A comparison of phase between a nonlinear theory and 2D particle in cell simulation in three-cavity klystrons
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摘要: 首先采用运动学理论和空间电荷波理论推出了计算中间腔间隙入口处调制电流相位的经验公式。采用调制电子束激励中间腔的非线性理论估算中间腔和输出腔间隙电压的幅度和相位，并提出了估算输出腔间隙入口处调制电流相位的经验公式。采用这些理论和二维粒子模拟比较了中间腔和输出腔间隙入口处调制电流相位、中间腔和输出腔间隙电压相位。中间腔和输出间隙入口处调制电流相位误差为2.627°（模型1）和3.857°（模型2）。中间腔间隙电压幅度的相对误差是1.47%，输出腔幅度的相对误差是5.42%，中间腔相位的误差是4.017°（模型2）和5.427°（模型3），输出腔的相位的误差是12.32°。最后根据二维粒子模拟得出了三种模型调制电流的相位与距离的关系。相关理论计算结果与2D的PIC模拟结果进行了比对，验证了理论估算结果的可信度。Abstract: This paper applies the theory of kinematics and space charge wave to conclude an experiential formula for calculating the phase of the modulated current at the entrance of the gap of the middle cavity. It also applies a nonlinear theory of cavity excitation by modulated electron beam to calculate the amplitude and the phase of the gap voltage of the middle cavity and the output cavity, and presents an experimential formula for calculating the phase of the modulated current at the entrance of the gap of the output cavity. With these theories and 2D PIC, it estimates the phase of the modulated current at the entrance of the gap of the middle cavity and the output cavity as well as the amplitude and the phase of gap voltage in the middle cavity and the output cavity. The errors of the phase of the modulated current at the entrance of the gap of the middle cavity and the output cavity are 2.627° (model 1) and 3.857° (model 2); the relativistic errors of the amplitude of gap voltage in the middle cavity and the output cavity are 1.47% and 5.42%, the error of the phase of gap voltage in the middle cavity are 4.017° (model 2) and 5.427° (model 3), and the error of the phase of gap voltage in the output cavity is 12.32°. Finally, the paper analyzes the phase of the modulated current versus the propagation distance in three models by 2D PIC simulation.
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图 1 栅网间隙示意图和输入腔r-z剖面图
Figure 1. Schematic diagram showing the gap of the conducting grid and the r-z section structure of the input cavity
图 3 输入腔和中间腔r-z剖面图
Figure 3. The r-z section structure of the input cavity and the middle cavity
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