On the Theory of Low-Frequency Oscillations in Gyrotrons

Magnetron injection guns (MIGs) used to produce the spiraling electron beams in high-power gyrotron oscillators are susceptible to parasitic oscillations in the 100 MHz frequency range. It has long been recognized that some electrons with large transverse velocities emitted from a MIG can be reflected in the region of magnetic compression and then trapped in the region between the gun and the resonator. These trapped electrons bounce back and forth in this region and are suspected of being responsible for the parasitic oscillations. So far, interest has focused on the analysis of the oscillations of a cloud of trapped electrons under the assumption that all electrode voltages are fixed. We propose a phenomenological model that not only considers the dynamics of the charge accumulated in the electron cloud, but also takes into account the fact that the gun and associated elements around it form a "cavity", which may have a mode that resonates with the trapped electrons. (In our study, we focus on the gyrotrons with cylindrical resonators in contrast to where a similar approach was used for interpreting the role of trapped electrons on low-frequency oscillations in gyrotrons with coaxial resonators where low-frequency TEM-modes may exist in the resonator region as well.) The conditions of instability for our model are derived, and some attempts to analyze field distribution, eigenfrequencies and quality-factors of low-frequencv modes in the gun region are undertaken.