Model of Finite Velocity Injection Into Coaxial Cylindrical Diode Based on Ramo-Shockley Theory

The space charge effect in various kinds of electron diodes has been extensively studied. Typically, the coaxial cylindrical geometric model is used for practical applications, such as the free electron laser and microwave source. In this article, based on the Ramo–Shockley theory, the charge sheet model is used to simulate a coaxial cylindrical diode. The true nature of the electrical characteristics of the diode in both stable and unstable regimes can be described. Effects of finite initial velocity injection on various aspects have been discussed, including the current density and the oscillation behaviors of the average charge density, the potential distribution, and the virtual cathode. Beyond the space charge limited (SCL) regime, once the initial velocity is nonzero, the diode displays a feature of oscillation, and the oscillating magnitude increase with higher initial velocity. However, the simulation results show that the oscillating frequency is not necessarily related to $\beta $ and significantly depends on the physical size of the diode. When the gap size is set to a level between micrometer and nanometer, we found that the oscillating frequency can reach the terahertz scale.