Electron-Stream Diode Instabilities with Elastic Collisions

Abstract

Instabilities can be induced in parallel-plane (diode) configurations when a very high current is passed through the diode, even if this current is neutralized by ions. This work extends Pierce's original calculation of the critical current for instability to find the growth rate for a wide input—current range, and then goes on to include collisions of the injected stream with background neutrals and allow for mobile neutralizing particles. Collisions damp the instability, increasing the value of input current at which onset of instability will occur; if the collision frequency ν is such that ωp2L/νv0<4π, approximately, then there is no time growth. Allowing the background ions to be mobile also eliminates this type of instability. The results without collisions compare favorably with some experiments involving essentially collisionless diodes; those with collisions included do not agree with some experiments involving collision-dominated triode lasers.