Macroscopic equilibria of relativistic electron beams in plasmas

Macroscopic equilibria of relativistic electron beams in plasmas, with return current and with or without an external magnetic field parallel to the beam, are investigated in cylindrical geometry. Bennett-type identities and general solutions are derived, and special examples are considered, in particular low-net-current, quasineutral configurations. A general expression for the current screening factor is obtained. Because of screening, relaxed versions of the Alfven-Lawson conditions determine whether beam propagation is possible. These conditions are easily satisfied for low perpendicular temperatures and sufficiently diffuse density profiles of the beam; they do not limit the beam current. Only equilibria with zero total charge, nonzero total net current, and beam profiles without sharp boundary, can be obtained from the equations and boundary conditions used.