摘要
This work shows the derivations and calculations of the starting behaviors using the Laplace method and the numerical method. Calculated results based on these two methods agree well when dealing with a uniform structure, while the numerical method is advantageous for the non-uniform and practical structure. The applicability of the zero-field and the outgoing-wave boundary conditions at the collector end is discussed. These two boundary conditions agree well when the beam-wave resonant line and the waveguide dispersion curve intercept at the backward-wave region but differ significantly at the forward-wave region. The beam-wave coupling strength of the TM-mode gyrotron is found to be strongly correlated with the starting current, which can be utilized to avoid the potential competition from the transverse electric (TE) modes. The starting current of the TM gyrotron exhibits an additional operating condition at the low-beam voltage that may facilitate the development of low-cost and tabletop gyrotron systems. The beam-voltage and magnetic-field tunings are investigated for an open-cavity structure with the numerical method. Interestingly, the TM gyrotron as well as the TE gyrotron exhibits a similar starting behavior, which warrants the potential applications of the TM-mode gyrotrons.