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In the relativistic klystron driven by intense relativistic electron beam, due to the influences of intense current and high electric field, especially the high Q value for the intermediate cavity, the nonlinear interaction between the intermediate cavity and the electron beam is very strong. It will significantly affect the performance of the device. According to the Maxwell equations and one-dimensional motion equation of electron, the self-consistent equation of the beam-wave interaction is obtained in the intermediate cavity. Based on these equations, the influences of the modulation depth and the modulation frequency on the amplitude and phase of gap voltage are studied respectively. The voltage amplitude obtained by the self-consistent equation is close to the voltage amplitude of particle in cell simulation, especially under the higher modulation depth compared with that obtained from the equivalent circuit model of conventional klystron. Meanwhile, the bandwidth of device becomes wide with the increase of the modulation depth. Finally, an S-band high-gain RKA is designed, and the corresponding experiments are done on the LTD accelerator. The output power with 1.1 GW is obtained, the gain is 49 dB.

Compared with the beam of conventional relativistic klystron, each beam of the multi-beam relativistic klystron has a low perveance and low space charge force, but it has a high conversion efficiency of beam-wave. According to these requirements, in this paper we investigate the generation and transmission of fan-shaped multi-beam intense relativistic electron beams by the experiment and the simulation with using the three-dimensional software, and analyse the electrostatic field distribution of the cathode end and the influence on the generation of the electron beams by establishing a three-dimensional model of electron gun. The emission currents by the particle-in-cell simulation, then the beam spot pictures of electron beam transmission in a hollow drift tube and multiple fan-shaped hole drift tube by the particle tracking solver are obtained. The theoretical analysis and explanation with the aid of the sheet beam theory are presented. The simulation and experimental results show that the beams rotate not only around their own center, but also around the center of the system in the transmission process of the electron beams in the hollow drift tube. Thus we can increase the transmission efficiency by rotating multiple fan-shaped hole drift tube to align the beams.