Chaotic Phenomena Of High Power Microwave (HPM) Source

High Power Microwave (HPM) source is a nonlinear system composed by the electromagnetic field and relativistic electron beam. Usually, HPM devices working in the high current and large field amplitude state, after the field reaches saturation, the nonlinear effects will become extremely strong so that the intrinsic nonlinear phenomena (for example limit cycle oscillation and chaotic behavior) of the system occur. These nonlinear behaviors directly influence the output characteristic of the devices. This thesis summarizes our study work on the nonlinear characteristics and laws of high power microwave source in nonlinear regime.Firstly, the integral-differential equation described the radiation field evolution is derived, and then the instability of its solution is also investigated analytically. By using the perturbation and iteration method, the threshold detuning and threshold linear growth rate of the unstable solution are analyzed and discussed in detail. The results show that the nonlinear instability of system can appear in certain parameter region.Secondly, we present the set of nonlinear partial differential equations that describes the wave-particle interaction, by analyzing the output power spectrum, the limit cycle and chaotic oscillation of the radiation field in the Traveling Wave Tube (TWT) Amplifier and the Magnetically Insulated Transmission Line Oscillator (MILO) are studied numerically, respectively. The researches of temporal and frequency characteristic of the output radiation field shows that: as in the linear regime, in the nonlinear regime after the field saturation, the current dominates the development of the radiation field. The radiation field evolves from a steady saturation state to a limit cycle oscillation state, and eventually to chaotic oscillation state as the current increases, the region in which the field exhibitslimit cycle or chaotic oscillation is called the "soft" and "hard" nonlinear regime, respectively:(1) In the "soft" nonlinear regime, the radiation field is characterized by period doubled bifurcation and the discrete power spectrum. The limit cycle oscillation is intermittent, so in the soft nonlinear regime the limit cycle oscillation can be avoided by slightly adjusting the current . detuning and length of the interaction region.(2) In the "hard" nonlinear regime, the radiation field is characterized by non-period of the field in time and the continuous power spectrum. The chaotic oscillation is continuous, so in the hard nonlinear regime this chaotic oscillation state can not be avoided by adjusting the parameter.In the nonlinear chaotic regime, the output power may become very high for some values of the parameter or very low for others. Therefore, the higher output power can be obtained by optimizing and adjusting the parameters.Finally, we analyzed numerically chaotic motion of electrons in the phase space. The results are concluded, the relations between the chaotic motion of electrons and chaotic behavior of the field are compared.