Design and Analysis of a High-Order Mode Ladder-Type RF Circuit for Stable Operation in a ${W}$ -Band Extended Interaction Oscillator

A stable high-order mode version of a ladder-type RF circuit (ladder cavity) is proposed to overcome the frequency limits of the commonly used fundamental mode counterpart for the development of millimeter-wave and higher frequency extended interaction oscillators (EIOs). The specific design for the stable operated circuit and its analysis based on the mode characteristic is carried out. The study of the transverse mode shows the potential of the TM 31 mode in establishing more sufficient axial electric field than the fundamental TM 11 version in a large size cavity. To enable the TM 31 mode to overwhelm other possible competing modes in the circuit impedance, the field distribution of the TM 31 mode is optimized in design through the analysis of transverse parameters. Key features that ensure stable operation are: 1) the large mode separation and nonoverlapping oscillation regions embodied in beam-loading conductance between related modes due to the specific design and 2) the large difference in the start-oscillation currents of the TM 31 and TM 11 modes based on the theoretical analysis. To demonstrate the circuit capability, a $W$ -band EIO with the proposed circuit has been designed. Simulations with a 3-D particle-in-cell code in CHIPIC predict a maximum output power over 10.6 kW around 93.1 GHz was obtained with a 20.5-kV and 8-A electron beam. The design provides a promising approach for making a stable high-order mode RF circuit applied in high-frequency EIOs.