The Effect of Finite Ion Mass on the Stability of a Space-Charge-Neutralized Electron Beam

Abstract

The dispersion relation is derived for a finite length one-dimensional electron beam neutralized by positive ions with zero electron and ion temperatures. Contrary to previously published results it is shown that finite ion mass does not produce stability. There are two modes of instability, electron space-charge waves and ion oscillations. Their relative importance at different lengths is considered.