Electrostatic component of self-focusing electron streams

Relativistic electron streams are shown to be both electrostatically and magnetically self-focusing; the electrostatic component can dominate. Moreover, steady-state reverse currents exist allowing steady-state stream currents in excess of the Alfv\'en limit. Many diverse phenomena (ion acceleration, stepped beam head and net current behavior, strong microwave generation) can be quantitatively understood as simultaneous-pinch phenomena. Limiting energies for axial acceleration of ions are given. Stream radius, focal length, limiting current, stream particle temperature, and plasma particle densities are calculated from initial conditions and are in agreement with experimental data. Conditions for target-implosion fusion studies are specified.