Theory of high-harmonic gyrotron oscillators with slotted cross-section structure

A linear-theory analysis of gyrotron oscillators with slotted cross section is used to calculate the net change in beam energy. In this formalism, geometric factors are clearly distinguished from the geometry-independent harmonic resonance terms due to the fundamental electron cyclotron maser and peniotron interactions. This separation of the interaction terms from the geometric factors simplifiers the physical analysis, and leads to a very compact form for the net change in beam energy. The theory is applied to slotted rectangular oscillators and to slotted cylindrical oscillators to show that a unified expression can be obtained for the start-oscillation condition. In sample applications of the theory, it is demonstrated that slots lower the start-oscillation condition in both cylindrical and rectangular geometries, and can lead to a decrease in this condition as harmonic number is increased in the rectangular geometry. It is also found that the peniotron interaction, which is easily identified in this formalism, may be very strong in slotted cavities