On the Theory of Synchronization of a Two-Mode Electron Maser with a Hard Excitation
Background and Objectives: Medium-power (10-100 W) THz continuous-wave electron cyclotron masers (gyrotrons) are of great interest for many applications, such as spectroscopy with dynamic nuclear polarization, plasma diagnostics, non-destructive testing, remote detection of radioactive materials, biomedical applications, etc. For these applications, a high frequency stability is required, with the possibility of frequency tuning within 1-2 GHz. In addition to the existing methods of frequency stabilization, the use of forced synchronization by an external stabilized driving source has recently attracted interest. In a typical situation, the maximal efficiency of a gyrotron is attained in the hard excitation mode. The aim of the work is to study the effect of mode competition on the operation of a gyrotron driven by an external signal in the case of hard excitation. Materials and Methods: The paper presents the results of theoretical analysis and numerical simulation of forced synchronization by locking with an external signal. Bifurcation analysis is performed on the basis of a simplified quasilinear model. Numerical simulation is carried out for a well-known model of the non-stationary theory of a gyrotron with a fixed high-frequency field profile. Results: The fixed points of the system are found and the partition of the parameter plane into regions with different types of stability is constructed. Phase portraits are presented that illustrate bifurcations occurring as the driving power increases. Based on the numerical simulation, the scenario of transition to the synchronous mode is studied. With an increase in the amplitude of the external signal, a saddle-node bifurcation occurs, as a result of which the basin of attraction captures the origin of coordinates. This leads to the fact that the synchronization mode becomes possible even with small initial perturbations. With a further increase in the driving amplitude, the spurious mode is completely suppressed, and the synchronization of the fundamental mode becomes the only stable state. Conclusion: Using the example of a simple quasilinear model of a two-mode electron maser, the scenario of transition to a synchronous mode is studied. The results are confirmed by numerical simulation based on the theory of a gyrotron with a fixed high-frequency field profile.