Mode competition and startup in cylindrical cavity gyrotrons using high-order operating modes

The problem of mode competition in cylindrical cavity gyrotrons is considered. The normalized variable equations are used to calculate the oscillation regions of possible operating modes in the energy-velocity-pitch-angle plane. The analysis is self-consistent and includes the effect of changing beam current, pitch angle, and energy during the startup phase. The time evolution of beam parameters during startup is computed for several types of startup methods and used to determine the oscillating cavity modes during startup. Depending on the type of startup chosen, the cavity can be made to oscillate in several modes or in a single chosen operating mode-even for high-order modes where many other possible operating modes exist. Some startup methods are seen to be less favorable than others, allowing for oscillation of unwanted modes and some methods are seen to be more sensitive to small beam/cavity misalignment. The accessibility to the high-efficiency hard-excitation region can also be determined and is seen to depend on the startup scenario. The startup analysis is linear whereas the stability and interaction efficiency computations are fully non-linear. The method is general and can be applied to any operating mode, with the mode competition analysis specifically useful for high-order modes where the spectrum is dense. The analysis of the accessibility to the hard-excitation region is applicable to high- and low-order operating modes. Both q=1 and q=2 longitudinal mode numbers are considered