Perveance and the Bennett Pinch Relation in Partially-Neutralized Electron Beams†

The concept of perveance as applied to electron beams with no electric field in the direction of flow is extended by a simple generalization to include-relativistic conditions and the effect of space-charge neutralization. For self-constricted beams this generalized perveance K is negative, and relates the root mean squared transverse velocity in the beam to the drift velocity. In this respect the perveance relation is virtually the same as the Bennett pinch. relation I 2=2Nk(Tc+Ti ) ; indeed if T is suitably defined the two relations are identical for beams which are completely neutralized by stationary ions. Finally some properties of electron beams are compared with those of current carrying plasma columns.