Intense electron beam propagation between two plane conductors

The properties of an intense relativistic electron beam propagating between two grounded plane conductors, including the important influence of an ion current, are examined. The steady-state and time-averaged equilibrium properties are obtained analytically by employing a one-dimensional model. It is shown that the ratio of the final forward ion current to the electron current can be expressed in terms of the electron energy, the potential depth of the last virtual cathode, and the electron-to-ion-mass ratio, although the forward electron current itself is a complicated function of the system parameters. Based on this investigation, it is found that the forward electron current is significantly reduced as the distance between the two conductors is increased. However, by introducing an ion current into the system and allowing a number of virtual anodes in the region between the two plane conductors, the forward electron current can be substantially enhanced.