron interaction is observed as a result of energy exchange between the forward circuit wave and two beam waves at the s harmonic; it is a three-wave interaction. Whereas the fast (slow) peniotron interaction is observed as a result of energy exchange between the forward circuit wave and the fast (slow) peniotron wave at s + 1 (s − 1) harmonics; it is a two-wave interaction. The polarization-variable approach is used to relate the RF displacement to the RF current density and the RF charge density. The dispersion relations are then derived by solving for the electromagnetic fields in cylindrical waveguide, consistent with the current and charge densities in the electron layer for each instability. The results are compared with existing theories.