Analytical Theory of an RF Generator Phase-Locked by the Resonant Load with Delayed Reflection

Abstract

The theory is developed which describes evolution of an RF generator (autooscillator) coupled by a waveguide with an outer resonator. The treatment is based on a simplified universal method which implies the following conditions to be valid: 1) the resonant load Q is much higher than that of the generator, 2) the generator-load coupling is weak, but non-zero, and, 3) the system evolution time is much longer than the lifetime of active medium particles. When the parameters of such a system, including the wave delay time, belong to an optimum region, the generator, after a delay, becomes frequency pulled to the outer resonator.

Zones of Frequency Locking by an External Signal in a Multimode Gyrotron of a Megawatt Power Level

“…(4) at the previous integration step. Motion equations (5) were integrated with respect to ζ from zero to the values ofζ ∈ [0, ζ ex ] with electron phases relative to the mode fields in the form of Eq. (10).…”

“…Earlier, synchronization of a gyrotron with an external signal was considered in [2][3][4][5][6] for simplified models with a small number of modes and stationary parameters of the electron beam at the entrance to the space of the beam interaction with the electromagnetic field. In [2][3][4][5], the phenomenological equations, which described field excitation by an external signal and were written with an accuracy of up to some coefficients, were used, whereas the excitation equations obtained in [6] turned out to be incorrect due to inaccurate formulation of the boundary conditions. In [7,8], the possibility of effective mode selection and stabilization of the frequency of the multimode gyrotron is demonstrated.…”

Stabilization of gyrotron frequency by reflection from nonresonant and resonant loads

“…The generator frequency stabilization by a wave reflected from a resonant load is widely used for differ ent types of generators in both microwave electronics [6] and optics [7]. One might expect that, in a gyrotron (as in these well known schemes), the frequency is captured in a narrow band equal in width to the load band [6][7][8] if the reflected signal phase (i.e., distance to the reflector) is chosen correctly. The amplitude and phase of the coefficient of reflection from the external cavity excited by the gyrotron radiation are …”

“…At Q/Q ex Ӷ R 0 Ӷ 1, the magnitude of the derivative is small: |dΩ/dω r | Ӷ 1; i.e., the radiation frequency is stabilized. The frequency stabilized solutions under consideration are stable at |dΩ/dω r | > 0 [6,8]. The results of numerical simulation (Fig.…”

“…In this study, we propose a method of gyrotron frequency stabilization by a wave reflected from a dis tant load. The influence of delayed reflections on the operation of active oscillators, including gyrotrons, has been investigated by many researchers (see, for example, [2][3][4][5][6][7][8]). However, specific schemes of gyrotron frequency stabilization by a reflected wave have not been discussed, because the reflected wave in a gyrotron with a conventional output quasi optical transducer returns to the operating space as a counter rotation mode, which weakly interacts with an elec tron beam [9].…”