Abstract: Four magnetron oscillator models are constructed and analyzed for the study of relativistic magnetron phase locking physics: the extended spoke model, the magnetron-specific equivalent model, the van der Pol equation, and the magnetron oscillator equation. The spoke model reproduces the magnetron specific conductance and susceptance features that are incorporated into other models. The equivalent circuit model and the magnetron oscillator equation model generate the same set of predictions concerning phase-locking condition, locking time, saturation amplitude and final phase. Both models predict a wider locking bandwidth and a shorter locking time as results of the frequency pushing effect. The van der Pol model solved in the fast time scale reveals the dependence of locking time on injection power and oscillator growth rate as well as on injection frequency.!
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机译：摘要：为了研究相对论磁控管锁相物理学，构造并分析了四个磁控管振荡器模型：扩展辐条模型，磁控管特定等效模型，van der Pol方程和磁控管振荡器方程。辐条模型复制了其他模型中包含的磁控管特定电导和电纳特性。等效电路模型和磁控管振荡器方程模型会生成关于锁相条件，锁相时间，饱和幅度和最终相位的相同预测集。两种模型都可以预测出更宽的锁定带宽和更短的锁定时间，这归因于频率推动效应。在快速时间尺度上求解的van der Pol模型揭示了锁定时间对注入功率和振荡器增长率以及注入频率的依赖性。
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