Nonlinear and Self-Consistent Formulation for TM-mode Gyrotrons

We build up a nonlinear and self-consistent theoretical framework for the TM-mode gyrotrons. Unlike the TE modes 1 - 2 , a new nonlinear TM wave equation is derived by considering the additional axial modulation on the beam due to the interaction with the axial electric field 3 - 4 . Together with the equations of motion of electrons, particle tracing simulation is conducted to model the oscillation and the amplification of the TM modes. For a uniform structure, the efficiency of the TM 11 mode at W band can achieve 30% with a tunable bandwidth around 1.6 GHz. Its beam-voltage and magnetic-field tuning properties are investigated. The efficiency can still remain high at low-beam voltage (< 20 kV) and relatively low pitch factor (~ 0.9), indicating an additional operating condition that may facilitate the development of low-cost and tabletop gyrotron systems. With proper optimization of the tapered structure, maximum efficiency can be enhanced to 35% with more than 5 GHz tunable bandwidth. This design shows great potential in applications for TM-mode gyrotron devices.