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.

中文翻译：

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W波段扩展相互作用振荡器的束波相互作用数值研究

基于能量守恒的基本原理和电子盘束波相互作用方程，结合振荡器的特征阻抗和品质因数，得到了扩展的相互作用振荡器（EIO）的自洽非线性理论模型。以W波段EIO为例，分析了工作参数和结构参数对扩展相互作用振荡器的振荡，输出功率和电子转换效率的影响。该模型的数值实现表明，电子束-波同步相互作用是振荡器启动的基本先决条件，谐振器中能量的正反馈是自发振荡的必要条件，每个间隙上电场幅度的分布直接影响束波相互作用的效率和输出功率，稳态时所有间隙中的电子轨迹都说明了转换效率。在18 kV的工作电压和0.5 A的直流电的情况下，可以预测输出功率为2629 W且电子效率超过29％的七间隙EIO模型将逐渐增加每个腔上的电场幅度分布。