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 is$i_0{\text{=104×10}}^{\text{−6}}{V}_0^{\frac{3}{2}}{\mathrm{/L}}^2$ . For a long conducting tube the limiting current is $I_0{\text{=160×10}}^{\text{−6}}{V}_0^{\frac{3}{2}}$ . These limiting currents are roughly 6 times as great as in the absence of ions.