Limiting Stable Current in Electron Beams in the Presence of Ions

Abstract

In electron flow, the net electronic charge may be neutralized by positive ions. In this case, for a given geometry there is a limiting current beyond which homogeneous flow is unstable. This limiting current is evaluated for flow normal to parallel plane equipotentials and for flow filling a conducting tube and constrained to motion parallel to the axis. For parallel planes at a potential V0 volts and spaced a distance L cm apart, the limiting current density in amperes/cm2 isi0=104×10−6V032/L2. For a long conducting tube the limiting current is I0=160×10−6V032. These limiting currents are roughly 6 times as great as in the absence of ions.