Models of driven relativistic magnetrons with nonlinear frequency-shift and growth-saturation effects

George L. Johnston; Shien Chi Chen; George Bekefi; Ronald C. Davidson

doi:10.1117/12.18549

1 April 1990 Models of driven relativistic magnetrons with nonlinear frequency-shift and growth-saturation effects

George L. Johnston, Shien Chi Chen, George Bekefi, Ronald C. Davidson

Proceedings Volume 1226, Intense Microwave and Particle Beams; (1990) https://doi.org/10.1117/12.18549
Event: OE/LASE '90, 1990, Los Angeles, CA, United States

Abstract

The driven van der Pol equation is widely used to model the behavior of regenerative electronic and microwave oscillators driven by an external locking signal. In the case of high-power microwave oscillators such as relativistic magnetrons nonlinear frequency-shift effects are believed to be important. They have been modeled by inclusion in the van der Pol equation of an additional cubic restoring force (Duffing) term. Use of the slowlyvarying amplitude and phase approximation to study the behavior of the driven van der Pol-Duffing equation has predicted stable single-valued locked behavior within a skewed range of values of the frequency mismatch. For parameter values consistent with the slowly-varying amplitude and phase approximation numerical solutions of the van der Pol-Duffing equation confirm this prediction. For oscillators with high growth rate such as the relativistic magnetron however the slowly-varying amplitude and phase approximation may be unjustified. Furthermore regardless of the satisfaction of the assumptions on which the approximation is based it may fail to predict the occurrence of complicated dynamical behavior of coupled oscillators with important implications for phase locking. Numerical solutions of the driven van der Pol equation show that the time of transient evolution to phase-locked states instead of depending solely on the frequency mismatch as conventionally assumed is also a function of oscillator growth rate and injection power level. Recent work suggests that the form of model oscillator equation appropriate for the magnetron may differ in both nonlinear growth-saturation and frequency terms from the van der Pol-Duffing equation. 1.

Citation Download Citation

George L. Johnston, Shien Chi Chen, George Bekefi, and Ronald C. Davidson "Models of driven relativistic magnetrons with nonlinear frequency-shift and growth-saturation effects", Proc. SPIE 1226, Intense Microwave and Particle Beams, (1 April 1990); https://doi.org/10.1117/12.18549

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