On the Adiabatic Self-Constriction of an Accelerated Electron Beam Neutralized by Positive Ions†

Abstract

An analysis is made of the behaviour under the influence of a longitudinal electric field of a space-charge neutralized electron beam. The energy lost by radiation and collision is neglected, and transverse velocities are assumed small compared with the drift velocity. It is found that the build-up of the self magnetic field causes the transverse oscillation of the electrons to be damped, but that this damping is counteracted to some extent by an outward diffusion due to multiple scattering of the electrons-on the ions. Inductive effects appear as an apparent increase of mass of the electrons The importance of the problem lies in the fact that such a beam represents a possible intermediate state in setting up a steady state relativistic beam of the form described by Budker.