The development of high-frequency, wide-bandwidth, high-power extended interaction oscillators (EIOs) has always been the focus of researchers working on millimeter-wave and terahertz electronic devices. However, these design objectives are affected by many structural and operating parameters, and traditional manual optimization and local optimization are no longer suitable for solving these problems. In this paper, based on a one-dimensional, nonlinear, self-consistent program of EIOs, a multiobjective optimization method that employs the nondominated sorting genetic algorithm II (NSGA-II) is proposed to simultaneously optimize device output power, bandwidth, and structure length. By using this approach, the optimization process of a 95-GHz EIO is presented, and the corresponding Pareto solutions are obtained after 500 generations with a population size of 50. The results show that the beam-wave interaction and the coupling mechanism lead to synchronization of the structural parameters and the electrical parameters with each other, and the coexistence of multiple objectives guides the zonal distribution of the optimal solutions. That is, the oscillators with fewer gaps have shorter structure length and higher power, whereas those with more gaps are prone to start oscillation and have wider bandwidth. Several sets of optimization results obtained using the proposed method agree well with the results obtained in the CST-PIC solver, which proves that the proposed algorithm is effective for optimizing EIOs because it considers multiple design goals and can serve as a theoretical basis for engineering development.

Based on the basic principle of energy conservation and electron disk beam–wave interaction equation, combined with the characteristic impedance and quality factor of the oscillator, a self-consistent nonlinear theoretical model of extended interaction oscillators (EIOs) is obtained. Taking the W-band EIO as an example, the effects of operating parameters and structural parameters on the oscillation, output power, and electron conversion efficiency of the extended interaction oscillator are analyzed. The numerical implementation of this model shows that the electron beam–wave synchronization interaction is a basic prerequisite for the oscillator to start, the positive feedback to energy in the resonator is a necessary condition for spontaneous oscillations, the distribution of electric field amplitude on each gap directly affects the beam–wave interaction efficiency and output power, and the electron trajectories in all gaps at steady state illustrate the conversion efficiency. At an operating voltage of 18 kV and a direct current of 0.5 A, a seven-gap EIO model with an output power of 2629 W and electron efficiency over 29% is predicted for gradually increased electric field amplitude distribution on each cavity.

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