| It has been shown in many experiments that by injecting plasma into the vacuum microwave devices, the interaction efficiency can be increased greatly, so that the output power can also be enhanced at the same input condition. In order to understand the physical mechanism behind the experiments, many theories have been put forward to explain this phenomenon. The conventional linear theories describe the linear part of the interaction between beam and wave very well. However, when the interaction efficiency increases in a large scale, we should consider the nonlinear effects. In this case, we must take account for the modulation of the plasma density. That is to say. the plasma density is modulated by the strong microwave so as to form a plasma Bragg grating. Since the steady state distribution of the plasma is related with the microwave field and its dielectric property varies with the electric field nonlinearly, the grating is nonlinear. We study the nonlinear plasma filled Cerenkov maser and linear plasma filled coupled cavity chain. The principal conclusions of this dissertation are given below:1. We study the nonlinear plasma grating filled dielectric Cerenkov maser oscillator cavity for the first time. The background plasma is modulated by the slow standing wave. The density grating is thus formed and influences the operating parameters of the oscillator, such as the frequency and Q value. Some novel conclusions are obtained: The magnitude of the electric field in the interaction region increases greatly as the background plasma density increases. This effect is beneficial to the beam-wave interaction because of the enhanced coupled impedance. However, the plasma density can't be increase without limit, only under a critical plasma density, can the radiation conditions be satisfied. This effects can be explained as follows: the radiation conditions are actually impedance matching condition in terms of microwave network, for a fixed dimension of a resonator and output transformer, only below the critical plasma density', the matching condition can be satisfied in the Smith circle map. This explanation can be applied to similar phenomena observed in many experiments.2. On the basis of the plasma density grating, we present an equivalent model to describe the non-uniform property of the plasma grating. In the first step, we treat the actual periodical distribution function as the rectangular periodical distribution function approximately. Further, the axia! uniform periodical property can be replaced by an anisotropic dielectric with uniform transverse and uniform axial property. The equivalent model can describe the inhomogeneity as a result of the modulation of the plasma density', so we can solve the dispersion accounting for the plasma grating effects more easily.3. In order to show the fact that the -licrowave modulates the background plasma density and the density grating influences the propagation of the microwave in return, the dispersion relation of the dielectric Cerenkov maser filled with plasma grating is derived when the modulation parameter is varied. The numerical results of the dispersion relation show some nonlinear effects: for a fixed geometry of a waveguid, beam parameters and plasma density, the increment of the modulation parameter may lead to a slight increment of the operating frequency, However, as the modulation parameter increases further, saturation may occur and the dispersion relations are hard to be separated, it is due to the overmodulation of the microwave power, this phenomenon itself belongs to the nonlinear effects. When the plasma density increases, the operating frequency also increases slightly, the temporal growth rate increases as well. There exists a nonlinear relation between the plasma density and the temporal growth rate. In addition, for a dispersive high frequency system, because of the requirement of the phase in-step between the beam and electromagnetic wave, the bandwidth are expected to be located in a narrow range. Our resu...
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